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UNIVERSITY OF

NORTH CAROLINA

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DIALECTIC AND PHILANTHROPIC

SOCIETIES

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LIBRARY UNIV. Of
NORTH CAROLINA

SUBSCRIBERS NAMES.

DR. Arne.
Mr. Avifon of Newcaftle.
Mr. Francis Afhbey.
Mr. Allen, Organijl ^Southwell.

Henry Bridgman, Efq;

Mrs'. Bridgman.

John Bagnal, Efq;

Robert Bell, Efq-,

■ Barnard, Ejq;

Captain Thomas Bourne.

Rev. Mr. Bugg.

Rev. Mr. Bowman."

Rev. Mr. Brailsford.

Dr. Boyce, Organijl andCompofer to his Ma-

jejly, and Majier of his Majejiys Band of

Mufick.
Mr. Butler, Organift of St. Margaret's, Weft-

minfter.
Mr. Burton, 2 Books.
Mr. Charles Burney.
Mr. Thomas Bower.
Mr. Berfanti.

Rev. Mr. Graham, Fellow of King's-Col-

lege, Cambridge.
Mr. Gardiner.
Mr. Garth, of Durham.
Mr. Gladwin.

JohnHewett, Efq;

Mrs. Hewett.

Rev. Mr. Hewett.

John Hawkins, Efq;

Charles Grave Hudfon, Efq-,

Francis Hurt, Efq;

Hutchinfon, Efq; of Chrift's Col-
lege, Cambridge.
Mrs. Hallows.
Rev. Mr. Hallows.

Dr. Hayes, Profejfor of Mufick at Oxford,
Mr. John Hutchinfon.
Mr. Hargrave.
Mr. Samuel Howard, Orga?iiJl of St. Brides

and St. Clements-Danes.
Mr. Herletine, Organijl at Durham.
Mr. Hawdon, Organijl at Hull.

Robert Copley, Efq;

Rev. Mr. Cole.

Mr. Cooke, Majier of the Choirijlers, and

one of the Gentlemen of the Choir of Weft-

minfter.
Mr. Cox, of the Gentlemen of his Majejiys

Chapel Royal.

Mr. Dodd.

Mr. Thomas Saunders Dupuis,

Dr. Johnfon, of Loughborough.
Mr. John Johnfon, 6 Books.

Her Grace the Dutchefs of 'Leeds.

Rev. Mr. Ludlam, Fellow of St. John's Col-
lege, Cambridge.

Rev. Mr. Lobb, Fellow of St. Peter's Col-
lege, Cambridge.

Mr. Layland, Organijl of Chefterfield.

Mifs Ford.

^ Rev. Mr. Gifborne, late Prebendary c/'Dur-
fc ham.

N msa*

Charles Meilifh, Efq;

Rev. Mr. Mafon.

Rev. Mr. Mudge.

Mr. Alexis Magito.

Mr, Miller, Organijl of Doncafter.

Ah,

SUBSCRIBERS NAMES.

Dr. Nares, OrganiB and Compofer to his
Majejly, and Mafier of the Children of his
Majejiys Chapel Royal.

Mr. Neville, of Jefus College, Cambridge.

Robert Price, Efq,
Mifs Plumtree.
Rev. Mr. Pixell.
Rev. Mr. Pegge.
Samuel Pegge, Efq- t
Mr. Porter.
Signor Pafqualino.
Signor Paflerini.

Dr. Ridlington, Fellow of Trinity Hall,
Cambridge, and Prof ejfor of Civil Law.

Dr. Randall, Profejfor ofMufic at Cambridge.

Thomas Robinfon, Efq; of Chrift's College,
Cambridge.

Mr. Rogers, Organijl c^Briftol.

Mr. Rayner, Organijl of Lincoln.

Rev. Mr. Shepherd, Fellow of Chrift's Col-
lege, Cambridge.

Mr. Stockdale, of Emanuel College, Cam-
bridge.

Rev. Mr. Stacey.

Mr. Savage, Gentleman of his Majejiys Chapel
Royal, and Almoner oj 'St. Paul's Cathedral.

Mr. John Chriftopher Smith.

John Smith, M.D. of St. Mary Hall, Ox-
ford.

Mr. Stanley, Organijl of the Temple and
St. Andrew's.

Mr. Scamadine.

Mr. Francis Sharpe.

Mr. Sharpe.

Mr. Benjamin Steele.

Dr. Robert Taylor.
Edward Toms, Efq;
Mr. Turner.
Mr. Tiffington, 2 Books.

Mr. John Valentine, of Leicefter.

Earl of Scarborough.

Countefs of Scarborough.

Hon. Charles Fitzroy Scudamore, Efq;

Sir George Saville, Bart. 20 Books.

Gervafe Scroope, Efq;

Robert Sutton, Efq-,

Mifs Arabella Sutton.

Rev. Dr. Smith, Mafter of Trinity College,
Cambridge.

Rev. Mr. Skynner, Public Orator of the Uni-
versity of Cambridge.

The Hon. Mr. Ward, 2 Books.

Benedict Willis, Efe

Rev. Mr. Wright.

Mrs. Wright

Rev. Mr. Wheeler.

Mr. Weideman.

Mr. John Worgan, M. B.

Mr. Wife, Organijl at Nottingham.

Mr. Wainwright, Organijl at Manchefter,

Mr. Ward, Bookfeller at Sheffield.

^S^^^^^^*^fe^^*^fe^^&^*S^^**^SS^*^^*&**^^*^^*^^^^i

ERRATA.

PAG. 12, at the begining of line 3, for Melody read Harmony.
Pag. 14, line 10, for Lais read Laxis.
P a g- 3 2 > Example vii. for Plate 8, read 9.

Pag. 40, line 7, of Article v. for as the falfe fifth, read has the falfe fifth.
Pag. 48, for Article iv. read iii.

Pag. 72, line 5, add, after defcending Continually, by fifths.
Pag. 82, Article v. ioxfami rezdfome.

CONTENTS.

/NTRODUCTION — — Page 1
The firfi Greek. Diatonic Syjiem * ■- « ■ 3

Its Divion into the Tetrachord Conjoint — ■ 3

The great eft immoveable Greek Syjiem •■■ ■ — 4

Its Divifion into Jive Tetrachords «* < j — 5

The fifteen Modes of Ariftoxenes ■ 1 — 7

Diver fe Opinions of Authors in regard to the Modes - — >— ^ '* <- , — — — - 8

Of the Enarmonic, Diatonic, and Cromatic Genera, with their refptclive Colours 9

The Addition of the four Greek Modes to the Cantos of his Church of Milan, by St. Ambrofe 10

fhe Changement of the Greek Letters into Roman, by Boetius — — ibid.

And afterwards reftained by Pope Gregory the Great > ' 1 1

Four more Greek Modes introduced by the fame Pope y* ■ =** ibid.

The Divijion of the above eight Modes into Aukatic, and Plagel — ■ ibid.

The Reformation of the Greek immoveable great Syjiem, by Guido Aretino ■ ■ ■ 1 2

The Addition of fix Syllables to the Roman Letters, by the fame Guido ■ 14

The Explanation of GuidoV Syjiem, divided by fix Hexachords, inftead of Tetrachords • ibid.

The above Syllables applied to the Hexachords in their Order upon the Left-hand for the Help of the

Memory in the Pratlice of Singing ■ * ■ — 15

The Introduction of Harmony by the fame Guido > ■ 16

The Continuation of the Progrefs of Mufic till now ■ ■ — ' — ■-- i -— — — 1 9

B O O K I.

CHAP. I. Of Mufic in general.

Art. I. THE Definition of Mufic ■ — — Page 21

IT. The general Divijion of Mufic — ; : s 22

III. Of Melody, and its Divifion • ■- — — — — ib.

]V. Of Harmony - 1 ■ ■■■ ■ — — ib.

V. Of the Divifion of Harmony — ■ ■■>■ ■ i — — — ib.

CHAP. II. Of Mufical Sounds.

Art. I. "~THE Definition of mufical Sounds ■ • ■ Page 23

II. Of the Number of mufical Sounds ■ ■ ib.

III. Of the different Intervals betwixt the eight original Sounds < >— — p— »^ ib.

CHAP. III.

Art

I. /"} F the new Modern general Syflem of Sounds '■ — — -— Page 25

II. ^ Of the various Names to the different Intervals of the above general Syjiem of Sounds ibid,

CHAP. IV.

Art. I. f~)F the general Divifion of the general Syjiem of Sounds, from which arife the Confonant

Syjiem of Progreffwn, or as commonly called Modulation Page 27

II. Of two Harmonic Movements added to the above Confonant Syjiem of Progreffion 29

ill. Of the Divifion of the fundamental Progreffion arifing from the above Syjiem 30

CHAP. V.

Art. I. f~)F the Harmonic Divifion of the Syjiem of Sounds, from whence arifes the Harmonic

Syjiem of Combination of Sounds . Page 3 1

II. Of the Divifion of Combination of Sounds — i— — > -~» > — — • 33

. CHAP.

CONTENTS.*
CHAP. VI.

Art. I. f\ F the different Scales ■■■

II. Of the>principal natural Scale -

Page 3+

, _ 35

III. Of its relative Scales- • ■ ib.

IV. Of the artificial Scaler commonly called the Minor Mode ■ . 38

V. Of its relative Scales 40

VI. Of Scales of 1"ranfpofition by the Confonant Movement - ■ 41

VII. Of the Scales tranfpofed from the natural Scale — ■ » - ib.

VIII. Of tranfpofing the artificial Scale — — — > 42

IX. Of the Number of Scales arifingfrom the Tranfpofttion — — - — — ib.

X. Of the different Scales of Melody in their different Keys * 43

XL Of the divers Pqfitions of the Unifon, rejpeclively to the different Keys ib.

BOOK II,

Containing the fundamental Contrapoint, by which the following Harmonic Code is

compofed — — --- — — — — Page 4^

PART I. The. Harmonic Code.

CHAP. I. Containing the Confonant Movement by defcending a fifth Low, or a fourth

High, commonly called the Skip of Cadence.

Art. I. (~)F the Confonant Combination — — — •— ' Page 46

II. Of the Simple Harmonic Combination — — 47

Of the Manner of doubling the two Confonants, the Fifth and Oclave ib.

III. Of the Compound Combination, and Firjl with the Seventh —— '■ 48

Of adding the Fifth and Oclave ib.

Of the Combination of the Ninth' — — ib.

Of introducing the Ninth injlead of the Oclave — — ■ ■. 49

Of joining the Oclave to the above Canon — ib.

Of paffing from one Difcord to another ■ 50

IV. Of full Combination ■ — ib.

V. Of the Seventh and Ninth paffing in another Difcord, called Falfes of Proportions 5 1

How to rejolve the Seventh and Ninth in afcending ib.

VI. Of uncommon Combination, as Falfes by Anticipation ■ 52

VII. Of Falfes by Change, as they are called by the Italian M afters • 5$

CHAP. II. Containing the imperfedl Confonant Skip of Cuide.

Art. I. f\ F the Confonant Combination • Page 54

II. Of the Simple Harmonic Combination i — ib.

Of doubling the two Confonants 55

III. Of the Compound Combination — — ib.

IV. Of Anticipations -■ ■ ■■ ib.

CHAP. III. Containing the perfect Auxiliar Skip of Third low.

Art. I. THE above Skip is not properly fundamental in continual Progreffion Page 56

II. Of the fimple and compound Combination ib.

CHAP. IV. Containing the fame Auxiliar Skip joined with the perfect: Skip of Cadence.

Art. I. 1 N fimple Combination — — — — ■ Page 57

II. In compound Harmony three Canons — — ■■■ —r 58

C H A P.

CONTENTS.

CHAP. V. Containing the fame Skip joined with the imperfect Skip of Guide.

TWO Canons in fimple Harmony — r : Page 5* '

CHAP. VI. Containing the imperfect Auxiliar Skip of Third high.

JN continual Progreffion - Page 59-

"* Of the fame joined with the perf eel Skip of Cadence — i . — — ib.

C H A P. VII.

T H E fame joined with the perf 'eft Skip of Guide 1 Page 60

CHAP. VIII.
O F divers Combinations with all the four Skips fundamental — -. ——————— page 60

PART II. Of the Harmonic Code.

CHAP. I. Containing the perfect Confonant Skip of Cadence.

Art. I. f) F tranfpofing the Scale in all Semitones, only, in Confonant Combination ■ Page 6$

I[. The fame Tranfpqfition with Harmonic Combination ■ •■ 64

III. With Compound Combination ■ > ib.

The fame with the Ninth i - 65

Of tranfpofing the artificial Scale with Simple Combination — — ib.

IV. The fame Tranfpqfition with Seventh *- ib.

Of the fame with Ninth in/lead of the Eighth ■ ib.

V. Of the fame Tranfpqfition in a better Manner < -■ ■■ • ■■■ • 66

VI. Of tranfpofing the natural Scale with the Refolution of the Compound Combination afcending 67

CHAP. II.

f\ F tranfpofing the natural and artificial Scale by the imperfecl Confonant Skip of Guidf Page 6%

CHAP. III.

f\ F tranfpofing the two principal Scales by perf eel auxiliar Skip of Third low, in continual Pro-
gression ' • • ' ■ ' Page 68

CHAP. IV.

Art. I. f\ F the Tranfpofition by the fame auxiliar Skip, joined with the Skip of Cadence — Page 69

Of the Tranfpqfition of the artificial Scale as above ib.

Of the fame Tranfpofition, but the Bafs Jkipping by major and minor Thirds in the natural

Way — — ■ ' — — 70

Of the Tranfpofition of the natural Scale with the fame Combination, but with the

fundamental Guide ■■■ ib.

The Manner of tranfpofing the artificial Scale by the fame Progreffion a Semitone higher ib.

II. Of the Tranfpofition of the natural Scale, by the fame Progrefiion in compound Combination ib.
The fame as the above, only different in the Combination to the Skip of Cadence, which is

with Third major — - — "— ■— ib.

Of the fame Tranfpofition of the artificial Scale by both the above Skips 7 1

III. Of the fame Tranfpofition and Progreffion^ but in compound and full Combination • ib.

CHAP,

CONTENTS.

CHAP. V.

Art. I. C\ F tranfpofing the natural Scale by the above auxiliar Skip of 'Third low, joined with the

Skip of the Guide — Page 72

II. Of tranfpofing both the natural and artificial Scales, as they happen in their natural Order,

by the above two Skips. • ■ ■- 73

CHAP. VI.

Art. I. f\F the Tranfpofition by the imperfecl auxiliar Skip of Third high, joined with the Skip of

Cadence ■• Page 73

II. The fame tranfpofition with compound Harmony ib.

The Manner of dividing the Oclave, in four and three Parts, with the fame Progreffwn ib.

CHAP. VII.

r\ F the Tranfpofition by the above auxiliar Skip, joined with the Skip of Guide ■ ■ Page 74

Of tranfpofing the natural Scale by the fame auxiliar Skip afcending a major Third, joined
with the fame Skip of Guide * -■ ■ ib.

CHAP. VIII. .

f\F the Tranfpofition of both Scales, by all fundamental Skips in compound and full Harmony Page J5

BOOK III.
CHAP. I.

Art. I. C\F figured Harmony — : ■ — •- — Page 78

II. Of the different Situation of the Bafs in figured Harmony : — - — ib.

III. Of the Inverfion by the Bafs Syncopes . 79

IV. Of varied and dimini/hed Bafs Notes ■ • 80

V. Of fome equivocal Combination ■■■ 82

VI, VII. Of fome particular Inverfion arifing from the artificial Scale — — 83* 84

VIII. Of fome irregular Combination in the artificial Scale '■ 36

IX. Of the different Motions and Variations of the fuperior Parts - 88

CHAP. II.

Art. I. flF Compojition in divers Parts ■ P a gc 90

II. Of Fugues and Imitations • - •■ ■ ■ 92

III. The Manner of compqfing the Fugues and Imitations — ■ 93

IV. Of compofing Canons ■ 96

V. Of Cadences .,.„,..■■. . — 98

VI. Of the Accent . ^

CHAP. III.

Art. I. THE Divifion of figurate Mufic Page 102

II. Of vocal Mufic — ■ ■ ■ ■ ■ • ' ■ ibid.

III. Of infirumental Mufic 1 103

IV. Of local Mufic, and firfi of facred Mufic ■ 104

V. Of Theatrical Heroic Mufic : 107

Of Comic Mufic — 1 ■ 108

VI. Of Chamber Mufic — — — =— — ■ ib.

DELL*

ftAftftiftSsUSfaftftsSUK

Ghap. IV.
Chap. VI

Art. V.

Chap.V.

ERRATA.

In the Contents.

Line 13. for Aukatic, read Autentic.
Line 1. for General, read Conjonant Divifon.
Line 6. for Page 41, read Page 40,
Line 7. for ibid, read 41.

In Book II. Part I.
Line 1 1. for Propofitions, read Poflpojitions.

In Book II. Part II.
Line 4. for Page 73$ read Page 72*

In Book III.

Chap. I. Line 1. for Page 78, read 77.
Line 7. for Page 36, read 86.

Page 14

In the Introduction.
Line 10. for Lais, read Laxis.

In Book I. Chap.V.
Page 32. Line 26. for Plate 8, read P/tfto 9.

In Book I. Chap. VI.

Page 34. L
Page 37. L
Page 39. L
Page 40. L
Page 42. L

Page 47. L
Page 48. L
Page 53. L
Page 57. L

ne it. for iVb^£, read AW.

ne 20, read <?«</ the Indicative defending Seven ferves only, &c.

ne 6. in the N. B. read, a;;i it's tranfpofed Scales.

ne 1 3. for as, read has the falfe Fifth A Flat.

ne 6. from the Bottom, for Seven, read Five more of different. Sic*

ne 2. from the Bottom, for eighty, read eighteen Scales.

ne 13* for F to B, read B to F.

ne 1 . for Conjonant, read Compound Combination.

ne 7. from the Bottom, read Firjl and Second Chorus.

ne 12. for :«/<?, read true fundamental Baffe fubfijl.

ne 5, read defending continually by Fifths is contrary, &c.

ne 24. omit Canon, and read Combination has no more.

Page 72. L

Page 78. L

Page 82. Art. V. read Of fome equivocal Combination.

Page 100. Line 36. for compacted, read divided in two Notes

DELL'

ARTE ARMONICA

THE

INTRODUCTION;

CONTAINING

An HISTORY of the Progress of MUSIC to this Time.

ATURE hath provided all Animals with certain Inf-Hn&s, neceiTary both
for their general and particular Prefervation. Brutes are limited to limple
InfHncts, by which they are wholly guided and directed. But Man is diftin-
guifhed by the Gift of Reafon, by which he is able to controul, regulate,
and ufe his feveral Inftincts and Propenlions, according to his Will and Plea-
fure. Moreover, there are implanted in him the Seeds (as it were) of feveral
ufeful and pleafant Arts, with the Power of cultivating and bringing them to Perfection.

One of thefe Seeds, and not the lead: confpicuous, is undoubtedly the Faculty of Sing-
ing, of which Mufic may be confidered as an Improvement j whofe Bufinefs it is to chear
the Mind, and to relieve it, not only from the Irkfomenefs of Idlenefs, the Gloom of Care,
and the Fatigue of domeftic Employments ; but likewife from the Power and Tyranny
of our boifterous Paflions, and many other Evils, which do but too often invade both
the Mind and the Body, as the Hiftory of Mankind moft plainly (hews.

Thus we may, upon the beft Ground in the World, aflferr, that Singing and Mufic are
born with Man, are congenial, and even interwoven into his Frame and Constitution.

But then, as every one was endowed with a Propenfity and Genius peculiar to himfelf,
and modell'd, as it were, according to the Singularity of his own Conflitution, there would
arife in the World an almoft infinite Variety of Taftes and Opinions, agreeable to the
different Genius and Temper of different Perfons and different Nations ; and Singing and
Mufic being differently purfued and cultivated, would at length be accommodated to the
Tafte of every partkular Country, and to the Turn of its Inhabitants.

Thus, the Mufic of the 'Turks, is entirely different from ours. The People of Fez,
Morocco, and other Parts of Africa, have again a different Kind, which to us, who are not
accuftomed to it, appears to be very rough and horrid; but it neverthelefs is highly pleafmg
and entertaining to them.

B Thuj

2 THE INTRODUCTION.

Thus, among the feveral Nations of Europe, there are found different Manners of Singing.
The Frensh, Polanders; Sicilians, Scotch, and other People, have every one a certain Mode
peculiar to their Idioms, and the Tafte of their Country ; which muft certainly proceed
from their different Tempers and Conftitutions, owing perhaps in a great Meafure to the
different Climates in which they live. There is alio a great Variety of Tafr.es and Opinions
among the Inhabitants of the fame Country,

One Man is better pleafed. with the brifk and lively, whilft another is more delighted with
the grave and pathetic.

Mufic, like all other Arts, is fubject to the various Viciffitudes of beginning, improving,
arriving at, what we may call, its perfect State, and afterwards decaying.

But of the different Epochas of the Improvements of Mufic, and the various Gradations
'by which that delightful Art hath arrived to its prefent State, we have in Truth but a very
fcanty and imperfect Knowledge.

Sacred Hiftory informs us, that Tubal, the fixth Defcendant from Adam, was the Inventor
of Wind Inftrmnents, from whence we may juftly infer, that thefe being contrived to imi-
tate the human Voice, Singing muft before have arrived at fome Degree of Perfection.

From the fame Hiftory we learn, that in Judea, in the Time of King David, a great
Number of Singers and Performers upon Harps, and other Inftruments, were employed in
the Service of God ; that therein were introduced both Pfalms and Hymns ; David, the
King, himfelf aflifting in thofe Performances.

In Imitation of this, and indeed as a Proof of it, thefe very Pfalms are ufed to this Day in
the Offices of the Chriftian Church.

But all this implies no more, than that Mufic exifted in thofe Times, and even was had in
great Honour and Eftimation : For no Mention is made when or how it was learned, nor
how far the Art had proceeded ; only we are affured, that the Jewi/Jj Lyre was mounted with
a confiderable Number of Strings, and that David was the beft Artift of his Time; and was
employed as fuch for the curing of his Predeceffor, King Saul, of his Phrenzy, as appears
from Samuel xvi.

All that from this Time (that is from the Age of King David) can be known, and that
not without fome Confufion, is, that Mufic had a new Epocha in Greece, where it began by-
Singing : That their firft Poets recited their own Compofitions, with a certain Manner of
Expreffion, elevating and lowering the Voice, as the Subject required, by the Help of the
Lyre, an Inftrument furnifhed with three Strings in fome Provinces, and in others with four,
which were fo difpofed, as to proceed from the Grave to the Acute, after the Manner of a
Scale, and were founded by the Touch of the Fingers, as the prefent Guitar, or Lute, is.
From whence it follows, that the vocal Performances of this early Age, could be no more
than fimple and plain Recitative, after the Manner of the Orator, C. Gracchus, at Rome,
who, according to the Teftimony of Cicero, in his Treatife de Oratore, Book III. Sect. 60,
made Ufe in fpeaking to the Public, not of a Lyre indeed, as mentioned above, but of the
Sound of a fmall Flute, which a Perfon, who flood privately behind him, held, and when-
ever he either funk his Voice too low, or raifed it too high, he was by this Means, namely,
by the Help -of the Tone of this Inftrument, recalled to the proper Pitch. According to
fome, the like had been practifed before by Demojlhenes, in Greece.

But as the Voices of Men are not of an equal Pitch, as to the Grave and the Acute, the
four Strings, which were affixed to the Lyre, were not fufficient for the Purpofe of every
Voice; therefore they added to the former four, three other Strings, gradually rifing higher ;
by which Means, they were now able to produce feven different Sounds, proceeding from

die

THE INTRODUCTION. 3

•the Grave to the Acute, as in the firft Example, Plate I. Thefe feven Strings were named,
according to their Place, upon the Inftrument, as follows.

The firft was the moll grave, and was called Hypate, which fignifies the principal, or the
moft honourable.

The fecond, which was fomewhat more acute, was termed Parhypate, that is, the next
to Hypate.

The third was called Lycanos, which is as much as to fay, that it was to be founded by
the indicial Finger.

The fourth they called Mefe, becaufe it was in the Middle of the feven Strings.

The fifth was called Paramefe, which fignifies the next to the Mefe.

The fixth was termed Paranete, being next to the Nete, or laft String.

The feventh they called Nete, which fignifies the new or laft String ; and this was the moft
acute of all : For it was the Cuftom of thefe ancient Times, as it is at this Day, in Lutes,
Violins, and other like Inftruments, to place the largeft, or Grave String, upperrnoft, and fo
defcend gradually to the fmalleft, or Acute, which was put at the inferior Part of the
Inftrument.

The Degrees, or Intervals, between one Sound and another, were ftiled Tones and
Semitones ; the Tones were divided into greater and leifer Tones, the common Meafure of
which was called a Comma ; there being none of thefe Commas contained in the greater
Tone, and eight in the leifer.

From the firft Grave, or largeft String, called Hypate, to the fecond String, Parhypate,
they eftimated the Diftance to be a Semitone, confiding of five Commas.

From the fecond to the third String Lycanos, the Diftance was a greater Tone.

From the third to the fourth String, called Mefe, they counted the Diftance to be a
Minor Tone.

From the fourth to the Paramefe, or the fifth String, a Semitone.

From the fifth to the Paranete, or the fixth String, a greater Tone.

From the fixth to the feventh, or laft String, a Minor Tone.

And thus thofe feven Strings made fix Intervals ; two of the greater Tone, two of the
leffer Tone, and two of a Semitone, as in the above-mentioned Example the firft, Plate I.

Such was the firft Scale of Sounds amongft the Greeks, which in their Language was
called Syftem, and correfponds with the modern Scale, beginning at B, and rifing thus, C,
D, E, F, G, A, excepting, that in the modern Scale, there is no Deftination of the Tones
into greater or leffer, but they are confidered as being all equal.

This Syftem o§ the Greeks was called by the Name of Tetrachord Conjunct, becaufe it
was conftructed of two Diateflarons, that is of two Fourths, each being compofed of four
Sounds in Sequence ; 10 that the Sound which was the Acute, or higheft Termination of the
firft DiatefTaron, ferved for the firft Grave Sound of the fecond j and both thefe Diateflarons
(at ppefent called Fourths) had the Order of their refpective Strings, equal in Point of
Interval, or Diftance.

For

• 4 THE INTRODUCTION.

For from the firft Grave String, or Hypate, they reckoned a Semitone.

From the fecond to the third, a greater Tone.

And from this to the fourth, a leffer Tone ; and, beginning from the fame fourth String,
which by that Means came to be the firft of the next DiateiTaron, the Diftance between
it and the fecond String was a Semitone, between the fecond and third a greater Tone,
and between the third and fourth, or laft String of the whole Tetrachord Conjunct, a leffer
Tone. In mort, jufl as it is feen in the Order of the above Scale, or Syftem, which
.-being divided in the Manner above-mentioned, formed two equal Intervals, the one Grave,
and the other Acute, as it is defcribed in the fecond Example, Plate I.

The above Divifion into Tetrachords, ferved to no other Purpofe, but to enable the
Ancients to transfer the firft Diateffaron into the Place of the fecond ; that is to fay, the
four Grave Sounds into the four Acute, or the four Acute into the four Grave, for the
Advantage of the Voice, as that was high or low. And the Lyre, when capable of thefe
Tranfpofitions, became a competent Regulator of different Voices in their different Pitch.

•But as thefe Tones of the Greeks were estimated by the Comma, which was but an
■imaginary Meafure, and had no Relation to any Thing certain, fixed, and known, and
•conlequently was liable to be underftood with more or lefs Latitude, the above Syftem, or
Scale of feven Sounds, was found to be imperfect, and, as it is faid, was amended in the
Time of Pythagoras. Probably one of their Singers, or Poets, which ever it was, vifited
the School of Pythagoras, in Italy, and learned from him (who appears, from Hiftory, to
have been the firfl that found out the Method of explaining, to the Human Underftanding,
the Diftance or Diverfity of Sounds, as they were high or low) that if one Sound was added
•to the feven contained in the above Scale, fuch added Sound, whether it were high or
low, would be found, in refpect of the others, perfectly confonant with that which was
fartheft from it, whether high or low ; and therefore in a Scale, which was to ferve for a
Syftem of Sounds, the Octave, or confonant Sound, ought neceffarily to be included ;
iince it would prove a fixed, fenfible, and intelligent Termination of an Interval or
Compafs, that included in it every poffible Divifion of Sounds, the Differences of which,
like Parts relative to a Whole, could only be determined by this Means.

Thus they added to the feven Strings, and at the Top of the Lyre, the deep String that
was wanting, which became Confonant with that acute String, which was fartheft off; fa
that the Suing called Hypate, which was before thedeepeft, came now to be but the fecond
deep String ; and its Interval or Diftance from the faid String, which they called
Proflambanomenos, that is to fay the added, was a greater Tone ; and the String Nete,
which was the Seventh in the former Scale, came to be the Eighth acute String,
perfectly confonant with the Proflambanomenos, which was the deepeft in this their new
Scale. . .

There fubfifted between thefe two Extremes of the Proflambanomenos, and the Nete,
an Interval certain and diftinct, which included in it the other fix Sounds of the Scale,
every one at their proper Diftance proportioned to the Whole ; and in this Manner they
improved their firft Syftem.

But, for the Information of thofe who are unfkilled in Mufic, we mail give a fhort
Explanation of that Interval, which by the Greeks was called Dia Pafon, and by the
modern Muficians the Octave, becaufe it includes in it the whole Natural Scale of the
Eight Primary Sounds of Mufic. %

Every one knows, that any Sound whatfoever being given, another, and even many,
may be given, that fhall be exactly fimilar to it, and neither higher or lower. But thofe,
who have no Knowledge of Mufic, have not perhaps obfeived, that over and above thofe

fimilar

THE INTRODUCTION. $

fimjliar Sounds above-mentioned, which by Muficians are diftinguifhed by the Name
of Unifons, an. Infinity of other Sounds may be given, either higher or lower, which
though they are not Unifons, and fimilar one with another, becaufe they are higher or
lower, yet they are confimilar j fo as they alfo feem to be only one Sound, though one
be high and the other low, the higher being abforbed in the lower.

Of this any one may be fenfible, by touching any Key of an Organ or Harpfichord,
together with any other Key, at the Diftance of an Octave ; he will find, that the Grave,
or deep Sound, abforbs in a Manner the Acute, or high one, and that it renders it, as it
were, undiftinguifhable, the Acute Sound ferving to no other Purpofe, but to ftrengthen
and inforce the Grave, or deep Sound. With good Reafon, therefore, thefe confimilar
Sounds, which are at the Diftance of an Octave, are called by Muficians confonant Sounds,
to diftinguifh them from thofe which being perfectly fimilar, are called Unifons : And all
the Sounds which are contained in the aforefaid Interval of the Octave, have in like Manner
every one, whether higher or lower, their confonant Octave -, for which Reafon, not only
the firft Octave, but alfo all the others, are capable of being inlorced in infinitum, both in
Height and in Depth, by additional Sounds.

It is alfo found, that befide the two extreme Sounds of the Octave, the fifth of the
ei^ht Sounds of the Octave, becomes alfo confonant with the firft deep Sound. This is
proved by Trial on the Organ, for touch whatfoever Key you pleafe in the Stop, called
Sefquialtera, in which Stop all the Keys are joined with their refpective Fifths, the fifth
Sound is fo clofely united with its deeper Sound, that it cannot be diftinguifhed j and thus
all the perfect Fifths, which confift of feven Semitones, are confidered as confonant, tho'
not fo perfectly as the Octave.

We return now to the Hiftory of the Progrefs of Mufic in Greece,

As Nature, for our common Good, has implanted in the Breaft of Man, the Love of
Glory, and the Defire of excelling in great Actions, and ufeful and pleafing Arts and
Knowledge, it is no Wonder that the mufical Art, which fprang firft in Greece from the
emphatical Recitations of the Poets, acquiring afterwards, by Degrees, a greater Energy
of Pronounciation, was improved into a Species of Singing, and at laft into Melody, and
foread itfelf in Progrefs of Time from Province to Province, but in different Manners,
according to the Genius and Turn of the Inhabitants of the Country. From hence there arofe
a Neceflity to increafe continually the Number of the Strings of the Lyre ; and moreover, new
Inftruments of Mufic, both of the Stringed and Wind Kind, were invented and introduced.

At length then to unite, and the better to diftinguifh, all the Sounds which they had
fucceflively introduced into their Lyre ; a new Syftem was eftablifhed, and was called the
greateft, and the unchangeable Syftem ; which was fo termed, becaufe it included, in their
Opinion, every other lefier Syftem, or Divifion whatfoever.

This Syftem confuted of a Scale of fixteen Sounds, which formed their Difdiapafon, or
double Octave ; that is, to their firft Diapafon, or Octave of the eight Primary Sounds,
there was joined another Octave, or eight Sounds, fimilar to the firft, but higher, as in
Example III. Plate I.

But as the firft Scale of feven Strings was divided into two lefTer Syftems of four Strings
each, which were named as above, the Tetrachords conjoined, from whence the deep
String, called th$ Prollambanomenos, which was the deepft Note in the Syftem, was
excluded. So in this new greateft Syftem, there was annexed three other Tetrachords :
From whence this Syftem came to be divided into five Tetrachords, the Note Proilamba-
aomenos being likewife excluded. Example IV. Plate I.

C The

# THE INTRODUCTION.

The firft of thefe five Tetrachords was called the Tetrachord Hypaton, the firft String
of which anfwering to the Note B natural, of our modern Scale, was named Hypate
Hypaton, that is the Hypate of the Tetrachord Hypaton.

The fecond String of the fame Tetrachord, which correfponds to the Note C, in our Scale,
was called Parhypate Hypaton*

The third String was named Lycanos Hypaton, which is the Note D, in our Scale.

The fourth String, which finifhed the firft Tetrachord, they called Hypate Mefon,
becaufe it ferved for the firft String of the fecond Tetrachord, which was called Melon,
at the fame Time that it was the fourth String of the firft Tetrachord, which String or
Sound corresponds with our prefent E.

The fecond String of the fecond Tetrachord Mefon, was called Parhypate Mefon, which
is the Note F, in our prefent Scale.

The third String was Lycanos Mefon, and the fourth Mefe, the fame as G and A, in
©ur firft Scale.

Then followed the third Tetrachord, called Synemmenon, or conjoined, which,
according to the Order and Nature of the two firft conjoined, ought to have the Diftance or
Interval of a Semitone, from the firft to the fecond String ; but as the faid laft String Mefe,
which coincides with the Note A, is diftant a whole greater Tone from the next String, called
Paramefe, which is our prefent Note B, they were obliged, in order to make the third
Tetrachord unite with the former, in the fame Order of Tones, to divide the Interval
betwixt the two Strings Mefe and Paramefe, by inferring a new Note, or Sound, between
them, diftant a Semitone from the preceding String, and a greater Tone from the following
Note higher ; which greater Tone confifted of nine Commas, viz. five between Hypate
and Parhypate, or from B to C, and four from B flat to B natural, (from which Divifion
arofe the Distinction of the greater and leffer Semitone) and the firft String of i.hii>
Tetrachord, called Synemmenon, correfponding to A in the prefent Scale, was termed
Mefe Synemmenon, and was diftant a greater Semitone from the fecond adjacent String,
which was called Trite Synemmenon, correfponding to the prefent B flat.

The third String, which was diftant a greater Tone, was called Paranete Synemmenon,
that is C ; and,

The fourth String, Nete Synemmenon, was fuppofed to be diftant a Minor Tone from
the third. In this Manner was the third Tetrachord constructed.

To pafs then to the other two Tetrachords, which were called disjoined, and made up
the five, into which the greateft Syftem was divided, they came next to the String
Paramefe, or B natural, which was feparated from the String Meie, by the abovefaid new
added String; and proceeding to the fecond String of the fourth Tetrachord, which was
called Diazeugmenon (which fignifies disjoined) they called it Trite Diazeugmenon, it
being diftant a Semitone from the firft String, and a greater Tone from the third, called
Paranete Diazeugmenon, which was diftant a leffer Tone from the fourth, called Netdiazeug-
menon : This fourth String then ferved, according to the Order and Method of the other
Tetrachords, for the firft String of the fifth, or laft Tetrachord, / which was named
Hyperbolaeon, that is, excelling or exceeding; the fecond String of this was named
Trite Hyperbolaeon, the third Paranete Hyperbolaeon, and the fourjth Nete Hyper-
tiolaeon.

Thefe two Tetrachords were nothing more than a Tranfpofition of the two former, an
Octave higher, or more acute, which correfponded, as has been faid, to the Notes B,
C, D, E, and E, F, G, A, in our prefent Scale.

Now,

THE INTRODUCTION. ?

New, in the aforefaid Difpofition of the five Tetrachords of the Syjlema Maximum, or
frreatefl Syftem, we mult obferve, that the third conjoined Tetrachord is not fimilar to the
Others ; for fince from the fecond String Trite Synemmenon, or B flat, inferted between
Mefe and Paramefe, to the third String Paranete Synemmenon, or C, there is reckoned to
-be the Diftance of a greater Tone, therefore from Paranete Synemmenon, or C, to Nete
Synemmenon, or D, there ought only to be a lefTer Tone ; whereas the Interval betwixt C
and D, in the firfr. and fourth Tetrachords, was calculated to be a greater Tone, and not
\ lefTer. From whence it appears, that, from the Time that the greateft Syftem was
divided into the abovefaid Tetrachords, the Artifts did no longer regard the Diftinction of
the greater and lefTer Tone, without which Diftinction the aforefaid Tetrachords were all
:five equally divided into two Tones, and a Semitone, in the fame Manner as it was divided
by the Pythagoreans.

But at this Time, and for fome Time after, the Ancients had no other Notes or Characters
.by which to diftinguifh and mark the Sounds of their Songs, but the above-mentioned
Names, appropriated to the Strings of their Lyre : From whence it may be inferr'd, with
■the greateft Probability, that their Mufic confifted of nothing more than fimple Melody,
in the Nature of Recitative, or rather of a melodious Utterance, Pronounciation, or
Expreflion, purpofely adapted to their poetical Compofkions ; and Strabo afferts, that the
ancient Poets rehearfed their Works to the Sound of fome Initrument, catching and
inveigling their Auditors by that Artifice.

Therefore, diverfifying one after another, this their nrft fimple Method, and introducing
alfo a certain Species of Chanting, in the Manner of a Song, and this proceeding in
divers Manners, according to the Difference of the Country, and Taftes of the Inhabitants,
they, at length, in order to be able to give a Name to every Note which they were
continually adding to their Inftruments, changed the Names of the Strings into the
Letters of their Alphabet, placing the firft. Letters to the graven: Sound, and the others in
Sequence, proceeding from the gravefl to the acuteft.

But as the Science of Mufic received daily Improvement, fometimes in one Province^
and fometimes in another, and from the public Places being introduced into Houfes or
Palaces, Temples and Theatres, and that in different Taftes and Manners, according to the
particular Genius of the Inhabitants of the feveral Provinces , from thence there arofe 'a
Variety in the" Order of their Scales, the Pofition or Places of the Sounds being by this
greatly multiplied, and the Letters of the Alphabet not being fufficient to denominate all
the different Places of every Sound, upon their Variation of Pofition, they were obliged to
increafe the Signs or Notes, or the Names taken from the Alphabet, by turning the Letters
to the Right Hand or to the Left, or placing them above or below, and adding befides,
certain Points, and other Characters.

This Diverfification of Modes was afterwards difKnguifhed by the Name of the
Country, where each was principally ufed*

AftfloxmuS) who appears to have been the firft that wrote regularly, and perhaps the beft
on the Subject of Mufic, diftributed the different Methods of Singing into fifteen Modes,
and thefe again into three different Pofitions, according to the different Parts of the human
Voice. Five were called Principals, which he placed in the Middle ; five others were called
Collaterals, but graver > and the remaining five Collaterals, but acuter.

- The Principals in the Middle were the Doric, the Iajiie or Ionic, the Phrygian, the
JEolic, and the Lydian.

The five Collaterals on the Acute, or higher Part, were the fame, but were diftinguifhed
by the Word Hyper, which fignifies above, that is, the Hyper Doric, the Hyper Iq/iic,
the Hyper Phrygian, the Hyper Molic r and the Hyper Lydian*

3 THE INTRODUCTION.

In the lame Manner to the Collaterals on the deep or grave Part, the Word Hypo was
prefixed, meaning the inferior, as the Hypo Dork, Hypo Tqftk, &c.

Thefe fifteen Modes were diftant a Semitone one from another j the Diapafon or
Octave being divided into twelve Semitones, or Intervals, of thirteen Sounds, every Sound of
the two Collaterals was diftant from its refpective principal, one Diateffaron, that is to fay,
a perfect fourth, confifting of five Semitones, as may be feen in Example V. Plate I.
wherein the fifteen Modes are placed over the Names ufed in our prefent Scale, which
iorrefpond with the ancient Greek Scale, or Diapafon, according to the Method of Arifloxenm.

Cafiodorus, writing to Boetius, fays, in the fecond Book of his Epiftle, that the artificial
Mufielhas fifteen Modes, agreeing in this with Arijloxenus.

Euclid, who follows Arifloxenus too, gives us but thirteen, at a Semitone's Diftance one
from another ; that is, he went not beyond the laft Semitone of the Diapafon, which he
confidered., as being divided, according to the Doctrine of Arifloxenus, into twelve Semitones,
and thirteen Sounds. He omitted the Hyper JEolic, and Hyper Lydian, placed by Arifloxenus
amongft the high Collaterals, beyond the laft high Note of the Diapafon.

'Cenforinus alfo makes Mention of thofe thirteen Modes.

Plato, fpeaking occafionally of thofe Modes, in the third Book of his Republic, reckons
them fix i and in another Place, namely, in the Piece called Laches, he mentions only four.

Apuleius talks of the JEolic, the lajlic, the Lydian, the Phrygian, and the Doric.

Ariflides Quintilian mentions fix, the Doric, the Phrygian, the lajlic, the Lydian, the
Mixdydian, and the Syntonolydian.

Julius Pollux reckons eight, Lucian four ; and many, confidering Greece as divided into
Doria, Molia, and Ionia, and that thefe were its proper Bounds, have named only the
Doric, the Molic, and the Ionic.

Phitarch afierts, that the ancient Modes were no more than three, that is, the Doric*
the Phrygian, and the Lydian.

Ptolomy, with whom agrees Boetius, confiders the Doric, the Phrygian and the Lydian,
as Principals. The Hypo Dorian, the Hypo Phrygian, and the Hypo Lydian, as Collaterals.

Apuleius, and Martian Capella, changed the Order ; Apuleius placing the Molic firft, and
Martian Capella the Lydian.

Lucian gave the firft Place to the Phrygian, and many others, whom, for Brevity Sake,
we forbear to mention, have given different Names to the Modes, and have placed them
in a different Manner j for which Reafon it is impofiible, in fpeaking of the ancient
Modes, to give any very diftinct. or certain Account of them, either as to. their Number,
their Names, Order, or Situation.

Straho, in the Place above quoted, fpeaking of the ancient Poets, fays, that as their
Poetry confifted of different Meafures, fo the Methods of rehearfing of it were different,
and one could not be ufed for another. Their Verfes having a certain determinate Order,
they diftributed them into three Claffes, one of which was the Dittyrambic, the other the
Tragic, and the third the Comic. To each of thefe Claffes they afligned a proper
Manner of Recitative ; from whence it came to pafs, that the Chants, or Mufic, derived
from the Nature of the poetical Compofitions, were called Modes. If the Verfes related
to any doleful Matter, they called it the Doleful Mode ; if to any Thing Bacchanalian,
the Bacchic, and fo of the reft; and as the Nations were different, and every one had its

proper

THE INTRODUCTION. g

proper Manner of reciting and finging peculiar to itfelf, they consequently denominated
thole Modes from the Countries where they were principally ufed, as the Phrygian, the Doric,
the Lydian, &c. The Doric Mode was ufed by the People of Doria } in that Part of
Achaia, which is now called the Morea ; and this Mode partook, fomething both of the
Lydian and the Phrygian, that is, both of the foft and the harm. The Phrygian Mode
was employed by certain People in Afia Minor, who being by Nature of a fierce and
cruel Difpofition, it was confequently of a fevere and furious Quality. The Lydian Mode
was introduced by the Lydians, a People of the Great Afia, of a chearful and gay
Temper ; and from thence it was called the moderate, or modeft Mode. This is the
Account given us by the aforefaid Author.

The above three Claffes, mentioned by the fame Author, were called Genera by the
Greeks, which three Genera they diflinguifhed into iix Colours, as they called them. One of
thofe Genera was named the Diatonic, another the Chromatic, and the other Enharmonic.
It is probable that the Dithyrambic was applied to the Diatonic, the Tragic to the Chromatic,
and the Nomic, or Comic, to the Enharmonic. To the Enharmonic Genus was affigned
one Colour, two to the Diatonic, and three to the Chromatic 3 which was called
Chromatic, or coloured, becaufe more Colours were affigned to it than to the other two.

Every one of the three Genera, with their Colours, were conflructed by the Diateffaron,
being divided, by different Intervals, into four Strings. The two extreme Strings, of each
Tetrachord of the greater!: Syflem, were called fixed or immoveable : The Other two, or
middle Strings, were moveable, becaufe they were differently tuned, according as each
Genus, and its Colours, required. Every one of the three Genera, and its Colours, had
their proper Species, which were divided in the fame Intervals of its Genus and Colour, but
in different Order, and in this Manner was diflinguiihed every Mode, Phrygian^
Lydian, &c.

The above Intervals, relating to every one of the Genera, and their Colours, were
differently divided by fome Authors, who followed the firfl Divifion of the firfl Syftem of
feven Strings, in Tones and Semitones, Major and Minor ; which Divifion cannot fubfift in
the Tranfpofition of the Scale, as has been demonftrated in the third Tetrachord of the
greatefl Syftem. But the Meafure of the abovefaid Intervals was juftly computed by the
Followers of Pythagoras, who confidered every Tetrachord of the fame greatefl Syflem,
as compofed of two Major Tones, one Semitone of four Commas 3 only that the
Diateffaron conflrucfed in this Manner, confifling of twenty-two Commas, the fmallefl
Intervals of the Genera become dividedby Fractions, and confequently not fo clearly intel-
ligible to thofe who are not fo well acquainted with nice Calculations. Therefore the befl
and the eafiefl Explanation of the above Intervals was made by Arijloxenus, as it is defcribed
by Euclid, (Introd. Harm.) Arijloxenus divided the Tone into twelve Parts, fix of which he
gave to the Semitone. In this Manner the Diateffaron v/as compofed of thirty Parts, being
two Tones, and a Semitone. Four Parts of the above twelve Parts he affigned to the fmall
Interval of the Chromatic, which was called Diefis Trientalis, namely, a third Part of a
Tone j to the fmallefl Interval of the Enharmonic, three Parts of the above twelve, which
was called the quadrantal Diefis Enharmonic, namely, the fourth Part of a Tone. The
Enharmonic Genus, being only difringuifhed by one Colour, was compofed of two quadrantal
Diefis, and of one Ditone, namely, from the firft String to the fecond, one of the faid Diefis,
or Quarter of a Tone 3 another like Diefis from the fecond to the third String, and one
Interval of a Ditone from the third String to the fourth 3 which three Intervals compofe the
perfect Diateffaron.

The Diatonic Genus was diflinguifhed by two Colours, one of which was named Molle,
and this was formed by three Intervals, one of fix Parts, namely, a Semitone 3 another of
nine Parts, or three Quarters of a Tone, and the other of fifteen Parts, namely, a Tone,
and one Quarter of a Tone. The other Colour was called Syntonum, the Intervals whereof

D were

io THE INTRODUCTION.

were fix, twelve, and twelve, or one Semitone, one Tone and one Tone ; and this is the
common Diatonic, which may be applied to the prefent natural Scale. The Chromatic
was diftinguifhed by three Colours ; the firft was named Molle, and was compofe of two
Intervals, each of one Triental Diefis, which is a third Part of a Tone, and another Interval,
confiding of twenty two Parts, namely, one Tone, and ten Twelfths of a Tone, which
three Intervals together make the perfect DiatefTaron. The fecond Colour was named
Sefcuplum, or Hemiolion ; and this was compofed of two Intervals, each confiding of
four Parts, and an Half of the twelve Parts, into which the Tone was divided ; and of
another Interval confiding of a Tone, and three Quarters of a Tone, or twenty-two Twelfths.
The third Colour was named Toniasum, and was compofed of three Intervals of fix,
fix, and eighteen Parts, namely, from the firft String to the fecond fix Parts, or one
Semitone, from the fecond to the third String, fix other Parts, and from the third Strinp-
to the fourth, an Interval of one Tone and an Half, or three Semitones. And in this
Manner the three Genera, and their refpective Colours, were divided.

Of the above fix Colours, which belong to the three Genera, only the Syntonum Diatonic
is the natural, which may be applied to the prefent natural Scale, in afcending and
defcending gradually, and by Skips, without any Alteration. The Toniamm Chromatic
may alfo be applied to the prefent Scale, with its third Minor, being compofed by three
Semitones ; but becaufe it is compofed of one undivided Interval of three Semitones, can
only afcend and defcend by Skips, but not gradually.

The other four Colours have all their Intervals unnatural, not only the lefTer, but alio
the greater ; it being impoflible to diftinguifh the Difference between a third Part and a
fourth Part of a Tone, by the common natural Senfatioh ; befides the Difficulty, or rather
Impracticability of a juft Intonation of thofe leifer Intervals, and alfo of the larger Intervals,
as the incompofite Intervals of nine, fifteen, twenty-one, and twenty-two twelfth Parts of
a Tone. Therefore it is natural to fuppofe, that the Chromatic, being applied to Tragic
Compofitions, as before faid, one of its Colours might be ufed to exprefs Pain, Cruelty, or
Rage, and the other to exprefs Grief, Horror, or Defpair j and the Enharmonic being
applied to Comedy, the Comedians might endeavour to ufe the Intervals defcribed in its
Colour. But we much queftion whether thofe Intervals were executed with an exact: and
juft Intonation, which feems impracticable, and think it more probable, that the Performers
of that Time, in their Manner of Singing in the Compafs of thefe Colours, did much the
fame Thing as is done at this prefent Time by fome Performers, who, to fhew their Ability,
afcend or defcend two or more Tones with their Voices, or Inftruments, by extremely fmall
and undiftinguifhable Intervals ; or, as it is done by fome Actors in the Comic Mufic, who
proceed with their Voices in Imitation of Laughing or Crying, or fome other charged
Expreflion.

This is in brief all which can be recovered of the ancient Greek Mufic, their Syftems,
Modes, and Genera, which can ferve no other Purpofe, but to gratify the Curiofity, being
all unneceffary to the Underftanding and Practice of the prefent Mufic.

In the above State and Condition, Mufic continued in Greece till it was fubdued and
conquered by the Romans •, and nearly in the fame Manner was the Art exercifed by the
Romans, without any remarkable Alteration, till the fourth Century, when the Emperor
Conjlantine the Great embraced the Chriftian Religion, in Confequence whereof Churches
were publickly opened for the Ufe of his Chriftian Subjects.

Not long after that Time St. Ambrofe, Bifhop of Milan, felected four Greek Modes,
namely the Doric, the Phrygian, the Lydian, and the Mixo Lydian, in order to apply
them to the Pfalms and Hymns of his Church of Milan : From whence afterwards Mufic
entered gradually, and was fpread into the other Churches.

In the fame Century, in the Time of Boetius, the Greek Letters which were before ufed in

the

THE INTRODUCTION. ir

the greateft or unchangeable Syftem, as it was called, were altered, and in their Place the
Letters of the Roman Alphabet were put, beginning with A, which was fet againft the
Note Prollabanomenos of the firft deep Note of that Syftem, and from thence proceeding
gradually, as far as the Letter P, which Letter was affigned to the Note Nete-hyperbolaeon, the
acuteft in the Syftem. But afterwards the Roman Letters were reftrained by Pope Gregory
the Great, to trie firft feven, A, B, C, D, E, F, G. After which the fame Letters
followed again, but in the fmall Character, to exprefs the next following Octave above;
and thus they left out all the other Letters from H to P, as ufelefs, and only tending to
Confuiion. The fecond Octave Acute was here confidered as only correfpondent to the firft.

This Pope added four others of the Greek Modes, to wit, the Hypo Doric, the Hypo
Phrygian, the Hypo Lydian, and the Hypomixo Lydian, to thofe four which had been chofen
by St. Ambrofe.

The four chofen by St. Ambrofe were named authentic, and prefelect ; and the four which
were added were called plagal, or fubfervient. And thefe eight Tones were united two by
two, one authentic, the other plagal, namely, the Doric with the Hypo Doric, the Phrygian
with the Hypo Phrygian, the Lydian with the Hypo Lydian, and the Mixo Lydian with the
Hypomixo Lydian.

Every two Modes thus united were reckoned as only one, the Doric and Hypo Doric,
called Protos, or firft, the Phyrgian and Hypo Phrygian, called Deuteros, or fecond, the
Lydian and Hypo Lydian, called Tritos, or third, and the Mixo Lydian and the Hypomixo
Lydian, called Tetartos, or fourth. But thofe Modes were afterwards feparated, and the
Authentic divided and diftinguilhed from the Plagal, in the following Order, namely, the firft
Authentic, the fecond Plagal, the third Authentic, the fourth Plagal, &c. the Authentic
being always placed the firft as prefelect, and the Plagal after, as fubfervient to the Authentic.
The Diapente being afiigned for the principal Form of the Mode, and the DiatefTaron for the
Difference, in a Manner, that when the DiatefTaron was found in the acute Part of the
Diapafon, as A, E, A, and the like, the Mode was authentic, and when the DiatefTaron
was in the lower, or grave Part of the Diapafon, as A, D, A, the Mode was plagal. And in
this Manner every Mode authentic and plagal had a Place in one of the ftven Species of the
Diapafon (which feven Species were reckoned beginning from A to A, B to B, and fo of the
reft, being in all feven Octaves) and when the Octave was divided geometrically, the Mode
was authentic, and when divided arithmetically, was plagal -, but the firft Chord was always
the grave Chord of the Diapente, to both the Authentic and the Plagal.

Guido Aretino, and his Followers, divided arithmetically only the firft, fecond, and third
Species, geometrically the fifth, fixth, and feventh, and the fourth Species arithmetically and
geometrically. But Henrico Glareano obferving, that every one of the feven Species of
Octave may be divided both arithmetically and geometrically, except the fecond Species,
beginning at the Chord Hypate, or B, and the fixth beginning at Paramefe, or F, B not
having its perfect Diapente, and F its perfect DiatefTaron, in the Diatonic Syftem, augmented
the Tones to twelve, beginning always at A.

Zarlino in the fame Manner divided the feveral Species into twelve ; but finding that
when the firft Species began in A, fome Notes of the Cant us Firmus, or plain Chant, were
not in their natural Situation, he, in his fecond Edition of his harmonic Inftitutions, began
the firft Species in C, following in that the Opinion of Ptolomy, according to which the
Order of the firft Species was Tone, Tone, and Semitone. But thefe Alterations were not
received by the principal Churches of Italy, ftill adhering to the eight Tones or Modes of
Guido Aretino ; and thofe eight Tones are called the Tones of the Church, under the Names
of Cantus Firmus, or Planus, and Cantus Gregorianus j and in the principal Churches of Italy,
particularly thofe in the Dutchy of Milan, which followed the Ambrojian Ritual, it never was,

nor

12 THE INTRODUCTION.

nor is now permitted, to the Precentors, or Mailers of the Choir, to tranfgrefs the' Order of
the Modes or Tones of Guido Aretino, in the Progreilion and Modulation of their
Compoiitions, in what is called Alia Breve for the Chapel.

This has been, and is now punctually obferved, out of Veneration for the two great
Perfbnages who firft introduced thofe Modes or Tones into the Church. However, it
occafioned amongft the Profeffors themfelves, a Confufion and Difference of Opinion, the
Rules being ill underftood, and never perfectly applicable to Harmony, which was not at all
tafted by the Greeks, or old Romans. And this Confufion arofe from mixing of the imperfect
Greek Modulations, as every one may difcern, by examining the above-mentioned Tones of
the Church, whofe middle and final Cadences are aim oft all imperfect and improper for true
harmonical Combination and Progreffion ; as may be feen in the Te Deum printed in the
Edition of the feven Greek Authors publifhed at Amjlerdam by Meibomius.

In the eleventh Century it may be faid, that the Art of Mufic entered from its Childhood
into Youth, under the Tuition and Direction of a Benedictine Monk, the aforementioned
Guido Aretino, fo named from being of the City of Arezzo, in c Tufca?iy.

He, in the firft Place, reformed the abovefaid greateft Syftem of the Greeks, as being
incongruous with Harmony, of which he feems to have been the firft that had any
Knowledge, and diftinguifhed it from Melody, as will be feen below.

The Order of the abovefaid greateft Syftem could ferve for no other Purpofe almoft, but
fimple Melody.

As to the firft Syftem of the feven Strings, or Tetrachord conjunct, it began with the
Chord Hypate (B of the prefent Syftem) diftant a Semitone from the next Chord lefs grave
Parhypate (now C.) This B could not fubfift either as a firft principal Note or Sound, or as a
Final, fince, being diftant a Semitone from its following Note, it could not be accented ; it
being neceflary to have the Accent fall upon a Note, between which and the next Note above
it there is an entire Tone. This any one may try by folfaing the Scale ; for he will find, that
Mi, which is a Semitone diftant from Fa, will naturally pafs to, and reft itfelf upon the
fame Fa, upon which Fa, as an accented Note, the Melody perfectly terminates. The
final Note can only happen to be Mi, as a fecondary Note in the harmonic fundamental
Combination, and by Way of Sufpenfion of the Harmony, as in a fufpended Cadence, but
never as a principal Note of Harmony. There muft be an Interval of a Semitone
between the principal Note of the Scale, and an Interval of a full Tone between
the principal Note of the Scale, and the next higher Note, it being neceffary for
the Melody to proceed by thefe two Intervals, to fall upon the principal Note of the Scale ;
as clearly appears in the Cadences in four Parts, where the Bafs defcends a Fifth, or afcends
a Fourth, the Mi Semitone, which makes the third to the Bafs, afcends to the Octave, and
the fuperior Part, which ferves as a perfect Fifth to the fame Bafs Note, defcends a full
Tone to the Octave of the Bafs, or may afcend to the third ; confequently the Note Hypate,
or B, diftant but a Semitone from its next Acute Note, can only ferve as a third Harmonic
to the fundamental Note ; and the next Note fuperior to this harmonic Third, muft have an
Interval of a full Tone between it and the Note next above it, which muft anfwer the
Purpofe of a perfect Fifth to the fundamental Bafs, in order that the faid Fifth and Third
may fall together, in Confonance, into the principal Note of the Octave.

Now the Syftem beginning with the Chord Proflambanomenos, the firft deep Note of
the greateft Syftem, fucceeds much worfe in refpect of Harmony. This Syftem being
far from the true natural Order, called by the Greeks the Diatonic, the Note Proflamba-
nomenos (which is A in the modern Scale) can be neither Principal nor Middle, neither
can it ferre as an Harmonic Note to the Principal, nor to its fundamental fifth Note, in
its firft Order of Combination. The principal Note of a Scale, which ferves as a Syftem, "

ought

THE INTRODUCTION. i 3

ought to be confidered as the Mother of all the Sounds attending it, they being all
included in it, and its confonant Octave above ; and the fifth, its intermediate Sound, being
confonant with the faid principal Note, is the Guide that directs the Progreffion, by
afcending or defcending a Fifth, and at laft conducts the Harmony to its Principal - t
as will be morefully explained in its Place, in the following Book.

A Scale of Sounds, which are not ftable, but fubject to vary, can never be a natural
Syftem of Sounds, which ought to be fixed and unalterable. The Chord Proilambanomenos,
or A, which ftands at the Head' of the faid greateft Syftem, has its third Sound naturally
fiat j and in defcending an Octave from A to A, the fixth and feventh are both naturally
flat ; but in afcending the fixth and feventh, muft both be altered a Semitone higher,
without which the Octave cannot be afcended gradually ; confequently here would be
required two Scales, one for afcending, and the other for defcending.

The Melody can very eafily defcend the Octave from A Acute to A below, by a natural,
or Diatonic Gradation, but then in afcending to the faid A Acute, you can never arrive
there, without changing the fixth and feventh Sounds a Semitone higher ; for the Diftance
between the feventh and Octave can never be more than a Semitone, in the natural Order.
Therefore a Scale, which has its third Sound diftant from the firft one Tone, and one
Semitone, that is a third Minor, cannot be the natural Scale, becaufe the fourth Note muft
have alio the Minor Third, which muft be altered in afcending the Scale. From hence it
is clear, that in the true natural Scale, the principal Note muft have its third Sound at the
Diftance of two Tones, that is of a greater Third ; from whence it follows, that the Sixth
comes to be a greater Sixth, which fixth Note ferves for a greater Third to the fourth Note,
which always has its third Note fimilar to that of the Principal ; that is greater, if it be
greater ; and lefs, if it be lefs. So likewife the feventh Note, which ferves for a greater, or
Major Third to the middle Note the Fifth, which is the fundamental Guide, ought to be
greater ; and in this Manner the Scale remains unalterable, and the principal Note of it
muft eafily be known ; for fince in the natural Scale there are only three Notes, which
have the greater Thirds, one of thefe three muft be the Principal; but then as the Principal
muft have not only the greater Third, but alfo the perfect Fourth, perfect Fifth, and
greater Seventh ; the Fourth, though it has a Major Third, perfect Fifth, and greater
Seventh, neverthelefs, as its Fourth is not juft, but falfe, cannot be a Principal.

In like Manner the fifth Note, though it has a Major Third, and perfect Fourth and
Fifth, yet, as the Seventh is Minor, it cannot be a principal Note of the Scale. From
whence it is evident, that the principal Note, of the natural Scale muft be the Note C, or
Parhypate ; and that the Greek Syftems, both the old one of feven Strings, and the greateft, or
immoveable, were ill difpofed, beginning with the Chord Hypate, or B, in the firft Syftem,
and the Chord Proflambanomenos, or A in the greateft Syftem.

It is manifeft, from what has been faid, that Guido Aretino had good Reafon for
reforming the ancient Syftem, by annexing a new Sound to the old deep one, which new
Sound he called Gamma (the prefent G) being diftant a Tone, in Depth, from the
Proflambanomenos of the ancient greateft Syftem.

He did not increafe the Number of Sounds, by adding the Note G, fof the Sake, as,
fome have imagined, of perpetuating by that Letter, his own Name, Guido, as the Inventor
of this Syftem ; neither did he do it, as others have more modeftly afferted, to preferve
the Memorial of the Commencement of Mufic in Greece. It was not owing to thefe
Caufes, we fay, but to pure Neceflity, which obliged him to put the Scale in fuch Order,
as would beft anfwer the Purpofe of Harmony j and if he began not the Scale by its true
principal Sound, which is C, it was probably owing to his Difinclination to change the
whole Order of Letters of the Alphabet, as eftablifhed by Pope Gregory, or perhaps to his
Veneration for him. However, beginning with the Letter G, he obtained the lower

E Octave

i 4 THE INTRODUCTION.

Octave of G, the middle Sound of the natural Scale, and the Guide of Progreffion in the
fame Scale ; and he obtained alfo along with it the Octave Sound of the feventh Note B,
which ferved him for a greater Third to the fame G j and by this Means the Harmonic
Order was preferved.

Quick not only mended the old greater Syftem, but he alfo introduced fix Monofyllables,
in order therewith to learn and practife the Art of Singing. Thefe Monofyllables were ut 5
re, mi, fa, fol, la, which, it is faid, he took from a Strophe, or Stanza, of a Latin Hymn,
written in Honour of St. John Baptiji, of which he chofe the firft and lixth Syllables of
>every Verfe, as is here feen.

at.

I — — 2

Ut queant Lais Refonare jibris,

Mira gefiorum Famuli tuorum
3 . 4-^-

Sohe polluti Labii reatum. .
5 _ f 6 —

Sancte Johannes.

It was abferved above, that the firft Letters of the Roman Alphabet were employed in
the ancient Syftem ; and that thofe were afterwards reftrained by Pope Gregory to the firft
•feven. Thefe ferved the Purpofe of learning to ling, by applying to its correfpondent Note
the Letter that denominated it. But Guido perhaps obferving, that thofe Letters exprefTed
the Progreffion of the Sounds in a very indiftincl: Manner, by Reafon, that in pronouncing
each Confonant, the Letter E is fubjoined thereto, as, BE, CE, DE, &c. at every Sound,
however different they were, nothing was heard but a Repetition of the fame Termination,
except when the Note fell upon the Letter A, and that this Uniformity, or Similiarity of
Terminations, could not but breed Confufion j and obferving, perhaps, in reciting the
Office employed on the Feftivalof St. John Baptiji, that the firft and fixth Syllable of the
firft Strophe of the above-mentioned Hymn, contained all the five Italian Vowels, he
thought proper to make Choice of them, and by their Means to render the Sounds more
diftinct in going through them with the Voice. But as the faid fix Monofyllables were
to be affigned to the eight Notes, or Sounds of the Scale, by which Means, in afcending
from the loweft to the higheft, two of them muft neceffarily be repeated.

• Therefore he diftinguifhed them by thefe different Stations, eveiy one containing a Scale
of fix gradual Sounds ; and he called thefe different Scales by the Greek Name Hexachord,
(that is, a Succeflion of fix Sounds) as -the Greeks called the different Partitions of their
Syftems in four Strings, or Sounds, Tetrachords, as mentioned before.

The firft Hexachord began with the Note Gamma, or G, comprehending G, A, B, C,
D, E, and this he called the Hexachord of B Durum, or B natural.

The fecond Hexachord began with the Note C, (being the fourth Note of his Syftem}
and comprehended C, D, E, F, G, A ; and this he called the natural Hexachord.

The third Hexachord began with the Note F, the feyenth Note in his Syftem, and
comprehended the Notes, F, G, A, Bb, C, D ; and this he called the Hexachord of B Mole,
foecaufe the fourth Note of the Scale muft be altered with a B Mole, or Flat.

For the better Diftinction of thefe Hexachords, he annexed to the Letters, which wers
already appropriated to the Notes of his Syftem, the fix different Monofyllables, which,
according to the Change of their Situation, they have in the three different Hexachords.

Thus to the Letter afcribed to the deepeft Note Gamma, he annexed ut t and called it
Gammut.

THE INTRODUCTION. 15

To the fecond Letter he annexed Re, and called it A re.

To the third Letter B, he annexed mi, and called it B mi.

To the fourth Note C, he annexed the Syllables Fa and ut, and called it C Fa ut,
namely, fa as the fourth Note belonging to the Hexachord of Gammut -, and ut as the firft
Note of the Hexachord of G.

To the following Note D, he annexed the Syllables Sol and Re, and called it D, Jbl,
re, namely, Sol as the fifth Note in the Hexachord of Gammut, and Re, as the fecond
Note of the Hexachord of C

To E, the next Letter, he annexed the Syllables La and Mi, and called it E la mi,
namely La, as the fixth and laft Note of the firft Hexachord G, and Mi as the third Note
-of the fecond Hexachord of C.

F, the following Letter in Acute, was called Fa, when confidered as the fourth Note of
the Hexachord of C, and ut as the firft Note of the third Hexachord F, and together was
named, F, fa, ut.

The next Letter G was called G, fol, re, ut. Sol as the fifth Note in the Hexachord
of C, Re, as the fecond Note in the Hexachord of F, and ut as the firft Note of its oWn
Hexachord, which is a Repetition of the firft Hexachord of Gammut, an Octave higher.

The next Letter A was named A, La, mi, re, namely La, as the fixth Note in the
fecond Hexachord of C, Mi as the third Note in the third Hexachord of F, and re as the
fecond Note in the fourth Hexachord G.

The following Letter B, was called B, fa, mi ; Mi as the third Note of the fourth
Hexachord G, which being a Repetition (as before faid) of the firft Hexachord Gammut,
is confequently of the B durum Clajfe ; and Fa, as it is the fourth Note in the Octave of
the third Hexachord F, which is in the Clafs of b Mole, becaufe the fame Letter B being
durum, or natural, would exceed, by a Semitone, the perfect and juft Fourth, in the
above Hexachord of F ; confequently B muft be diminifhed a Semitone with a b Mole
to make it a perfect Fourth ; as has been explained before, in the Defcription of the third
Tetrachord of the greateft Greek Syftem.

The other following Letters are named and difpofed in the Manner clearly defcribed in
the fixth and feventh Examples, Plates II. and III. both containing feven fucceflive
Hexachords. By the Means above-mentioned, the ancient greateft Syftem was augmented
with the Note Gamma in the Grave, and with five Notes more in Acute, as appears in
Plate III. Example VII. And this Augmentation was neceffary for the proper Diftribution
into the divers Scales belonging to the different Parts, Grave, Middle, and Acute, in
Harmonic Compofitions.

By the Help of the above Monofyllables, applied to the forementioned Hexachords,
Guido taught his Difciples to'ftudy and practife the Art of Singing. And, for a better
Help to the Memory, he difpofed the fame Hexachords, in their Order, upon the left
Hand, as is fhewn in the fixth Example, Plate II. above-mentioned, explaining the divers
Mutations in afcending and dcfcending the whole Scale. In afcending the Scale, the
deepeft Note Gama, or G, was called Ut ; A, the fecond Note, Re ; B, the third Note,
Mi; C, the fourth Note of the fame Hexachord of G, was called Fa ; D, the following
Note, Sol; and E, the laft Note of the fame Hexachord, La, when they proceeded na
higher ; but if they went on afcending to F, D was called Re, E mi, F Fa, G Sol, and
A La ; and, proceeding higher, G was called Re, A mi, B being flat Fa, C Sol, and D
La; but afcending to the next Note E, D was called Re, E Mi, F Fa, G Sol, and A

La;

*6 the introduction.

La ; and proceeding to the next Notes ftill more acute, A was called Re, B mi ; the reft
in the fame Order as above explained, changing the firft Hexachord into the fecond,
the fecond into the third, the third into the fourth, &c. and when thefe Hexachords, or
the whole Scale, is tranfpofed higher or lower, the general Rule is, that the Note which
is marked with a Diefis, or -Sharp, mull: be called Mi, the next below it Re,
-and the Note next above it Fa. On the contrary, when a Note is, contra marked with a
b Mole, or flat, that Note muft be called Fa, confequently the Note next below it Mi %
and the Note next above it Sol, in afcending the Scale by a fharp Third, and Re in
-afcending by a flat Third.

By the Help of the different Applications of the above Monofyllables to the Notes,
every one learned how to diftinguifh immediately the Scales, in all the Tranfpofitions that
might happen ; a Method of Practice which continues to this Day in Italy, under the
Name of Solfaing, and in fome other Countries, with fome Variation.

The Monofyllable Ut was afterwards changed into Do ; becaufe that in the Italiaii
Pronounciation, the Sound of the Vowel XJ is not thought fo pleafing and agreeable, nor
fo proper for Mufic.

Guido alfo changed the ancient Manner of writing Mufic. The Method before was to
ufe the Letters of the Alphabet, by which the feveral Notes of the Scale were diftinguifhed ;
and to write them all upon one Line, one after another, in Length, as mentioned by
Boetius. But Guido fubftituted in their Place certain Points difpofed upon, and between, four
Lines, and afterwards five, from whence came the Name of Counterpoint, in Compo-
sition of Mufic, and prefixed, at the Beginning of one of the Lines, one of the Letters,
by which all the Points upon and between every Line were regulated and afcertained.
For Example, the Letter C being placed at the Beginning of any Line, the Point upon
that Line was called and efteemed the Note C, the Point in the Space next it was D, the
Point on the next Line E j and fo the reft in Sequence. So in defcending, the firft
Point, or Note, in the Space next below the Line, marked with C, was B, that on the
Line next below A, and 20 from Space to Line, the others followed progreflively j and
when any other Letter was placed upon any of the Lines, the Point upon that Line was
the Note or Sound denominated by that Letter j and all the Points upon the Lines and
Spaces above and below were reckoned from the Line marked with the Letter, fo that,
from any Letter placed upon any Line, the Order of the Scale, both higher and lower, was
immediately known.

But the greateft Improvement which Guido made in the Science of Mufic, was the
Introduction of Harmony, by joining it to Melody, and forming therewith different
Compofitions of two, three, and four Parts. Thefe Parts confifted of different Notes,
varying in their Order, one amongft another, but united harmonioufly together, fo as to
afford infinite Pleafure to the Ear. This Harmony was as fimple as poflible, confifting
only of a Combination of the firft or principal Note, with its Third, Fifth, and Octave,
which he difpofed in the moft agreeable and harmonious Manner. Guido adapted this
Harmony to the Chants, or Tones of the Church.

He alfo published a Treatife of Mufic under the Title of Micrologus, with his Intro-
duBorium, and alfo an Antiphonaicum, for the Ufe of the Church -, for which Cardinal
Baronus, in his Annals, inferted the following remarkable Note.

His quoque pojlremis temporibus, fcilicet, BenediBi OBavi Papa, Guidus Aretinus Pro-

fejjione Monacus, Mujicus in/ignis innotuit, qui, maxima omnium ad?niratione, novam ad-

difcendt Muficam rationem invenit ; ita ut puer paucis meyifibus difceret, quod pluribus annis

-vix homo quilibet, pollens ingenio, ante capere potuiJJ'et, qua etiam de Gaufa Romam vccatus

eft ab epdem BenediBo Ponti-fice, poftea r oero 'Joanne vigejimo BcnediSli Succeffbre anno atatis

trigejimtk

THE INTRODUCTION. i 7

trigcfimo quarto^ edidit de Mufica Librum, quern Microhgum ?iuncupatum dedicavit Tbeobaldo
' Epifcopo Aretino.

All thefe Improvements, which Guido introduced, extending themfelves, by Degrees,
from Italy into the other Chriftian Kingdoms, and States of Europe, were generally received
by the whole Church ; and thus the Precentors, or Matters of the Choir, in every particular
Church, who before had only taught the Chant Choral, called Canity Firmus, or Gregorian
Chant, laid themfelves out to become Imitators of Guido ; and purfuing his Rules, to grow
even Compofers ; every one ftriving not only to join Parts, in an harmonical Way, to the
Cantus Firmus, or Gregorian Chant, but even to devife, and invent new Tones, or Specimens
of Melody: Infomuch, that by the Eafe and Facility of Solfaing, Melody itfelf made great
Advances, and became greatly varied from the ancient Greek and Roman Manner.

However, the Melody of this Age being compofed of Notes fo long, that one of them,
fometimes ferved for a whole Period, the new Improvements, which were daily making,
required" the breaking of thofe long Notes into fhorter Times and Meafures ; fo that the
original Notes and Points introduced by Guido, were daily found to be iniufficient for the

ti & r r • • i n- i . • i o •

rurpoie or writing and expreliing the new invented Strains.

To remedy this Defect, an Advocate of the Parliament of Paris, called 'John de Muris,
who was a Lover of Mufic, and flourimed in the fourteenth Century, invented certain new '
Notes or Characters, by which the different Lengths, or Times of Sounds, might be
commodioufly expreffed, which proved of great Advantage and Benefit towards the farther
Improvement of Melody.

Thefe Marks, or Characters of Mufic, were of different Figures, to denote the different
Length of the Time, and formed in the Manner defcribed in Plate IV. Example VIII.
Fig. i> 2^ 3, 4, 5, 6, 7, 8, 9, and 10.

The firft Characters, Figure 1, was called Maxima, and contained two Lqngs : The Long
(defcribed in the fecond Fig.) contained two Breves : The Breve (third Fig.) two Semi-
breves : The Semibreve (fourth Fig.) two Minims : The Minim (fifth Fig.) two Semi-
minims, or Crotchets : The Semi-minim (Fig. 6.) two Chromas or Quavers (Fig. 7.)
And in Procefs of Time the Semi-chroma, or Semi-quaver, two of which make one
Chroma, or Quaver ; and afterwards Bifchroma, or Hemifemi-quaver, two of which
make one Semi-chroma, or Semi-quaver, and a Note equal to half of the triple Bifchroma,
were added, as in the Fig. 8, 9, and io»

Under the above Notes are fhewn the correfpondent Marks, which ferve to indicate the
Times and Meafures which the particular Parts are to obferve, in retting or joining with
the others ; each of the Marks exprefling the fame Number of Meafures as its correfponding
Note, namely, the Note called Maxima, and its correfponding Reft, contain eight
Meafures : The Long in the fecond Fig. and its correfponding Reft, contain four Meafures :
The Breve two Meafures, the Semi-breve one Meafure ; the Minim half a Meafure ; the
Semi-minim a Quarter of a Meafure ; the Chroma half a Quarter ; eight Chromas, fixteen
Semi-chromas, and thirty-two Bifchromas being contained in one Meafure, as appears in ',
the Figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, Plate IV.

Now, by Means of thefe Meafures, the Time was divided into two, four, and eight
Parts : But then there being apparently an Occafion for a Meafure, which mould divide
the Time into three Parts ; therefore the Meafures were diftinguifhed into two Sorts ;
namely, of common Time and triple Time. In the common or ordinary Time, marked
as in Plate V. Example IX. each Meafure is divided into four Parts, except in the Alia Breve,
in which each Meafure, containing one Breve, is divided in two Parts: The fame for the
Time a Capella, or Chapel Time, which contains one Semi-breve, or two Minims.

F Befides

18 THE INTRODUCTION.

Befides thefe Marks, there have been added to the Character, that diffingu'imed the"
common Time, called the ordinary Time, the following other Marks, |, £-, $ y> reprefented
' in the above Plate V. Example IX.

The firfl containing two Semi-minims, or four Chromas , the fecond four Chromas, or
eight Semi chromas ; the third fix Semi-chromas, and the iaft twelve Semi-chromas.

In the triple Time the ancient Marks have been difcarded ; and at prefent there are
but three Sorts, whereof the firfl is h the fecond I, the third i, by which is meant, that
the fifft contains one Semi-breve, and one Minim, or three Minims ; the fecond three
Semi-minims, and the third three Chromas. There are in Ufe alfo other Signs, or
Figures, which partake, as it were, of both the common and triple Time : Thefe are
reprefented thus, |, f, and may be divided into three, and into two Times, which is to
be found by the Accent of the Notes in their Progreflion, The firfl Mark generally
ferves for triple Time, the fecond expreiTes rather common Time, to wit, when they are
Semichromas tied together by three ; for when they are all tied together* they appertain
to triple Time.

To thefe Notes alfo; when it was neceffary, was added a Point, which fignified, that
the Note to which the Point was added, was to be lengthened or increafed with half its
own Value j for Example, if to the Note called a Breve, a Point was added, it was to be
held out a Semi-breve longer ; and fo a Chroma with a Point obtained the Length of a
Chroma, and of a Semi-chroma j and fo of the reft. Under the Example of the above
Signs or Marks of the different Time, in the fame fifth Plate, are reprefented all the
different Notes, which belong to each of the fame Marks.

Monfieur de Muris changed alfo the Letters which Guido Aretino ufed to place at the
^Beginning of the Lines, whereon the Notes were written j and inflead of mem, he
invented three Signs, or Characters, which were placed in like Manner at the Beginning
of the five Lines. Thefe were of three different Forms, as may be feen in the fame fifth
Plate, Example X.

One was called the Key of F, and was to ferve for the Bafs ; the other the Key of C,
which ferved for the middle and higher Voices 5 and the third was called the Key of G, and
ferved for Inftruments of the highefl Sound.

The Key of F was differenced according to the two Lines whereon it was placed. If
that Key appeared on the fecond Line from the uppermoft, it ferved for the Bafs j but if it
Was found on the middle Line, it ferved for the Baffe called Baritone

The Key of C ferved for four middle and acute Voices. The firfl on the fecond Line
from the Top was the Key for the Tenor, which is the Voice next above the Baritono. If
the fame Key C was placed on the middle Line, it ferved for the Contralto or Counter-
tenor, which is next above the Tenor. But, if it was placed in the fourth Line from the
Top, it ferved for the fecond Soprano or Treble j and when placed on the lafl or lowed
Line, for the firfl Soprano or Treble.

The third Key was called the Key of G, which was for the ufe of the mofl acute
Inftruments, and was placed on the fourth Line from the Top and the lowefl Line.

Each of thefe Keys is diflant from the next Key to it a Third j and all of them, except
three, continue in Ufe to this Day.

The three that are in fome Meafure difufed are the Key of F on the middle Line, called
the Baritono j the^ Key of C on the lowefl Line but one, for the fecond Treble ; and the
Key of G upon the laft Line, for the Ufe of the moil acute Kind of Inftruments. Thefe

, \ have

THE INTRODUCTION, 19

have been difcarded ; becaufe the 6thers, which are retained, are fufficient for the Purpofe
of common Mufic in four, five, and fix Parts. But neverthelefs in the more folemn
Mufic of the Church, compofed for two and more Chorufles, in eight, and fifteen real
Parts, they are all frill made ufe of, and particularly for four Choruffes, where they are
heceifary for the commodious Diftribution of the Parts.

In the above fifth Plate, under the Example X, are expreffed the Marks of the Repeats,
Directs, &c. of which there is no need to enter into a diftinct Enumeration and Explanation
in this Place, the Infpection of the Example, where they are clearly reprefented, being
fufficient for the Information of every Reader.

After thefe Inventions of 'John de Maris, Mufic was daily improving, not only iri
Melody, but even in Harmony itfelf. And as divers Inftruments, the beft adapted to
Mufic, were now more commonly ufed than they had been, namely Harpfichords, Viols,
Violins, Tenors, and Bafs-Violins, &c. and as thefe derived from the Voice the fweeteft
and moil pathetic Melody, fo on the other Hand, the Voices acquired from them, as being
the moft ready and eafy in the Execution, the Diminutions of the different Notes, in Airs
and other quick and lively Movements ; inlbmuch that the Vocal Performers and Inftrumental,
.ftriving to outdo each other, they have by Degrees arrived at that Perfection, which at this
Day we have the Pleafure of hearing. The good Effect of this Emulation appears more
eminently in Inftrumental Performances. For Skill and Ability in Inftrumental Mufic
depends foiely uport Genius, and Inclination afiifted by Application, and intenfe Practice :
But to excel in Vocal Mufic, befides a natural Genius for Mufic, there muft be not only
Practice and Application, but alfo an admirable Voice, which is very uncommon. And
this we apprehend to be the Reafon that in this Age we find fo many more excellent
Inftrumental Performers, than we do Singers ; which neverthelefs is recdmpenced to us by
Nature herfelf ; fince, generally fpeakingj a moderate Singer always pleafes more, than the
beft Hand upon an Inftrument, the Voice being the beft Inftrument becaufe it is natural,
and confequently riio're pleafant than any artificial one whatfoever.

Moreover Harmony itfelf gained confiderable Advantages, by the Improvements iri
Melody. It was obferved, that in the Dimunition of Notes, Sounds were found out, which
contributed much to the pleafing of the Ear, and that many of thofe Dimunitions might
be performed upon a fimple Ground, not only in their proper Situation, but alfo out of it,
and even reverfed. For Example, it was perhaps obferved that the feventh of the fifth Note
of every Octave or Scale whatfoever, never failed to pleafe whenfoever it was properly
introduced ; and that not only when it was conbined with the fundamental Note, or
Ground in the Bafs, but alfo with the firft Natural, and fimple Chords of the principal
Note of the Scale ; infomuch, that if they were reverfed amongft themfelves, and even if
the fundamental Bafs was tranfpofed into the intermediate, or middle Sounds, they ftill
afforded a perfect Harmony, by being refolvcd into the following Sound. This feventh
Sound was therefore introduced ', and from thence there fprung the Chords of the greater
Fourth, the falfe Fifth, and the greater Sixth ; the Chord of the perfect Fourth and Sixths
which proceeds from the perfect Chords of the principal Note of the Scale, having before
been difcovered by Guido Aretino.

From the aforefaid Seventh of the fifth fundamental Note, they pafied afterwards to the
Sevenths of the other Sounds of the natural Scale ; which being firft introduced into the
Harmony, by the firft fimple Combination, which in the proper mufioal Term is called
Preparation, were alfo found to be pleafing to the Ear 5 by pafling into another fimple
Accord, called by Muficians, Refolution.

From the feventh they proceeded td the ninth Note of the principal Scale, or the Note
next above the Octave of the fame Principal : Though the Relation of the Ninth to the
Ground Note, was not perfectly underftood, becaufe few Compofers are practifed in Writing

20 THE INTRODUCTION.

in eight or more real Parts, but only in four or five Parts ; where the fundamental Ninth
paries under another Denomination, almoft continually ; and confequently has a different
Preparation and Refolution, becaufe the Bafs is not found in its true Place. Alfo finding
by the Example of the fundamental Sevenths, that even the Ninths (though under the
Name of a^Second, falfe Fifth, or Seventh diminifhed) became harmonical and pleafing,
they were admitted in Time into the harmonic Combination.

Now, by Means of thefe added Sounds, or Notes, which amongfl Muficians go by the
Name of Difcords prepared and refolved, Mufical Compofitions became, as they are at this
Day, the Subject of Study and Labour ; there being compofed Canons, Fugues, and
Imitations, fingle and double, of different Subjects united together, which conftitute the
rnoft agreeable Study, but require great Practice and Application.

From the Middle of the laft Century to the prefent Time, the harmonic Art has
arrived at its Ne plus ultra ; and the Method of forming a Compofition with an Union of
all the Eight primary Sounds of any Scale whatfoever, hath been found out, and is practifed
•in Italy in the grand and folemn Compofitions for the Church for eight real Voices, doubled
and trippled, in two diftindt Choruffes, without Inftruments, and for fixteen Parts alfo
doubled and trippled, in four feparate Choruffes, as ufed in the great Church of Milan*
■called the Domo.

The Rules for thofe Compofitions will be made very clear and intelligible by Means of
the Canons or Rules of the harmonic Code, in the fecond Book.

Thus we have given a fhort Hiftory of the Progrefs of Mufk, from the Time it was
firft introduced into Greece by their Poets, fo far as we think neceffary for the underftanding
of the different Terms, Modes, &c. gradually introduced and practifed from thence unto the
prefent Time j and to lead the Reader into the more ready Acquaintance with the enfuing
Treatife on the Harmonic Art.

DELL'

ARTE ARMONICA:

O R,

A Treatise of the Compofition of MUSIC.

BOOK I.

Containing the general and particular Definitions and Divisions of the
Whole Harmonic Art, the Modern Syftem of Sounds, with Two
New Syftems of Combination of Sounds, and their Progreflion,
formed by the Author.

To which are added,
All the SCALES arifing from the above SYSTEMS.

CHAP. I.

The Definition of Mufic in general, and its Divifions.

Article I.

)i^M^^j H E Word MUSIC has been applied to many and various Subjects ;
$df^%,®i. but, in this Treatife, it fignifies no more than a Succeflion of Sounds in
&U T |jl themfelves agreeable and properly expreffed, which alone, or differently
combined, in changing from low to high, or from flow to quick Movement,
or vice verfa, delights and gives Pleaiure ; confequently the Sounds are the
Matter of Mufic j the Difpolition of thofe Sounds, either alone, or combined
in a pleafing Succemon, is . the Art and the End to affect the Paflions with agreeable
Senfations, which become more or lefs fo, not only from the Degree of Perfection the
Art is arrived at, but alfo from the different Conftitutions and Habits of the Auditors, as
remarked in the Introduction.

G Of

22 Of the Composition c/ MUSIC.

Of the Divifion of Mufic.

Article II.

"VXT E mail firft divide Mufic into Melody and Harmony, and this regards in general every
yV Species of it. Afterwards we fhall diftinguifh it into Vocal, Inftrumental, and Local,
from being ufed in the Church, Theatre, Chamber, &c. every one of thefe havino- fome
particular Rules, over and above the common Rules relative to Harmony, which particular
Rules will be explained in the laft Book.

Of Melody and its Divifion.
Article III.

T? VERY Tone, Air, or Song, formed by Progreflion of different Sounds, but following
**4 alone one after another, or by two or more finging the fame Sound, is called Melody.
This may be divided into Natural and Artificial, but both are the Daughters of Nature.

The Natural is deprived of every Ornament, and is not fubject to any Rules, bein<*
prac~tifed by People ignorant of Mufic.

The Artificial, on the contrary, is improved and adorned by the Harmonic Art, to which
it is made a Companion, proceeding together by fixed Rules, excepting where Invention is
concerned, which depends almoft entirely upon Nature.

Of Harmony,
Article IV.

Hp H E Antient Writers of Mufic, as many Moderns, call the different Ratios of the
■*■ fuppofed Intervals of the Sounds, by the Word Harmony. So Euclides in his
Introduction to the Harmonic Art ; the fame by Gaudentius the Philofopher, as by Nicomacm
the Scholar of Pythagoras. Ptolomy defines the Harmony, a Knowledge of the Difference
of the Sounds in regard to their Acutenefs or Gravity : The fame by Zerli?io in his
Institutions and Demonstrations Harmonic j alfo Huygens calls his Cyclo Harmonic in his
Cofmotheoros, Dechales, Cotas, JVallis, Malcombe, and of late Mr. Eular in his Tentatem
. Nove Theorie Mufice ; fo Dr. Smith, Head of Trinity-College, Cambridge, in his learned Book
intitled, The Harmonic. All, and many others, have ufed the Word Harmony to be
applied to the Ratios of the above fuppofed Interval betwixt the- different Sounds. But in
this Treatife, where the Sounds are not confidered in the Ratios of their fuppofed Intervals,
but only in the immediate Effect, which alone, or combined in their Progreflion, produce
into the Senfation ; we fhall define, that Harmony is a Product of the Progreflion of two,
three, or more different or diflbnant Sounds (distinctly perceived by the Senfation) joined
together and artificially combined. We fay, a Progreflion of different and diflbnant Sounds
together combined, becaufe a Ample Combination of Sound, without Progreflion, cannot
be called a compleat Harmony, being no more than a Beginning of Harmony, which
fignifies nothing, as a fimple Word is not a Difcourfe, or an Oration, but only a Part.

Of the Divifion of Hannony,

Article V.

TTARMONY mull be divided into Fundamental and Figurate, both Daughters of the
•" Art : The Fundamental is the only practical Theory of the Harmonic Art ; it is

diftinguifhed

Of the Composition c/ MUSIC. 23

diftinguifhed from all other Mufical Compofitions by the Name of fundamental Counter-
point, which is fo called from Points, inftead of Notes, being applied ; and fundamental,
becaufe properly it is the Foundation of the Harmony ; as the Bafs Part, which is the
lowed of all the other Parts, is alfo called fundamental, for being the Harmony regulated
by its different Motions. By this fundamental Counterpoint are compofed feveral Examples,
which We call Canons, into and by which are defcribed and explained all the Laws or
Rules of the Harmonic Art, or of Compofition of Mufic, all ordinarily joined in one
Harmonic Code, which will be explained in the next Book.

The fio-urate Harmony is ufually called by the Muficians the figurate Mufic, becaufe it
is formed with divers Figures, Movements, and Times, at Pleafure -, but it is ftill fubject to
the Laws and Rules which will be laid down in the Harmonic Code of the fundamental
Harmony. The figurate Harmony may be a Compofition of two, three, four Parts, and
as far as fixteen, and more real Parts joined together with Melody. The Explanation of
this figurate Mufic, with its Divifions, and its Relations to the fundamental Harmony, will
be made after we have digefted the Harmonic Laws, or Rules, prefcribed by the
Harmonic Code, in the next Book.

C H A P II.

Gf the Mufical Sounds, their Definition, Number, and

different Intervals,

The Definition.

Article I.

IT belongs to Phyfic to define and explain the Nature of Sound in what Manner it
is produced and propagated, and alfo what Bodies are moft fit to produce it, and
into how many Species it is to be divided, with the Properties of every one. But
Mufical Sounds, which are occafioned by the human Voice, or Inftruments proper for
Mufic, muft be fweet and equal in all the Degree of Acutenefs, or Gravity, and
confeq,uently pleafant in themfelves ; it being evident, that a bad, unequal, and ill-difpofed
Voice, like a bad Fiddle, or all other Inftruments ill-tuned, or played, cannot afford any
Pleafure, which is the very End and Defign of Mufic.

Of the Number of Mufical Sounds.

Article II.

'TpHERE are no more than eight original Sounds in Mufic ; but thefe Sounds may
* be tranfpofed more acute, or more grave, ftill retaining the fame Number and
Order j and tho' the Intervals may be infinitely divided, fo as to comprehend all pofiible
Sound, yet the Octave of every Divifion will have a fimilar Sound, either grave or acute,
and by Octaves may be multiplied at Pleafure, as was mentioned in the Introduction.

Of the different Intervals of the eight original Sounds.

Article III.

*T^HE original eight Sounds proceed from the Grave to the Acute, and vice verja,
•* by two different Intervals. It was taken Notice in the Introduction, that the Greeks

diftinguifhed

24 Of the Composition c/ MUSIC.

diftinguifhed the Intervals of the Sounds of the firft Diatonic Syftem of the Tetrachord

conjoined, by the Names of Tone Major, Tone Minor, and Semitone : Afterwards in

their Syftem called the greate'ft and unchangeable, they were obliged to divide the

Interval of the Major Tone, between the Chords Mefe and Paramefe (that is, A, B, in

the modern Syftem) in order to add a new Sound, which was called Trite Synemmenon

(now called B flat) this new Sound was the firft Note of the third Tetrachord, which was

•added conjoint to the two "firft ; by this Addition was fuppofed, that the Intervals of the

fame third Tetrachord arofe in the fame Order as in the firft and fecond, beginning with

a Semitone : From the above Divifion has arifen the fuppofed Difference of the Semitone

in Major and Minor, confiding of one Comma, to wit, the Major Semitone five Commas,

and the Minor four; as from the Chord Mefe, or A, to the added Chord Trite

Synemmenon, or B flat, five Commas, and from the fame Trite Synemmenon to

Paramefe, or B natural, four Commas j fo from Paramefe to the Chord Trite

Diezeugmenon, or C, five Commas, confequently a Major Tone from Trite Synemmenon,

to Trite Diezeugmenon, which Difference in Major and Minor was not confidered by

the Pythagorea?7S, nor by the Follower of Arijloxenus ; the Pythagoreans confidering

all the Tones of the greateft Syftem, as Major of nine Commas, and the Semitones all

of four Commas, which makes the Pythagorean Lima, as has been told in the

Introduction, and the Followers of Arijioxenus, by which were calculated the Tones in

twelve Parts, and the Emitones, or Semitones, in fix Parts, confequently all equal, and is

more than probable, that the above Difference in Major and Minor Tones, and Semitones,

was never confidered in Practice. The above greateft, and unchangeable Syftem, was

divided into Semitones by Arijioxenus, which certainly is the beft of the Greeks who have

wrote in Mufical Matters, and in that Manner he diftinguifhed his fifteen Modes by the

Diateffaron, or perfect Fourth, which is formed by equal Semitones, as" has been feen in

his Diagrama, Example V. Plate I. mentioned in the Introduction. If thefe Semitones

had been fuppofed not equal, the DiatefTarons , by which the fame fifteen Modes were

compofed, , fhould have been partly imperfect, being evident, that the Minor Tones being

divided into two Minor Semitones, and the Major Tones in one Major, and one Minor

Semitone, confequently fome of the fame Diateffaron muft be formed by different

Semitones, in regard to their Latitude. But after the happy Invention of Harmony, and

the great Progrefs which Mufic has made, particularly from the laft Century to this Day,

it is now evident, and clearly demonstrated by Experience (as will appear in the

following Books) that the Divifion of the Tones and Semitones into Major and Minor,

is inconfiftent both with Melody and Harmony, and never fubfifted, but only in the

Imagination of the Authors, which followed the firft Divifion of the old Greek Syftem

of the firft four Strings of the Lyre, and fucceflively of the feven Chords, called the

conjoint Tetrachord, as has been done by Ptolomy, followed by Boetius, and by almoft

all the Authors which have treated of Mufic, till the prefent Time. But now in the

prefent practical Syftem of the Mufical Sounds, all Sounds are divided by two Intervals,

to wit , by equal Tones, and equal Semitones, thefe confidered as an half Part of the,

Tone ; and the Tones being all divided into Semitones for Sake of the Tranfpofition of

the two principal Scales, confequently the original eight Sounds are augmented to the

Number of thirteen Sounds, divided by twelve Intervals of a Semitone each, as will

appear in the following Chapter.

CHAP.

0/ //;f Composition «/ MUSIC, 2 r

CHAP. III.

Of the new Modern and General Syftem of Sounds^ and of
the Names of its different Intervals. .

Article I.

$^RQ T is called a general Syftem, becaufe it comprehends all other Syftems, Scales,
«3) J (3 and Divifions ; it is alfo called the new Modern Syftem, to diftinguifh it from that
h£££&Z of Guido, which was called the Modern Syftem, but now is called the old Modern
Syftem of Guido : This new Modern Syftem is exprefled in Example I. Plate VI.

The firft loweft Sound of this Syftem is C, which might properly be called A, being
the firft Letter of the Alphabet, as the Romans have already done to the firft Sound of the
Greek Syftem : But as this Alteration would have changed all the old Notes or Letters applied
to thefe Sounds in the Time of Boetius, and afterwards reftrained by Pope Gregory (as
mentioned in the Introduction) it has not been made either by Guido t or in the prefent
new Syftem; only the Order is different, by beginning with the Sound named C, inftead
of the Sound named A, as the Romans have done, or with the Sound G, as Guido.

From the Principal and loweft Note named C, to the Sound D, its following Note, is
-an Interval of one Tone ; alio from D to E, is a like Interval j but from E to F, there
is only a Semitone s from F to G, the fifth Sound, from G to A, the fixth, and from
A to B, the Seventh, is an Interval of a Tone each ; and from B to C the eighth Sound,
which is the Octave of the firft principal Grave Sound of the Syftem, is the Diftance of a
Semitone. This Syftem being formed of five Tones and two Semitones, as is exprelTed
in the firft Example, Plate VI. above-mentioned.

Of the various Names to the different Intervals of the above Syftem.

Article II.

TH'E two Sounds, which are formed by the Interval of one Tone, is called a Major,

or natural Second, as C,D. D,E. F,G. G,A. and A,B. as to £,F. and B,C.
which are only diftant a Semitone ; this Interval is called a Minor Second ; the Whole
of the Octave being compofed of five natural Seconds and two Minor, which is the fame
as five Tones and two Semitones, mentioned in the laft Article : Two Semitones making
a Tone j fo two Minor Seconds make a natural or Major Second.

T T
Two major Seconds following each other, as C, D, E. make an Interval called the

3 Maj.

natural Sharp, or major Third C,E,

The Flat or Minor Third, is formed of one fecond Major and one Minor, as

Mfij. 1, 2 Min. Min. 1. 2 Maj. » Min,^ Min. 3?

D, E, F, or E, F, G, making the Flat Natural, or Minor Third D, F, or E, G, or
ethers like.

The fourth Sound F, being diftant from the Principal C, two Major Seconds and
one Minor, or two Tones and one Semitone, is called the perfect Fourth, as being
confonant with the Octave of the principal Note.

H f he

£6 £>/ the Composition t>f MUSIC.

The (harp or falfe Fourth, is compofed of three Major Seconds, which is three Tones,
is F to B, and are alfo called by Muficians, the Tritone.

Two Major Seconds* and two Minor, is the Interval called falfe or lefTer Fifth, which
Is the fame as two Tones and two Semitones, or as the Tritone, as from B afcending to F.

The Interval of three Major Seconds and one Minor, or three Tones and one Semitone,
as from the principal Note C to the fifth Note G, or from D to A, whatfoever other
Sounds of a like Interval is called the perfect Fifth, which is confonant with its grave
Sound, as has been explained in the Introduction.

The Interval from C to A, which is the fixth Sound of the Syftem, or other like
Interval, being formed by four Major Seconds and one Minor, or four Tones and one
Semitone, is called the Major Sixth*

The Minor Sixth is compofed with three Major Seconds and two Minor, or three Tones
and two Semitones, as from E to C afcending, or other like Interval.

The feventh Sound in this Syftem is B, which being diftant from the Principal C five
Major Seconds and one Minor, or five Tones and one Semitone, therefore is called Major
Or fharp Seventh, as all other like Intervals.

It is called Minor Seventh, when formed by four Major Seconds and two Minor, or four
Tones and two Semitones, as from D afcending to the C acute, or from the fifth Note
G to F, above the Octave, or other like Interval.

The laft Sound of this Syftem is the Eighth, which is called the Octave, and is the
principal perfect Confonant after the Unifon j it is compofed by five Major Seconds and
two Minor, or five Tones and two Semitones. All the abovefaid Intervals are within the
Compafs of the Octave.

But there are fome larger Intervals, which partes the Limits of the Octave j the firft Two
are called the Major and Minor Ninth ; the Major is compofed of fix Major Seconds and
two Minor, or fix Tones and two Semitones, as from D grave to E acute in the fuperior
Octave j the Minor is compofed with five Major Seconds and three Minor, or five Tones
and three Semitones, as from E grave to F acute of the fecond Octave.

The other fuperior Intervals of the following fuperior Octave, as the tenth, the eleventh,
twelfth, thirteenth, fourteenth, and fifteenth, are confidered as being the Repetition of
the third, fourth, fifth, fixth, feventh, and eighth ; and fometime both Ninths are confidered
as Seconds in the Compofitions of Figurate Mufic; but in the fundamental Harmony
they are calculated at thefe proper Diftances of ninth, tenth, eleventh, &c. and is only for
the greater Facility of putting the fimple Figures of the Sounds belonging to the firft Octave,
inftead of the double Ones.

Firjl N.B. Befldes the above explained Intervals, there are fome others, as the fecond
fuperfluous or extreme Sharp j the fuperrluous Fifth, Sixth, and Octave j alfo the Seventh
diminished, which not being concerned in the fundamental Harmony, will be explained in
the laft Book of the figurate Harmony, being all thefe Sort of Combinations inverted of the
fundamental.

Second N.B. The falfe Fifth before-mentioned, is the fame Interval as the falfe Fourth ;
the Difference is only for the Sake of the Names. B, in afcending to F, muft pafs C,D,E.
which in all are five primary Sounds, namely B, C, D, E, F. which are the proper
affigned Names to their refpective Sounds -, and from F afcending to B, are only four primary

Sounds,

0/ ^ Composition c/ MUSIC. 27

Sounds, with thefe proper Names, F, G, A, B ; one is called falfe Fifth, being a
Semitone leffer than the perfect Fifth ; and the other is called falfe, or Major Fourth,
being compofed of one Semitone more than the perfect: Fourth j but both the faid Sounds
are in the fame Diftance of fix Semitones, or three Tones, which is the fame, as it is
evident, confequently the Sounds, being in the fame Interval^ the Difference is only in
being tranfpofed, the Grave in Acute, or vice verfa ; but their Progreffion is always the
fame, afcending one, and defcending the other,

Third N. B. All the above Intervals muft be diftinguifhed into confonant and diffonant :
The Confonant are all theUnifons, Octaves, and perfect Fifths, as has been explained by
Experience, in the Introduction! and all the other Intervals, as fecond, third, fourth,
falfe fifth, fixth, feventh, Major and Minor, are diffonant, confequently cannot be called
confonant, but only Harmonic j the Firft as confonant, being confidered as one Sound,
cannot be called Harmonic, but only Melodic, and the diffonant, fo called, being diftinctly
perceived by the Ears, when joined with the Confonant, made Harmonic the fame
Confonant, as will clearly be explained in the Fifth Chapter of the Harmonic Syftem.

Fourth N.B. The abovefaid diffonant, or Harmonic Sounds, muft be confidered
diftinctly, as Major, or (harp, and Minor, or flat, being their natural Progreffion different,
the Major afcending, and the Minor defcending ; but this Rule is altered on divers
Occafions, as will appear by the Canons in the next Book.

CHAP, IV.

Of the Confonant Divifion of the Syftem of Sounds, from which
arifes the Confonant Syftem of Progreflion, or Modulation.

Article L

[T was defined in the firft Chapter, Article IV. that Harmony confifts in a
1 H Progreffion of diffimilar and diffonant Sounds combined together. Thefe diffimilar
?§3Sl and diffonant Sounds are diftinguifhed into Loweft, Low, Middle, Acute, and
very Acute. The loweft Sound, which now becomes the Subject of this Article, is called
the fundamental Bafs, which is always fuppofed to be lower by one Octave, than the
common Bafs of the figurate Harmony j and by being founded fo low, can only proceed
by large and proportionate Intervals : Experience (hews, that the Trumpets and French-
borns, in the loweft Notes, can only proceed by Fifths or Fourths, whereas in the high
Notes they may poceed not only by Tones} but alfo by Semitones ; the fame muft be
fuppofed in the fundamental Bafs : Its moft natural Progreffion is to rife or fall a Fifth, or a
Fourth, which produce the fame j rifing a Fifth, is the fame as falling a Fourth, and
rifing a Fourth, is the fame as falling a Fifth, as will be demonftrated in its proper Place,
with Examples*

Thefe two Movements, of Fifth defcending, and of Fifth afcending, arife from the
confonant Divifion of the general Syftem of Sounds, by Means. of the two middle Sounds,
which divide the Syftem in two equal Parts, as in Example II. Plate VI. namely, C,
principal Sound to F, middle Sound; andG, alfo middle Sound to C Acute, the Octave of the

1 2
Principal being both Parts compofed of two Tones in the Grave, C, D ; E, and a

"£* k 'T ; *± X

Semitone in Acute, E, F ; alfo G, A, B, two Tones, and B, C, the Acute Semitone,
making every one of the two faid Parts an Interval of a perfect Fourth ; and G Bafis of

the

s8 0/ A Composition c; M U S I C.

the Acute Fourth, forming the .perfect confonant Fifth to C principal Bads of the firft
Part ; fo C the Octave, at the Top of the fecond Part, makes the confonant Fifth to F
middle Sound, at the Top of the firft Part, or Divifion.

From this Divifion arifes our two fundamental Syftems, General and Natural ; the
general paffing through all the Semitones of the Scales of Tranfpofition, and the natural
'through the eight original Sounds of the natural Scale. Thefe two Syftemsof Progremon
are alio called Confonant Syftems, being formed by the two Confonant Fifths afcending
and defcending, or by the Fourths, which are the Inverfion as before mentioned.

The firft of the above two Syftems which is defcribed in Plate VII. is called general,
becaufe proceeding in its Courfe continually by perfect: Fifths, it divides the Octave in all the
Mufical Sounds which ferve to Harmony, being thirteen Sounds, divided by twelve
fuppofed Intervals. The other, which is alfo defcribed in Plate VIII. is called the natural,
becaufe its Progreffion proceeds only on the eight Primary Sounds of the natural Scale,
and in that Progreffion mull be ufed one falfe Fifth, as will be explained in its proper Place.-

The abovefaid four Notes, from which arifes their Thirds naturally fharp, are diftinguilhed
frorfr the reft of the Notes of the Octave, and commonly called the four principal Notes
thereof; but in Reality only the firft Note and the fifth are the two principal and
fundamental Notes, becaufe the firft principal Grave Sound C, is the Produdfor of all the
Sounds, in its Octave, and the fifth Sound G is the only Confonant to the principal C,
iind the fame G becomes the neceffary Guide of the Harmony in the Progreffion, fo, as
by proceeding only by Skips of Fifths above or below, the Harmony pailes fucceffively,
not only the Primary Sounds of the natural Scale, but alfo thefe divided by Semitones,
as before faid, as will be demonflrated in its proper Place. J

The faid fifth Sound of the Octave is called the fandamental Guide, becaufe after having
introduced the Combinations of Sounds into the different Tones and Semitones of the
Scale, it reftores the fame Sounds, and their Combinations, to the firft principal Note of
the Scale. But in regard to the Interval of the fecond Fifth, between the other two
Notes, F and C, the firft Note F indeed is confonant with the Octave C Acute, which is its
Fifth, but it is not confonant with the Confonant Grave C, being only diftant an Interval
of a Fourth, which Experience fhews, that it is not confonant, but diffonant, and
confequently only Harmonic, as explained before. The Octave indeed is confidered in
Harmony as the fame Sound of the principal ; and this Reafon may affect both the- fourth
and the fifth, becaufe they are neither of them confonant with both the Extremes of
the Octave , but as the fifth C is confonant with C Grave the Principal, and the Octave
C Acute is abforbed by the fame Grave Sound C, being evident (as has been demonstrated
by Experience in the Introduction) that the Grave Sound abforbs all its Acute Confonant
Sounds, confequently the Diftance, or Interval of one Fourth from G to C Acute,
fubfifting, the Grave Sound C is not perceived, and for the fame Reafon the Confonant
Fifth between F and the Octave C Acute, fubfifting, its principal C Grave is not
perceived, but only the Interval of one Fourth, which is not confonant : For this Reafoa
-only the Fifth is the Confonant Sound with its Grave and Principal.

Thefe two principal and fundamental Sounds, the Principal and its Fifth, muft be
'confidered as the original and firft Foundation of all the Combinations and Progreflions
of the Sounds in their own Scale ; and may both be ufed in Melody and Harmony,
without changing their Place, as it is ufed by the Bagpipe, which keeps continually
playing the principal Note, as the Foundation of Melody j and the confonant Fifth,
which is the fundamental Guide of the Sounds of its own Scale, may alfo continually
ferve for a ftable Foundation under all Combinations and Progreflions which can be formed
in its Scale ; as is commonly ufed in Cadences, particularly in Church-Mufic, in the laft
and final Cadence, when the Pedal of the Organ being ufed upon that Occafion, which

Of the Composition of MUSIC, 29

is played with the Foot in one of the lowefl fundamental fifth Sounds of the Organ, it is
always kept firm under the Harmonic Progreflion of the Subject Melody, or Fugue,
propofed in the Beginning, and repeated, as Epilogue, before the final Cadence, with both
the Hands employed in the Harmonic Combinations and Progreflions of the faid Subject,
till at lafl it refolves into the Cadence. Therefore the above two Sounds, Principle and
Guide, are called the two original, and flable, or immoveable fundamental Sounds,
being diflinguifhed by this Name from the other two fundamental BafTes deriving from the
Motion of the fifth high and low, which BafTes are called the fundamental BafTes of the
Progreflion of Harmony.

The two firfl immoveable, and the two lafl moveable BafTes, are called fundamental.
The two firfl continually founding the fame Note, without any Regard to the Progreflion,
and Combination of the fuperior Parts in the Courfe of the Octave : On the contrary, the
other two follows the Harmony, conforming to the Rules of the fundamental Progreflion ;
therefore thefe two lafl BafTes are the principal Object of this prefent Syflem of Progreflion,
or Modulation.

The two firfl Intervals in the fuperior Divifion of Example II, Plate VI. the firfl from
the extreme Grave Sound C, to its fifth G, and middle Sound of the Syflem ; and from F,
alfo middle Sound to C extreme Acute, both being of a perfect Fifth afcending, we call
them the indeterminate imperfect Skips confonant of the Guide, namely, from the
Principal, or from a Guide to another Guide, it is called indeterminate, becaufe by thefe
Skips the Harmony cannot be terminated, except in fome Inflances, for the Sake of
Expreflion ; and it is alfo called imperfect, becaufe from thefe Skips arife all the imperfect
Irregulars, and fufpended Cadences, with other Imperfections, which will be demonflrated in
the next Book. On the contrary, the other two Skips, as in the under Divifion of the
fame Example II. Plate VI. from C above, to F below middle Sound, and from G alfo
middle Sound, to C Grave below, both defcending with a perfect Fifth : Thefe, and all
other of the fame Kind, we call them the terminate, perfect, confonant Skips of Cadences,
that is from the Guide to the Principal, becaufe from thefe Sort of Skips arife all perfect,
middle, and final Cadences, by which the Harmony is terminated, and it is called perfect,
becaufe it may be joined with the following Thirds to the Fifth ; namely, the Seven and
Nine, as will be explained in the next Book : But it mufl be diflinguifhed, that when
the Combination of the lafl Note is compounded, the Cadence is not terminated, becaufe
thofe abovefaid fuperior Third, which mufl be prepared in the antecedent Combination,
wanted after to be refolved, and for that Reafon the lafl Note of the perfect terminate
Cadence, mufl be of fimple Harmony, and not at all compounded by higher Thirds than
the two which compofe the Fifth, as will be demonflrated in the next Book.

Firji N. B. The fundamental Bafs, proceeding by the imperfect confonant Skips of
Guide, rifes continually, paffing through all the Sounds of the Octave 5 on the contrary,
with the perfect confonant Skip of Cadence, it falls continually, paffing alfo all the Sounds
of the Octave, as it is delineated in Example III. Plate VI.

Second N. B. It mufl be remembered, that when the Bafs afcends a Fifth, it is the
fame as defcending a Fourth ; alfo defcending a Fifth, is the fame as afcending a Fourth,
as before-mentioned ; the fame is afcending a Third as defcending a Sixth, and defcending
a Third, as afcending a Sixth, as in Example IV. Plate VI.

Of two Harmonic Movements added to the two Confonant.

Article II.

*"TpO the above two confonant Movements, have been added two other Harmonic

A Movements, viz. of a Third low, and the other of a Third high : Thefe two

Movejnents, or Skips, are not abfolutely fundamental, the firfl of Third low deriving

I from

30 Of the Composition p/ MUSIC.

from the perfect confonant Skip of Cadence, and the other of a Third high, from the
imperfect Skip confonant of Guide, both ferving as Auxiliaries to the other two
fundamental ; therefore we call the firft defcending a Third, the perfect auxiliar Harmonic
Skip of a Third low; and the other afcending a Third high, the imperfect auxiliar Harmonic
Skip of a Third high j they are both called Harmonic, being derived from the Motion of
the Third, which is Harmonic, and not confonant, as will appear in the next Chapter : but
the firft Skip of a Third low is diftinguifhed by the Term perfect, as deriving from the
perfect Confonant Skip of Cadence, partaking of its Perfection. The other, on the
contrary, is called imperfect, deriving from the imperfect confonant Skip of Guide, and
alfo partaking of its Imperfections, as will clearly be demonftrated in the next Book.

With the two confonant Skips, and their two Auxiliars, the fundamental Bafs is able
to perform all pofiible Harmonic Progreflion ; therefore we call it the true fundamental
Syftem of the faid Harmonic Progreflion.

Of the Divifion of the fundamental Progreffion arifing from the above Syftem.

Article III.

^p HE different Scales which arife from the feven Primary Sounds, excluding the
* Octave, as a Repetition of the firft Sound, were diftinguifhed by fome Greeks, and by
all the old Romans, as alfo by Guido and his Followers, in feven Species, which is the
fame as to fay feven Octaves : The Difference of the feven Species was made by the
different Situation of the Semitones, without any other Diftinction j and the pafling from
one Species to another, was called Modulation, as the Greeks have called the pafling from
a Mode to another. This Word Modulation has continued, and ftill is continued by
Mufkians; but in this Treatife it is called by the common Name Progreflion, which
fignifies in Melody the moving from one Sound to another, and in Harmony, from many
divers Sounds combined, to another different Combination, proceeding from one Place to
another, in tranfpofing the Scales, which Term Progreflion may be eafily underftood by
all Sorts of People ; with this Progreflion is formed all Sorts of Mufic.

This Progreflion is made in two different Manners, therefore we fhall diftinguifh them
in natural or fimple, and in mix'd or varied ; the natural or fimple Progreflion, is only
formed in the natural Scale, pafling through its relative, and fubordinate Scales, without
changing the original Primary Sounds j and this Progreflion arifes from the above-
mentioned natural Syftem of Progreflion, as from the general Syftem of Progreflion arife
the Progreflion which we call mix'd or varied, becaufe it tranfpofes the Scales in every
one of the Semitones, which divides the Primary Sounds, and by this Tranfpofition is
changed and altered the firft Order of the Sounds, as will be clearly explained in the
Articles of the particular different Scales.

Firft N. B. The general Syftem of Progreflion before-mentioned, is formed by
thirteen Scales, every one of which proceed by perfect Fifths defcending or afcending ; and
in this Manner all the faid Scales are divided into thirteen Sounds by twelve Intervals of
an equal Semitone, by the Progreflion of a perfect Fifth, and all the Sounds of a different
Denomination formed by the two Motions of the Fifth, are diftinguifhed as is clearly
exprefled in Plate VII.

Second N.B. The other natural Syftem of Progreflion is formed by eight Scales, which
ferves to every one of the primary and original Sounds, all proceeding alfo by Fifths
afcending and defcending j but becaufe between the eight Primary Sounds, two of the
fame are only in Diftance of a Semitone, when the others are of a full Tone, as has
been feen in the general Syftem of Sounds ; therefore, when the fundamental Bafs moves
from the fecond Semitone B, cannot proceed with a perfect Fifth, which in afcending is
F fharp, which Note or Sound is not in the natural Scale, confequently muft neceflarily

proceed

Of the Composition «/ MUSIC. 31

proceed with a falfe Fifth to F natural. The fame in defcending with the fame Motion
of a perfect Fifth, the Bafs muft alfo necefTarily proceed with a falfe Fifth from the Note
F to B natural.

Third N. B. The above faid falfe Fifth is fupported in defcending by the perfect Skip
of Cadence, but not in afcending with the imperfect Skip confonant of Guide, for the
Reafons which will be demonftrated in the next Book.

Fourth N. B. The above Divifion of the Progreffion explained in this prefent Article,
is one of the principal and neceffary Notions for more eafy attaining the compleat
Knowledge of the whole Art.

CHAP. V,

Of the Harmonic Divifion of the Syftem of Sounds, from
whence arifes the Harmonic Syftem of Combination of
Sounds, with its particular Divifions.

Article I.

HE Terms of Confonant and Harmonic were always ufed as fynonymous.
The Thirds and Sixths, the Fifths and Octaves, have been, and at this very
Time are, reciprocally called Confonant or Harmonic ; only with the
Diftinction of calling the Thirds and Sixths imperfect Confonant, not in regard to the
Degree of Confonance, but becaufe they may be altered into Major and Minor ; and
the Fifths and Octaves perfect confonant, becaufe they cannot be altered. It feems very
clear, that the Term Confonant fignifies two Sounds, which refemble each other, and
being founded together, can fcarcely be diftinguifhed, as it is demonftrated by Experience,
in the Introduction : For which Reafon a Progreffion made with a Combination of two
Octaves, or two Fifths following each other in a Compolition of two, or three Parts, are
juftly forbidden in Practice, becaufe they are confidered as fimple Sounds, without Harmony.

Harmony muft be confidered as the Union or Combination of difTonant Sounds,
which Word DifTonant fignifies, that there is heard two diftinct Sounds, as abovefaid,
or, in vulgar Terms, a Combination of difTonant Sounds, diftinguifhable by the
Ear, as has been defined in the fourth Article of the firft Chapter, for which Reafon
the fimple Fifths and Octaves cannot be Harmonic, particularly the Octaves, which being
the more perfect confonant, is always abforb'd and confounded with its Grave Sound j
and, on the contrary, the other Intervals cannot be confonant, as mentioned in the
antecedent Chapters - y but the Fifth, when divided into two Parts by a middle Sound, it
becomes Harmonic, being diftinguifhed in and by two fucceflive Thirds, confequently
if all the Sounds which compofe their general Syftem, were difpofed in fucceflive Thirds,
all the fame Sounds would become confonant and Harmonic, refpectively from one .Fifth to
another"} and in this Manner will be formed an Harmonic Syftem difpofed, as in
Example VII. Plate IX.

But of all thefe Thirds, Experience mews, that only the firft Third, which divides
the fifth Sound from the Principal in two Thirds, is properly the original and efTential
Harmonic Sound j efTential, becaufe it divides the perfect Fifth, which is confonant, in
two Thirds, confequently the Fifth becomes alfo Harmonic, as mentioned before, and
original, becaufe the firft Third is the Root of the following other Thirds, and becaufe
an Air," Song, or Tune, may be compofed for two Voices, or Inftruments, with only

Thirds

32 Of the Composition 0/ MUSIC.

Thirds, or Sixths, as is known by Practice; to which two Parts may be added d
proper Bafs, which together, or without the Bafs, will make an agreeable Harmony,
and give great Pleafure to the Ear; which is not poffible to be done with only the
Combination of Fifths, and Octaves -, and becaufe the fundamental Bafs is always joined
with its confonant Fifth, which Fifth, when it is divided by the Third, making two
Thirds, one Major, and one Minor, and being added to the Octave of the Principal,
Fifth, and Third, in this Combination are compofed all the Primary Sounds Harmonic,
with the two confonant ; namely, the two Thirds Major and Minor, by which is formed
the Fifth and the Fourth, from the Fifth to the Octave ; alfo the two Sixths, Major and
Minor, the Major between the fifth G, and the Octave of the firft third E ; and the
Minor between the fame third E, and the Octave of the principal C. This Combination,
which is the Root of all Combinations compound, and full, make one fimple Accord, by
which may be made a Counterpoint fundamental in fix real Parts, and in figurate Mufic
in eight Parts, by only the Inveriion of this fimple fundamental Accord, which
Compofition will be agreeable, without the Combination of any fuperior Thirds, as
Seventh, Ninth, &c. by Muficians called Falfes, or Difcords. And fo far as regards the
Combination of the above fuperior Thirds, Experience fhews, that they cannot be added
abruptly, being not agreeable to the Ear, for being fo diftant from their principal and
fundamental Ground; but when introduced by the fimple Accord fundamental, which
is, as before told, their very Origin, or, in the Mufician's Term, well prepared, will much
improve and augment the Pleafure thereof.

From the above Reafons it is manifeft, that the natural Harmonic Syftem of the
Combination of Sounds, arifes only from the Harmonic Divifion of the general Syftem
of the fame Sounds into fucceflive Thirds, which being compofed of the eight natural
and original Primary Sounds, confequently produces eight Harmonic Scales difpofed, as
in Plate "&&$ Example VII.

From the Order of the Divifion in the above Example, it is apparent, that this
Syftem produces three Major Thirds, and four Minor, which are not only Harmonic
one with another, but alfo confonant at the fame Time with their Fifth below, and above.
The firft Third of the general Syftem of Sounds, is the Note E, which is Harmonic
with C, the Principal, and with G, the fifth Sound of the general Syftem, and is
confonant with B, the feventh Sound, B being its perfect Fifth.

The fecond Third G is confonant with its Principal, and with D its Fifth above, and
Harmonic with E below, and B above.

B, the third Third, and the feventh Sound of the Octave, is Harmonic with G below,
and D above, and is confonant with E, its Fifth below, but is not confonant with F above,
it being a falfe Fifth, compofed of fix Semitones, therefore is difibnant and only
Harmonic.

D, the fourth Third in the firft Harmonic Scale, is Harmonic with B and F, and
confonant with G below, and A above.

F, the fifth Third, is confonant with C above, Octave of the Principal, but not with
B, its Fifth below, which is falfe, as abovefaid, confequently it is only Harmonic ; and
it is alfo Harmonic with D and A, its Third below and above.

The laft third A of the fame firft Harmonic Scale, is confonant with D below, and E
above ; and Harmonic with C and F, its Thirds above and below.

As the fundamental Bafs in all its Progrefiions, muft be joined with its two confonant
Sounds, the Fifth, and Octave, to which it is neceflary to add the Third, without

which

Of the Composition of M U S I C. 33

o.>

which the Accordj or Combination, is only confonant, and not Harmonic, as before
explained ; therefore all the Art of combining the Sounds, confifts in keeping firm, one,
two and three Sounds, which compofes the original, fimple Combination, in the antecedent
Combination fimple, or compound, that may be, which Sound, by the fucceeding Motion of
the fundamental Bafs, are changed into the fuperior Thirds (called falle by the Muficians)'
and afterwards in the fubfequent Motions of the fame Bafs, they mud be again
introduced by a proper Refolution into one of the three Sounds of the fimple Accord^
with the Third, Fifth, or Octave. This is all which may ferve for a general Solution of
the Myftery of the Combination of Sounds, fo confounded, and intricate, as commonly
it is fuppofed to be.

The Method and Order of all the pofiible Combinations of Sounds, in every pofTible
Progreffion, will be demonftrated by the Canons of the Harmonic Code, in the next
Book, and clearly explained with all their different Diftinctions and Exceptions.

Of the Divifeo?i of the Combination of Sounds.

Article II.

THE Combination of Sounds is an Agreement of three, four, five, or more Sounds
altogether, difpofed in the Order of the Harmonic Syftem, as third, fifth, feventh,
ninth, &c.

It is divided into three different Kinds of Combination , which we call the firft fimple,
the fecond compound, and the laft the full Combination : This Divifion is alfo neceffary
for attaining the Knowledge of the Harmonic Art. .• .-. ' ■;

The fimple Combination is compofed of the firft and fecond Third, which makes the
perfect Fifth to the fundamental Bafs, in whatfoever Scale, as in the Difpofition of the
Harmonic Syftem, and with or without the Octaves, and the double Notes, it is called
common Chord, or perfect Accord, by Muficians.

I The compound Combination is made by adding one, or two^ of the fuperior Thirds
to the two firft j as the feventh and ninth, or the eleventh and thirteenth ; which two
laft are commonly marked fourth and fixth, for the Facility of ufing the fimple Figures,
inftead of the double ones.

The full Combination is fo call'd, when to the above compound Combination are added
one or two Thirds more, fo as to be united to all the fuperior Thirds, which compofe the
Harmonic Scale.

The refpedtive Thirds, which compofe the Compound, or full Combination, are marked
with Figures under, or over, the Bafs Notes, as may be feen in fome Canons in the next-
Book, and in fome Examples in the laft Book. Thefe Figures denote the divers fuperior
Thirds concerned in the Combination to the Bafs Note j for Example, the firft Third
above the Fifth, being the feventh Sound, is marked with a 7, the following third Note
with a 9 ; but the other fuperior Thirds to the ninth, which are the eleventh and
thirteenth, are marked thus, 4th and 6th, for the Facility of the fimple Figures, as
mentioned before.

The fimple Combination has no Occafion for Figures, having no fuperior Third to
the firft two, which compofe the Fifth.

Thefe fuperior Thirds which compofe the Compound, and full Harmony, cannot
fubfift in the Beginning, or in the firft Combination of the Compofition, which muft be

* K iimple.

34 Of the Composition c/ MUSIC, '

fimple, with only the Third, Fifth, and Octave, this Combination being the Productbr
of the following compound Accord, as before told ; and the fame fimple Combination
muft be adapted in the fame Beginning to the principal Note of the Scale, in which the
Compofition of the Mufic is compofed, except by fome Accident, for the Sake of fome
particular ExprefTion, by which the Compofer may be obliged to begin the Compofition
with the compound Combination of the fundamental Guide of the chofen Scale, and
ordinarily and particularly in the Compofition of Recitatives and Airs of a pathetic Nature,
and grave Time ; in which Sort of Combination, the principal Note of the Bafs is almoft
always omitted, and its compound Accord is fuppofed prepared by the fuppofed antecedent
Accord, notwithftanding it is not exprelfed ; but this happens very feldom, and almoft
never in gay Movements. Neither can the fame fuperior Thirds fubfift in the final,
perfect Cadences, where, in two or three Parts, the fame final Cadence muft be only in
Confonance, namely, with only the Octaves, and in four Parts may be joined the fifth ;
in five or more Parts the faid Cadences may be Harmonic, namely, with the Addition of
the third, becaufe in five Parts the fundamental Sound, and its Fifth, becomes doubled by
their Octaves ; fo the third Sound, which is the firft Harmonic, and confequently the
more fenfible, being not doubled, cannot opprime the confonant Sounds, when they
are doubled.

This muft be obferved, that when the Scale is with the Major Third, this fame fharp
Third muft not be in the extreme Part acute of the Combination, but in the Middle, or
near the Middle, all fharp diffonants being the moft fenfible. For the above Reafons, the
fimple Combination may be called the terminate Accord, and the compound, or full
Combination, which properly belongs to the fifth Note of every Scale, being its fundamental
Guide, muft be called the indeterminate Accord, or Combination, becaufe the compound,
or full Combination, necefTarily requires a fubfequent Combination for its Refofution
into the perfect fimple Combination, in which only the Harmony may be terminated.

CHAP. VI.

Of the different Scales, their different Ufe, and their Diftin£Hon.

Article I.

HERE are many Scales arifing from the general Syftem of Sounds, belonging to
Harmony, and alfo to Melody ; but only one is the Principal, which is the true
Copy of the very fame general Syftem, and it is the Spring of all other Scales,
Divifions, and other Syftems ; therefore it is called the Principal Scale, and it is alio called
the Natural Scale, as being derived properly from Nature, being analogous to the human Voice,
and to Senfation, which Voice cannot naturally and eafily afcend, or defcend all the Degree
of the Scale, without mixing the Tones with Semitones j and if any Perfon will try to
afcend or defcend by fucceflive equal full Tones, he will find it very difficult ; and our
Senfations take no Notice of any Sound of alefier Interval than of a Semitone; confequently
this principal Scale is in its proper and moft natural Order, riling from the loweft to the
higheft Sound, and defcending without any accidental Nfljfr, either flat, or fharp ; its Sound,
and their Names, being unalterable.

To the above principal, and natural Scale, another Scale different may be joined alfo as
Principal ; and is called the Scale of the minor Mode, or of the flat Third by Muficians :
This Scale has hitherto been known but imperfectly, the Order of their Sounds being
confidered not different from the Order of ours fubordinate, and relative Scales to the
Principal, and it is not a long Time it has been accommodated as a principal one, by the
Practice of the Muficians ; for this Reafon, and to. (Jiftinguifh it more properly from the

other

Of the Composition of MUSIC.

other principal natural Scale, it is called in this Treatife the Artificial Scale : The Difference
of thefe two principal Scales will be explained in their refpective Articles.

Befides the above two principal Scales, there are two more, which may be confidered
as principal ; thefe two Scales arife from the confonant Divifion of the general Syftem of
Sounds explained in the antecedent fourth Chapter ; namely one from the Progreflion
of the confonant fifth afcending, as F to C, G to D, &c. and the other from the confonant
fifth defcending, as from G to C, C to F j F to B flat, &c. from whence arifes the Divifion
of the natural Scale in thirteen Sounds, divided by twelve Intervals, each of one Semitone,
but in two different Manners, by which are formed the two Scales, one afcending and the
other defcending ; but the Diverfity of thefe two Scales relates only to the Denomination
of the Sounds themfelves, which are the fame under different Names ; confequently the
two Scales may be confidered as only one, called by Muficians the Scale of Semitones ;
the Ufe of which is for tranfpofing the natural and artificial Scales higher or lower, as will
be explained in their different Articles.

From the other two Scales, the natural and the artificial, arifes their proper relative
and fubordinate Scales, and from the other two of Tranfpoiition, their different tranfpofed
Scales, which Scales will be explained all fucceflively.

Befides the above Scales, there are many others, which ferve only for the Melody
of the Parts, as is fhewn in the laft Article but one, belonging to this Chapter, and
delineated in Example XVII. Plate XVI.

Of the Principal Natural Scale.

Article II.

THIS Scale, which, as has been faid, is the very Copy of the General Syftem * of
Sounds, and the Mother Scale, is compofed of a Major Second from C to D j of a
Major Third from C to E ; of a -perfect Fourth from C to F ; of a perfect Fifth from C
to G j of a Major Sixth to A ; a Major Seventh to B j and from the fame C to C Acute,
an Octave, as has been explained in the General Syftem of Sounds. But as the fundamental
Bafs, with its different Movements, may pafs through all the eight Sounds of the Scale ;
therefore every Sound muft have its proper Scale difpofed into an Octave, to diftribute to
the different Motions of the fame fundamental Bafs, its proper and refpectively different
Combinations.

Thefe Scales are formed with the fame Sounds of their principal Scale, natural or
tranfpofed, as may be ; and as the principal natural Scale is formed by eight Sounds, therefore
there arifes eight Scales, feven of which are the relative Scales, and fubordinate to the firft
principal Scale, as in Example VIII. Plate X. namely, the Scales ofD, E F, G, A, B, and C
Acute ; this laft having its Sounds in the fame Order as the Principal, is confidered as a
Repetition of its firft Principal; but, on fome Occafions, muft be alio confidered as relative,
as will be explained" in its proper Place ; the other fix are the proper Relatives, having their
Sounds difpofed in different Order of the firft Principal, as it is in the above-mentioned
Example VIII. Plate X.

Of the Relative Scales arifi?ig from the Natural Scale, and of their

refpe&ive Order to the fame.

Article III.

HP HE firft Scale in the above Example VIII. Plate X. is the principal Scale natural,
■*■ which has its Sounds difpofed, as has been explained in the antecedent Articles.

The

3# Of the Composition of M U S I C.

The following fecond Scale is the Scale of D, which is the firft Relative, and has the
Fourth and Fifth both perfect, but differs from the Principal in the firft Third, and
Seventh, both Minor.

The third Scale E, has alfo the Fourth and Fifth perfect, but the firft Second is Minor,
and confequently its firft Third Minor, as alfo the Sixth and Seventh both Minor.

The fourth Scale F, is only different from the Principal in the fourth Note B, which
is a falfe Fourth.

The fifth Scale G, is the fame as the Principal, except the feventh, which is Minor.

The fix-th Scale A, has the Fourth and Fifth perfect, but the Third, Sixth, and
Seventh, are Minor*

The feventh, which is the Scale of B, has its Fifth falfe, and differs from the
Principal in its Second, Third, Sixth, and Seventh, being all Minor.

The eighth Scale is the fame as its Principal, being its Acute Eccho, but may be
confidered as relative on fome Occafions, as below will be explained.

The above fix Scales, D, E, F, G, A, B, not only differ from the Principal, but
alfo from each other.

The two Scales of E and B are the moft imperfect, E being deprived of its proper
Guide, which mould have been B, if it might have its Fifth perfect, which is falfe, as
mentioned ; and B cannot be properly a relative principal Sound, for the fame Reafon of
being deprived of its own perfect Fifth : Therefore thefe two Scales cannot fubfift in natural
progreflion, but with fome Limitations, as will appear in the next Book.

Firfl N. B. It was mentioned, that the two extreme Sounds of the Confonant Divifion
of the general natural Syftem of Sounds, C, C, and the two middle, F, G, are commonly
confidered as the four principal Sounds of the Octave, following the firft Opinion of
Pythagoras, which after accidentally hearing the Harmonic Noife of the above four
Sounds expreffed by four Hammers, as is afferted by the common vulgar Hiftory j and
after weighing the four Hammers, and making many Experiments with hanged and ftretched
Strings, he fixed the Ratios of the Intervals, which he fuppofed to be betwixt the
Sounds of the above Quadruple, for exemplifying to the human Underftanding the
Difference between the Gravity and Acutenefs of the Mufical Sounds.

But of the above four Sounds are only two which properly may be confidered as
principal, in Point of Progreflion (as mentioned in Chap. IV. Article I.) C Acute, is only
the Repetition of the principal Grave C, and the fourth Sound F has its fourth Sound
imperfect, and falfe in B, therefore the Harmony cannot proceed in the natural Scale with
the perfect Confonant Skip of Cadence, from the fame F to B, without Preparation, but
only from F to C Acute, with the Confonant imperfect Skip of Guide, being the Acute
C, its perfect Fifth. But G, the fifth Sound of the Scale, being the perfect Fifth of the
principal C Grave, the Octave of which makes its perfect Fourth above, and the fame
G falling directly into the principal C, with the Confonant perfect Skip of Cadence,
muft be confidered as the only fundamental Guide of the Scale, having, in its fundamental
Combination, the two Harmonic indictive Notes, the Major Third, and the Minor
Seventh (as before told) the other Confonant perfect .Skips, which happen in the
Progreflion of the Harmony in the fame natural Scale, as D A, or E B, and A E, can
only ferve as relative or fubordinate Guides.

C, the Octave of the Principal, (as before mentioned) may become, in the Progreflion

Gf the Composition of MUSIC. 37

of Harmony, the Guide to F, into which it falls directly, as G to C principal, but becaufe
F cannot be a principal Sound of the Scale, having the falfe fourth B, and C Acute, as Guide,
is deprived of its indicative Minor Seventh ; confequently ferves only for a relative Guide
to F, and F only is fubprincipal relative in the natural, or fimple Progreflion.

By confidering the two indicative Notes, all the Sounds are eafily diftinguifhed from
their principal Sound of the Scale, and from their fundamental Guide.

G, the fundamental Guide, is rtot different in its Scale from the principal C, only in the
feventh Note, which is Minor, deriving from the perfect Fourth of the Scale j and this
feventh Note muft be Minor, which is a neceffary Condition appertaining to all
fundamental Guides, and may alfo be called the fundamental Seventh, to diftinguifh them
from the Sevenths of the relative Guides.

The third of every fundamental Guide, which is B in the natural Scale, and naturally
fharp, which muft be always fharp in all the fundamental Guides of the different
principal Scales, may alfo be called fundamental Thirds.

The above two Notes, the Third Major, and Minor Seventh, of the fundamental
Guides, being the Notes which indicate the approaching of the principal Note of the Scale,
may alfo be called the Harmonic, fundamental, indicative Notes ; namely, Major Third
Indicative afcending, and the Minor Seventh defcending Indicative. The Indicative
afcending ferves to both the natural and artificial Scales, and their tranfpofed Scales ;
and the Indicative' Terves only to the« natural Scale, and its tranfpofed Scales, for to
diflinguifh them from the artificial, and its tranfpofed Scales (as more clearly will be
explained in the following Article of the Scale artificial.)

The Major Third afcending* goes directly to the principal Sound of the Scale, and the
Indicative Seventh Minor defcends directly to the Major Third of the Principal, each of
them proceeding by Semitones, which is the fhorteft. Way, and confequently the moft
natural, both Notes leading into the firft fimple Combination of the principal Note of
the Scale, with a contrary Motion.

The falfe Fifth between the Major Third, and Minor Seventh, may alfo be called
the Harmonic Indicative Minor Fifth j and the two Notes being inverted, becomes the
Indicative Harmonic Major Fourth,

Second N. B. It was mentioned at the Beginning of the firfl Article of this Chapter,
that the natural Scale is the Spring, or the very Mother of all Sorts of Syftems, or
Scales, that may be formed with the Mufical Sounds ; and we have feen firfl arifing the
Scales relative, and the artificial Scale ; alfo the Scales of Tranfpofition. Now we mall
fee that the Syftem of Combination of Sounds arifes alfo from the fame Mother Scale.

The natural Scale, which makes with its Scales relative a perfect Quadrate, as appears
in Example VIII. Plate X. forms the Harmonic Scale with the Diagonal, which defcends
from the firft Scund C, to the laft C in the oppofite Angle ; from the firfl: C it paffes to the
firft harmonic third E, from the third to the fecondG, which is the fifth of the firfl: principal,
from G it paffes to B, the third Third of the Harmonic Scale, and feventh of the firfl: Principals
fromB it paffes toD, which is the fourth Third of the fame Harmonic Scale, and the ninth
of the natural ; from the ninth it paffes to the eleventh Note of the natural Scale, and the fifth
Third of the Harmonic, from the eleventh to the thirteenth, and from that to the
fifteenth, the laft, which are the fixth and feventh Thirds, which forms the Harmonic
Scale, and all Laterals of the above firfl: Diagonal are difpofed by Thirds, and the oppofite
Diagonal, with its Laterals, gives all the Octave, which is the general Magazine, not
only of the Mufical Sounds, but alfo of all poffible others.

L "Third

3$ Of the Composition of M U S I C.

third N. B. From the above fyftem of combination of founds, which alfo makes a
perfect quadrate with the fcales of every one of thefe founds, is manifefted the natural fyftem
Of progreflion, alfo by its firft diagonal defcending to the oppofite angle, proceeding
always by fifths, as is to be feen in example VII. plate IX. the oppofite diagonal, and its
laterals, gives alfo the octave, and from the diagonal and its laterals, the fyftem of the
natural progreflion, it is reftored to the natural fcale, the oppofite diagonal gives the fame
octave, as is to be feen in example VI. plate VIII. all that confirms the new two fyftems
of the combination of founds, and of their progreflion.

Of the Artificial Scale, commonly called the Scale of the Minor Mode, or

the Flat Third.

Article IV.

\T7" E have feen in the Introduction, that the old Greeks have begun their firft fcale
* » with only four founds, difpofed in four firings of their lyre, by the intervals of
femitone, tone and tone ; afterwards, for the benefit of their voice, were augmented with
three other founds, by three other firings added to the lyre, in all feven firings, with which
was formed their diatonic fyftem, or fcale, and the two tetrachords conjoined, which
tetrachords being not fufficient for the different voices high and low, were augmented to
five tetrachords difpofed in fixteen firings, which together was called the greateft, and
unchangeable fyftem. Arijloxcnes diftinguifhed his fifteen modes by tetrachords (which
properly are diateffaron) each diftant a femitone, one from another) dividing the
octave in twelve femitones. Guido Aretino, not finding the tetrachords of the Greek proper
for the harmony, he added to each tetrachord two founds in the grave, by which he
formed his hexachords, as are all diftinctly explained in the above Introduction. From all which
* it feems very clearly, that the Greeks, old Romans, and Guido, with all his followers, have not
known other fcales than thofe producted by their tetrachords and hexachords, without any
diflinction : Moreover, the firft diatonic fcale, with the addition of the chord proflamba-
nomenos, was divided in feven fpecies, as before-mentioned, in four fpecies the fifths,
and in three fpecies the perfect fourth, with confidering only their diflinction and
difference by the different fituation of their femitone, confequently without the notion of
the principal fcale, nor in the major mode, nor in the minor mode ; and being tranfpofed,
the octaves, and their fpecies, were always confidered in the fame order of their tetrachords
and hexachords. The different modes and melody of the Greeks and Romans never forted
from the tetrachords, but- only pafTing from one to another; and the harmony of Guido
never paffed his hexachords, only pafling from one to another, all without changing
the chords of the greateft and unchangeable fyftem, excepting in the occafion of the three
genders and their colours, for which the Greeks were obliged to change the order of their
tetrachords with two moble, and two ftable firings, , as explained in the Introduction.

But by the gradual progrefs of the harmony, it now is perfectly clear, that one natural
fcale muft fubfift, and it is the principal , and alfo another fcale different in the order of
their founds from the firft principal, which fecond fcale muft be confidered as a principal
one, which is here named the artificial fcale, being perfectly accommodated, and
fucceflively accomplifhed by the art, in imitation of the firft principal natural, in regard to
the manner of afcending the octave, but different in its third found. This artificial fcale
may be applied to every found of the natural fcale; but in this treatife it is applied to the
fcale of C, with minor third, becaufe the firft principal fcale being in C with major third,
may more eafily be known the difference between each other.

The efTential difference between the natural and this artificial fcale, are as follows. The
firft third in the natural fcale is major, or naturally fharp, but in this artificial fcale, is minor,
or flat. The fecond found, or note 4 of both fcales, is diftant a major fecond, or full tone,

which

Of the Composition »/ MUSIC 39

which is a neceiiary condition in all the principal feales, as it is the perfect fourth and
fifth ; and as the natural fcale has its fourth note, with its third major, being the fame
fourth, the fubprincipal relative note of the fame natural fcale, as before-mentioned,
this artificial fcale has alfo the third of the fourth note flat, the like hath its principal note:
But becaufe all fundamental guides muft have their thirds (harp, as their indicative notes,
for to pafs to the principal note, which fharp thirds are the feventh major, or fharp, in the
order of their principal feales ; and as it is not poffible to pafs gradually from the minor,
or flat fixth, to the major feventh, being diftant three femitones, which properly is an
interval of a minor third, confequently art has been obliged to change the minor fixth into
the major fixth, in order to help the melody, in afcending gradually to the major feventh,
which major feventh becomes the necefTary indicative fharp third of the fundamental guide,
in order alio to afcend gradually to the octave of the principal note. On the contrary, in
defcending from the fame Octave to the principal note, or only to the fourth note of the fcale,
which (as has been faid) muft have its third flat, like its principal, the above major third
of the fundamental guide muft be changed into a flat feventh of the fcale, in order to
defcend gradually to the fixth note, which alfo muft be changed into a flat, to become a
Hat third to the above fourth note of the fcale, which being the fubprincipal relative,
muft have its third flat* as above-mentioned. This occafions two different feales, one
for afcending, and the other for defcending, which two feales happens only in the fcale of
the principal, and of the guide, the other relative feales are not changed, as may be feen in
example IX. Plate XL and the above two different feales of the principal, and its guide,
fei ve only for the melody of the parts, and of the bafs, when it is not fundamental, as
often happens in figurate and comon raufic : For example, the common bafs defcending
gradually from the octave to the guide, it may pafs either by the feventh and fixth major,
or minor at pleafure* but when the fame common Bafs makes the accent in the fixth note
defcending (as above-faid) from the odtave, in this cafe both the fixth and feventh muft
be minor ; but this minor fixth may afterwards be changed at pleafure, when the accented
note is not fhort, in major fixth, before defcending to the fundamental guide, which guide
muft have its major indicative third, as mentioned before. Thefe different accords, or
combinations, will be demonftrated in the laft Book, which treats of figurate mufic j the
fundamental bafs being not concerned in the combination, arifing from the gradual move-
ment of the common bafs, which combinations are almoft all inverted from the fundamental
combinations.

N. B. It has been mentioned, that the major third and the minor feventh, in the com-
bination of the fundamental guide of the natural feales, and its tranfpofed feales, may be
called fundamental, and harmonic indicative third, and feventh, to diftinguifh them from
the thirds and fevenths of the relative Guides, and becaufe they indicate the approach of
their principal fcale by afcending the third to the fame principal, and the feventh defcending
to the major natural third of their principal fcale the natural, and tS^ tranfpofed feales ;
both proceeding by femitones by contrary motion. But in the artificial fcale, and its
tranfpofed feales, where the firft third is flat, confequently the fourth Note of the fame feales,'
which become fevenths in the combination of their guides, refolving after into the flat
third by defcending a full tone, inftead of a femitone, as in the natural fcale ; for this reafon
the third of this artificial fcale, being minor, cannot clearly be indicated by the fame feventh
minor by defcending a full tone ; becaufe, for example, fuppoiing the above artificial fcale
being C, with flat third, its guide G, with its feventh minor F, defcending to E flat, the
fame is done in the fcale of E flat by the fame note F, as fifth of its guide, B flat defcending
alfo to the fame E flat, and notwithftanding that F defcends into the principal note, as fifth
of its guide ; and in the fcale of C the fame F defcends as feventh of the Note G guide
into the third flat of the fcale, is not clearly perceived as indicative feventh : Therefore
inftead of the fame feventh, the ninth minor to the guide, which is a minor third above
the minor feventh, and a minor fecond above the octave, or double octave of the principal
note, becomes byway of fupplement the harmonic fundamental, and indicative note, falling 7

b Y

40 -(^ /j^ Composition ^ MUSIC.

by a femitone into the perfect fifth of the fcale ; and the fame ninth being flat, which in
the natural fcale is major, determines the artificial fcale of minor third by defcending in
contrary motion Of the indicative third, which afcends to the principal note of the Icale, in
the fame time that the ninth defcends to the fifth, as abovefaid. .

Of the relative Scales to their principal artificial Scale.

Article V.

AL L the relative fcales to this artificial fcale are different from their principal fcale, and
alfo from each other, as may be feen in Ex. IX. Plate XI.

In the antecedent Ex. VIII. Plate X. of the natural fcale with its relatives, the third
fcale, which begins in E, and the feventh fcale B, are the moft imperfect, as has been
mentioned : But in the artificial fcale the moft imperfect in their relatives are the fcales
of D and A. The fcale of D, which is the fecond fcale in the above example, and the
firft of the relatives, /ias the falfe fifth A flat, and the fixth fcale of A flat, which is the
fifth of the relatives, has the falfe fourth D, and this is an effential difference between the
two principal fcales, the natural and the artificial ; the natural fcale having the falfe fourth
between the fourth note and the feventh ; and the falfe fifth, between the fame feventh
note and the octave of the fame fourth note; and the artificial fcale has the falfe fifth
between the fecond found, or note of its fcale, and its fixth found, and the octave of the
fecond note ; but in the artificial fcale may be changed the falfe fifth, and falfe fourth into
perfect on fome particular occafions, as will appear in the canons of the harmonic code in
the next book ; and for the fame reafons before given, the two fcales relative D and A flat
of the artificial fcale, as the other two, F and B, in the natural fcale, cannot be freely
ufed in harmony, but with fome limitations and exceptions, as will appear in the fame
canons of the harmonic code.

The two principal notes, the principal and its principal guide, have both two fcales, one
afcending, the other defcending, as above-mentioned ; the difference between the other
relatives is clearly apparent in the above Ex. IX. Plate XL and the fame explanation done
for the relatives of the natural fcale, may be applied to thefe of the artificial fcale, in the
fame Ex. IX. Plate XI.

Of the tranfpojing Scales.

Article VI.

t ~T^ W O are the fcales of tranfpofition, both arifing from the two fundamental confonant
-*■ movements of the perfect fifth afcending, and defcending, which movements gives
thirteen founds, divided by twelve intervals of a femitone each ; and notwithftanding that
from the two above motions of afcending and defcending, there arifes two fcales, thefe
two fcales are compofed of the fame founds, but of a different denomination, as may be
feen in Ex. X. Plate XII. in the firft line of this example is defcribed the afcending
progreflion, and the defcending in the fecond line : The afcending progreflion begins with
the note F afcending to C, and the defcending progreflion begins with the note B ; which
two notes, F and B, being the two indicative notes of the natural fcale, one defcending
and the other afcending, in contrary motion, gives firft the feven primary founds, before
they pafs to thofe, which divides fucceflively all the tones of the octave in two femitones.
By the rirft fcale afcending are produced the notes of the fharp denomination, and by the
other defcending, thofe of the flat denomination, as it is explained in the fame above
example. Thefe different notes marked fharp and flat, before mentioned, are the fame
founds, but only different in their denomination, and in their natural place in the fcale,:
For example, in the afcending fcale the note D fharp pafles to A fharp its perfect fifth ;

this

Of the Composition " &f MUSIC. $t

this A fharp muft be noted in the fame place, where is noted A natural, only with the
addition of the (harp fign : In the other defcending fcale the note F naturally defcends
to B flat, being its perfect fifth ; this B flat muft be noted in the place of B natural^ with
the addition of the flat iign b y but thefe different places and names change not the found ;
the reafon of it is evident ; for D fharp to A (harp is an interval of five founds, with their
proper names and places ; fo from F defcending to its fifth B flat, this B flat cannot be
named A fharp, nor A fharp B flat, being both fix names to fix confecutive notes in the
place of their proper fcales ; from this Reafon it is apparent, that the figns- of fharpand
flat b, are onlv neceffary to put the founds with their proper names in their proper place
'of their different fcales. The fign of fharp augments the found of an equal femitone ; fo
A fharp being augmented of one femitone, is the fame found as B flat, diminifhed a
femitone from B natural, but named and put in the place proper to their particular fcales :
The fame happens in all other fharps and flats. All this will appear very clear in the expla-
nation of icme equivocal accord, which will be done in the laft book ; where will be
demonftrated, that with only a fimple compound accord, the harmony may pafs into divers
oppofite fcales fharp and flat ; and that will be the laft evidence of the unfubfiftance of the
divifion of tones, and femitones into major and minor. From the above two fcales afcending
and defcending, arife two other fcales proceeding gradually by femitones, as are difpofed
in Example -XII. Plate XII. Thefe two fcales are properly the fcale of tranfpofition, into
.every degree of which two fcales, both the natural and artificial fcales, may be tranlpofed.

ads of thefe two fcales of tranfpofition are alfo the fame, but of different deno-
mination, as thofe of the other two principal fcales ariling from the motion of the fifth,
before explained ; confequently both thefe two fcales may be confidered as one, notwith-
ftanding the divers pofitions, and names, as is commonly done by the muficians.

N. B. The figns of fharp and flat b, when they are put in the beginning of the

'compofition immediately after the fign of the key, and before the fign of time, which

Les the rheafure, fignifies that the fcale is not natural, but artificial, or tranfpofed from

natural, becaufe the natural has its found without any of the above figns j and when

fame figns are accidentally put betwixt the compofition, the fharp indicates that the

ncte is tranlpofed a femitone higher, and the flat a femitone lower, confequently the fcale

becomes changed by the fame figns, namely, more acute by the fharp, and more lower by

the flat; .

Of the Scales tranfpofed from the Natural Scale.

Article VII.

A S the principal natural fcale may be tranfpofed into every one of the thirteen founds
J** 1 of the fcales of tranfpofition, confequently every tranfpofed fcale muft have their
founds tranfpofed into the fame order of their original mother fcale ; and being thirteen
founds, from which mull be abftracted the extreme acute, being confidered as a repetition
of the fame natural fcale, but higher, remains twelve founds, which muft have their proper
fcale, to which is added five more of a different denomination ; the twelve fcales ariling from
the afcending fcale of tranfpofition, and the five of different denomination from the other
defcending fcale, as are all defcribed in Example XIV. Plate XIII'.

The firft fcale is the firft original fcale, the fecond is the fame original fcale tranfpofed a
femitone higher, the third is tranfpofed a tone higher, the fourth three femitones hio-her ;
and fo of the reft, proceeding higher by femitones. All thefe fcales may be ufed, but
fome of different denominations are more eligible than others : For example, in the ninth
fcale of the above Example XIV. Plate XIII. which reprefents the fcale of G fharp, in
order to afcend the octave, muft be ufed the note F, double fharp, which is marked
thus ( X ) commonly, but improperly called diefis enarmonic, and in Englijh extreme
fharp, which is the propereft term : But in afcending to the fame odavc G (harp by the

M other;

q% O/ ffe Composition e/ MUSIC,

other fcale under the denomination of A flat, which reprefents the found as G fharp,
confequently of the fame fcale, there is not occafion of any double, or extreme fharp, as
is apparent from the oppofite fcale to the above ninth fcale, which is the fourth fcale in
thole of different denominations in the fame above example, for which reafon the fourth
fcale of D fharp, is abfolutely improper to be chofen, having two notes double fharp F x,
and G x, confequently the fcale of E flat, which contains the fame founds, as the fcale of
D fharp, is the proper fcale to be ufed» The feventh fcale of F fharp is generally better
than the fcale of G flat. The eleventh fcale in A fharp is evidently impracticable, havino-
three notes extreme fharp, but in changing the denomination to B flat, which is compofed
' of the fame founds of A fharp, becomes very eafy and natural. Thefe extravagant fcales
may happen by accident, in the middle of the compofitions, but they never muft be chofen
for principal fcales. This is what is to be obferved in general, in regard to the tranfpofition
of the fcales.

Of the Tratifpoftion of the Artificial Scale.

Article VIII.

r T"*HE artificial fcale, as before faid, has two different fcales, one afcending, the other
-"- defcending, every one forming thirteen fcales tranfpofcd from the principal, from
which may be deducted the laft fcale, being compofed of the fame founds, but one
octave higher, therefore muft be confidered only twelve, with five more of different
denominations, but being two fcales, one afcending, the other defcending, as before-*
mentioned, the fame twelve fcales, and the five of different denomination, are
augmented to twenty-four, and ten more of a different denomination, which are divided
in two examples, as may be feen in Example XV. and XVI. Plate XIV. and XV.
the firfl of which belongs to the afcending fcale, and the other to the fcale defcending,
every one of them having joined their fcales of different denomination.

The fame explication, which was made ufe of in the tranfpofed fcales from the
natural, will be fufficient for thefe two examples of the tranfpofition of the artificial fcale,
the principal difference being in having its firft third flat, and the fecond third, which
forms the perfect fifth, confequently fharp, contrary to the natural fcale, which hath the
firfl third fharp, and the fecond flat, as has been explained ; only it muft be remembered
to chufe always that fcale which is the eafieft, avoiding the double fharps, or double flats,
notwithfta nding the variety which adorns this art, it muft be attended with the greateft
facility.

Of the Number of the different Scales arifivg from the two Scales of

Tra7ifpofitio?i.

Article IX.

T^ ROM the two principal fcales of tranfpofition in Example XIV. Plate XIII. and Examples
■*• XV. and XVI. Plates XIV. and XV. arifes twelve principal fcales, all tranfpofed from the
natural fcale, with five more of a different denomination, as has been explained in the feventh
article ; and becaufe the artificial is diftinguifhed by two fcales, one afcending, the other
defcending, this occafions twenty-four tranfpofed fcales, twelve from defcending, and twelve
from afcending, with ten more of different denomination, which ^together amounts to
thirty-four fcales, which being joined with the twelve fcales, andjsssi more of different
denomination, derived from the natural fcale, as above explained, makes in the whole
fifty-one fcales, all principal j and every one of thofe principal fcales having their proper
feven relative fcales, which joined all together are three hundred and fifty-feven relatives,
which joined with their principal, amounts in the whole to four hundred and eightjffcales,
almoft all of them being ufeful to the harmonjc art, in the vvav of variety. *

N. B.

0/ ^ Composition c/ MUSIC. 4^

N. B. The muficians have commonly given, and frill give indifferently, the names of
key, tone, or mode, to the feales of founds) but thefe equivocal terms in this treatik-
have been diftinguifhed.

The name of key fignifies properly the fign of mark, which is put before the feales
belonging to the melody of the different parts, as the key of C, or F, or G, belonging to
middle, low, ov high parts, as fopranos, contraltos, tenors, andbaffes.

The term tone has properly been applied to the intervals exifting betwixt two founds,
which gradually follow one another in the fcale, as between C, D, or D, E, &c. and is
called femitone, when the diftance or interval is not a full tone, as E, F, or B, C.

And the name mode, which is the lefs equivocal, fignifies properly a certain particular
manner of finging, as mode or manner, French^ Scotch, Polones, or Sicilian, juit as the
Greeks did in their modes Iom'c, Doric, &c.

For the above reafons thefe equivocal terms have been diftinguifhed throughout the
whole of this treatife ; and inftead thereof we have ufed only the proper term of fcale,
which properly fignifies a feries of founds in an order gradually difpoied from grave to
acute, or vice verj'a ; and without any further explanation, it may be underflood by all
who will, or can underftand it, and the other terms applied feparately, as above
explained, namely, the word key, to the different feales of melody, the other word tone
to the intervals, and mode, as manner.

Of the different Scales of Melody and their different Keys*

Article X.

*Tp H E feales which belong to the melody of every part, are made ufe of in order to fuit
•*• the different acutenefs, and gravity of the different voices or inftruments.

Thefe feales are in number eight, every one having its proper different key, which
fhews the order and place of the founds in every fcale ; and thefe keys are defcribed in
Fig. VI. Example X. Plate V. and explained in the Introduction of this Treatife, where
alfo has been mentioned, that now they are reduced to the number of five, but are all
ufed in great church "mufic in eight and fixteen parts, as diftinctly explained in the fame
Introduction : Therefore we have now defcribed in the Example XVII. Plate XVI. all
the eight feales, with their limited founds defcending and afcending.

Every fcale has its proper key, to which fucceffively follows that fcale afcending and
defcending, which is proper to every one of the different voices. The notes of thefe feales
have their proper limits, which muff not be paffed in afcending or defcending in compo-
fitions, where all the different voices are joined, as in full choruffes, and in three or four
voices, or more : But in compofitions for fome particular voices, the limits of thefe feales
may be exceeded according to the compafs of the voices. The inftruments, as violin, oboe,
and violoncello, are not obliged to the above limits, which may be palled according to
their particular practice and ufe.

Of the divers Pofitions of the Unifon refpeElively to the differe?it Keys.

Article XI.

ALL the notes in Example XVIII. Plate XVI. which are under the different keys of
•**• F, C, G, in their different places, are all unifons, being all the fame note C, from
their place or different pofition to the correfpondent unifon C, in all the other feales, is

known

44 0/ ^ Composition c/ MUSIC.

known the diftance of every found in their refpedtive fcales, and that ferves to keep every
part in its proper compafs, and alfo the eafier and more immediately to know the diftance from
one key and fcale to another, and confequently for applying the proper notes which belong
to every particular voice, every one of which cannot exceed their nearer parts in the acute
or grave, but they muft be always below the nearer acute, and higher than the grave part.

Now fince we have known what is mufic in general, its founds, its different fyftems, and
their divifion and fcales ; we mail pafs on to digeft and explain the fundamental harmony,
its laws and rules, contained in the next books.

END of the First Book.

DELL'

ARTE AR MONICA:

O R,

A Treatise of the Composition of M U S I C.

BOOK II.

Containing the Fundamental Harmony, explained by the Fundamental
Counterpoint ; by which are Formed all the Canons, orderly joined in
one Harmonic Code, containing and explaining all the Laws and Rules
of all poflible Combinations of Sounds, and their Progreflions ; and flrft
the following Defcription of the faid Fundamental Counterpoint, and of
its Compofitions, which make the Code Harmonic.

Of the Fundamental Counterpoint,

N the fifth article of the firft chapter of the antecedent book, the harmony
was divided into fundamental and figurate : The fundamental becomes now the
fubject of this book. It is called fundamental, becaufe properly it is the bafis
or foundation of harmony, and is the only practical theory of the art ; which
is explained by a courfe or feries of harmonical compofitions, compofed by a

fundamental counterpoint, as we call it, as has been mentioned in the above-faid article,

Chapter I. Book I.

This fundamental counterpoint was never hitherto known, and confequently never ufed,
being very different from the counterpoint commonly ufed in church mufic, and in teaching
the compofition of mufic. In the counterpoint formerly, and now in the vogue, the bals
and the parts move either gradually or fkipping at pleafure : For this reafon the compofition
of mufic cannot be learned otherwife than imperfectly, and by a long practice, without
knowing the derivation of the particular rules belonging to the divers combinations of founds

N and

.46 Of the Composition c/ MUSIC. 33ook 1L

and their progreffions. But in the counterpoint here introduced, the motions of the bafs*
and alfo of the parts, are limited j the bafs moving only by its competent fkips, and the
other parts moving gradually, without fkipping ; in this manner the different motions of
the bafs are all diflinguiihed, alfo the different combination of the founds formed by the
parts to every different and particular motion of the bafs, which in fimple progreffion paffes
through all the eight original founds of the natural fcale, and in mixed or varied progrefc-
fions thro' all the lemitones of the fcales of tranfpofition. By this means it is very eafy to
know diftinctly all the general and particular rules of the combinations and progreflions of
founds j which rules it would be almoft impoflible to demonftrate, without the above diftinct
and fucceffive order. This order appears very clear by the fuccemon of the compofitions
of the fame fundamental counterpoint, which compofitions are called canons, becaufe every
one contains and mews a law or rule to be obferved in the compofition of mufic ; and all
the fame canons joined together are called the harmonic code, becaufe it contains all laws
and rules of harmony.

This harmonic code is divided into two parts ; the firft part contains the divers combina-
tions of the founds, fimple, compound, and full, belonging to the divers motions of the
bafs in fimple and natural progreffion : The fecond part contains the fame different com-
binations belonging alfo to the different motions of the bafs, but in mixed and varied
progreffion. The whole code is divided into chapters, and every chapter into articles.
Every chapter contains one of the fundamental motions of the bafs ; as by fifths or thirds
afcending and defcending, and in its articles all different combinations which belong to
the fame motion of the chapter, as fimple, compound and full ; in fimple progreffion in
the firft part, and in mixed in the fecond part of the fame code.

The First Part of the HARMONIC CODE.

CHAP. I.

Of the confonant perfeEl fundamental Movement of the Bafs, comonly called

the Skip of Cadence.

H E movement of the fundamental confonant perfect fkip of cadence is the
principal of all other movements or fundamental fkips, being the more natural,
and confequently the more pleafant. It is called perfect, not only becaufe it goes
directly to the cadence, by which are perfected all harmonical compofitions, but alfo for
being capable of all the gradual compound combinations, as has been mentioned, and as
will clearly appear in the following canons in their refpective articles.

Article I. Of the Confonant Combination.

CANON I. Plate 17.

'"TpHIS combination is called confonant, becaufe it is only compofed of two confbnants,
* fifth and octave; and becaufe it is not joined with fome harmonic founds, as the
third or tenth, cannot be called harmonic.

In this canon the fundamental bafs moves with the perfect confonant fkip of cadence
paffing through all the notes in the natural fcale, accompanied only with the fifth and
octave, which changes alternately. The firft part begins with the fifth, which defcending
a tone, paffes to the octave of the fucceeding note of the bafs ; the fecond part, which

begins

Book II. Of the Composition oj MUSIC. 47

begins with the octave, keeps firm, and is changed into a fifth at the next note by the
motion of the bafs : The lame progreffion and combination are continued by the bafs and
the parts till the end of the canon j the two parts, when one defcends, the other keeps
firm, proceeding in this manner by fourths and fifths, in defcending the fcale together with
the bafs.

Firfl N. B. This canon being only confonant, and confequently not harmonic, cannot
fubfift in two or three parts ; but it is of ufe in five or more parts, for doubling the two
confonants, the fifth and octave.

Second N. B. The bafs in the fecond meafure in all canons of fimple progrefTion, and
alfo with the compound by feven, ufed in this chapter, being in the note F, paries to the
note B, which is a falfe fifth defcending, or a falfe fourth afcending, confequently the
note B being deprived of its perfect fifth, may be considered as a falfe fifth, as it is ;
but this falfe fifth B to5®, being prepared in the antecedent combination of the note F by F
its octave, pafTes as a juft fifth, and the ear is not offended. Moreover, thefe two notes B
and F, which are the two indicative notes of the natural fcale, muft neceifarily be diftant
fix femitones, by which notes muft alio the bafs fundamental pafs with its progreffion,
notwithstanding that the fame interval is not a perfect fifth ; otherways proceeding by a
perfect fifth, it tranfpofes immediately the fcale. There is another reafon which arifes from
the two principal liable and immoveable fundamental bafTes, but it is omitted, as the
explanation would be too long, and the above two reafons being Sufficient for practice.

Article II. Of the fimple Harmonic Combination.

CANON II. Plate 17.

*Tp HIS canon fhews the rule of ufing the fimple combination, commonly called the
-** common accord, which is compofed by the third, fifth, and octave.

The part which begins with a fifth does not defcend to the octave, as in the firft canon,
but afcends a tone higher to give the third to the fucceeding bafs note, which cannot be
done by the other parts in a gradual motion. The fame third afcending with the following
note, gives the octave to the bafs note, which octave having no other harmonic found, or
confonant, near to pafs into, muft reft in its place, as has been done by the fame octave
in the firft canon, becoming the fifth to the following bafs note j which fifth pafTes to
the third, and from the third to the octave, continuing the fame progreffion in all the
canon. The other parts proceed in like manner. The firft and fecond part moving by a
third and fourth between each other j and the fecond and third parts move by a fifth and
fixth between each other, all the parts proceeding in contrary motion to the bafs ; the bafs
defcending, and the parts afcending, as it appears in the canon.

Of doubling the two confonant Fifth and OBave, making fix real Parts.

CANON III. Plate 17.

HP HIS canon is formed by the union of the two antecedent, from which union the
■*• parts of the fifth and octave being confonant, confequently of a lefter fenfation in
refpect to the third, which is harmonic, therefore are doubled. In this canon is only to
be obferved, that the two parts which are doubled defcends with the bafs -, on the contrary
the three other parts afcend, as in the fecond canon.

By the contrary motion of the parts, the two confonant parts are doubled, without
proceeding in unifons in fifth and octave, with the other two parts : The third needs not
to be doubled in fimple combination, being perfectly harmonic ; if doubled, it would make
the parts lefs fenfible.

Article

48 Of /& Composition of M U S I C, Book II

Article III. Of the Q^^^mt Csmhinatkn.

CANON IV. Plate 18.

*[VTOW it muft be obferved in what manner the ample combination may be changed
T^ into the compound combination, which is done by adding of two of the luperior
thirds to the fimple combination, as the feventh and ninth, &c. The feventh found of the
natural fcale, or whatfoever fcale tranfpofed, or not tranipofed, is the firft third above the
other two thirds which compofe the fifth : This feventh is called by practitioner's diffonant ;
and difcord, or falfe, by the Italians, as well as other fuperior thirds, the ninth, eleventh,
and thirteenth ; but notwithflanding thefe terms (particularly that of diffonant) are
improperly ufed ; however, to prevent miftakes, we mail hereafter ufe the term of
difcord or falfe, and alfo the terms of preparation and refolution of the above difcords.

The feventh being confidered as difcord, confequently muft be prepared, which term
fignifies that it muft be before a concord in the preceding combination, (the concord
founds are the thirds, perfect fifths, and octaves) and after becoming difcord in the
fucceeding meafure, or note, it muft become again a concord in the fubfequent note ; and
this is called refolution of difcords, or falfes. Thefe difcords, with their preparations and
refolutions, not only regard the parts with the bafs, but alfo betwixt one another of the
fame parts. In this prefent canon, the feventh is prepared by the third, in the firft part,
and again refolved into a third, by defcending one note : The fecond part, which begins
with a fifth to the bafs note, afcends a note to the third, in order to prepare the feventh, in
the next note, which feventh is afterwards refolved into a third, both the parts continuing
the fame progreflion alternatively. The two parts proceeding betwixt each other by fourths*
refolved into fifths, as in the canon.

Of the Manner of adding the Fifth, and O&ave, to the above Canon,

CANON V. Plate 18.

IN the above canon is wanted the fifth, and octave, to make up the complement of the
* compound combination to the antecedent fourth canon, which has only the third and
feventh j but by adding the firft canon, they will compofe the prefent canon with the
third, fifth, feventh, and octave j where the two firft parts proceed betwixt each other by
feconds prepared by the thirds, and refolved into thirds j the fame proceeding as between
the third and fourth part j this fourth part, with the firft part, moves by fixths, and the
fecond with the third part by thirds, but the firft part with the third, alfo the fourth part
with the fecond proceeds from the fifths to the fourths, defcending the parts with the bafs,
two by two, as it is in the canon.

Of the Combination of the Ninth,

CANON VI. Plate 18.

"TPHE ninth, being a third above the feventh, which feventh being prepared by the
-*• third, and refolved into the third, confequently the ninth muft be prepared by the
fifth, and refolved into a fifth in defcending like the feventh. The two parts which
compofe this canon, gives alternately the fifth and ninth to the bafs, proceeding between
each other by a fifth and fourth, like the feventh.

The

Part I. 0/ A Composition cf MUSIC. 49

The Ride of i?itroducing the Ninth, inftead of the OElave^ with the Third,

Fifth, and Seventh.

CANON VII. Plate 18.

T> Y joining the fourth and fixth canon together, is formed the combination of third,
.-*-' firth, feventh, and ninth, inftead of the octave, as in this canon.

The ninth arifes from keeping firm the fifth, inftead of defcendmg to the octave j the
two parts which moves from the ninth to the fifth, proceed betwixt each other by fourths,
refolved into fifths ; the two higher parts defcend together by thirds, and alfo the two lower
parts ; only when the two firft parts move, the two lower keep firm, making a combination
of third, fifth, and feventh, between them all, and by the two fuperior parts defcending,
the feventh is refolved into a iixth, and the fifth paffes into a fourth, which refolves again
into a fifth ; likewife the two other parts afterwards defcending, the fixth becomes a feventh,
and the fourth a fifth, proceeding continually in the fame manner ; alfo betwixt the third
part, and the two fuperior, which makes an accord of third and fifth, the two higher parts
defcending become a fecond and fourth ; the third part afterwards defcending the fourth,
is refolved into a fifth, and the fecond into a third.

A T . B. In the fecond bar, or meafure of the firft part, the note G, which forms the ninth to
the bafs note, and it is afterwards refolved into the fifth F, in the following meafure, marked
thus *j may at firft fight feem a difcord, becaufe, being a falfe fifth, it may feem not prepared by
the antecedent note, as it is prepared in the fecond and third canon, where it is prepared by
the octave ; but here the ninth is confidered as an appogiature, which is a combination of
the fame antecedent note, inftead of the octave, which as octave of the principal relative
note of the bafs, fhould always be underftood j and as the fame note F is expreffed in the
antecedent meafure by the bafs note, this ferves for the preparation of the falfe fifth, and
notwithstanding that the falfe fifth is not prepared by its antecedent note, but the preparation
arifing from the other founds, or notes, which may fubfift in the fame combination, the ear
is not offended.

Of joining the clave to the above Ca7ton, making eight real Parts.

CANON VIII. Plate 19.

-HpHE difpolition of this canon into eight parts, confiftsin uniting the feventh canon with
•*■ the fecond, in the following manner. It muft take the four parts of the feventh
canon, which gives the feventh and ninth to the bafs prepared, and refolved, as in the
canon, and the three parts of the fecond canon ; by this means the fifths and thirds are
doubled, becaufe it being betwixt the feventh and the ninth to the bafs, the octave becomes
more fenfible, as dilTonant with the fame feventh and ninth : Beiides, as all the fuperior
thirds, excepting the fundamental feventh, very often ferves as appogiatures to the following
note, and particularly the ninth to the octave, confequently the fame ninth ferves inftead of
the doubled octave, and it is at the compofer's pleafure to ufe the octave, or the ninth. If
the compofer would fupprefs the ninth, and ufe only the octave, in that cafe the fecond
canon muft be joined with the fifth canon, by this means the octaves are doubled like the
thirds and fifths. But if the compofer would double the octave, at the fame time when the
ninth fubfifts, he muft add two parts more, which are the two confonant parts in the firft
canon; this will make a compofition of ten real parts, in which the part which defcends
from the ninth to the filth, proceeds continually by fourths, and confequently, when the
fame part which defcends from the fifth to the octave, is inferior to the other, which
defcends from the ninth to the fifth, it proceeds always by fifths ; which progreflion is

O . permitted

£0 Of the C o m p o s i T I o N of M U S I C. Book II.

permitted in compound and full combination, becaufe the harmony is not only complete^
•but alfo the octave is doubled, as is the fifth j but in fimple combination, it cannot fubfift.

Of faffing from one Difcord to another.

CANON IX. Plate 19.

THIS canon is compounded of three parts, which conftantly keeps firm in the firft
fimple combination belonging to the natural fcale, in which the bafs continues its
progreffion. The firft part begins with the third to the bafs, which third, according to
the rules of fimple combination, would afcend to the octave, but here it keeps firm for
the preparation of the feventh, as in the rules of the compound combinations ; this
feventh, which, according to the fame rules of compound combinations, ought to be
refolved in defcending to the third, but keeping firm in the fame note, is changed into
the eleventh, commonly called the fourth, by the motion of the bafs : This fourth would
have been refolved by the rules of the compound combinations, by defcending to the
third, but keeping firm, it is refolved into the octave, by the progreffion of the bafs,
which refolution- belongs properly to the full combination ; after that the octave paffes to
the fifth, as in the manner of the fimple combination, which fifth continuing firm in its
note, prepares the ninth, and this ninth continuing firm, is changed in the thirteenth,
commonly called the fixth, by the progreffion of the bafs, as in full combination ; at laft
this fixth, or thirteenth, is refolved by the fame bafs into the tenth, or, as commonly
called, the third. The other parts proceed in like manner, remaining always firm, all being
refolved by the progreffion of the bafs.

N. B. This canon cannot be of ufe in the progreffion, as it is, being formed only
to fhew the paflage of the feventh and ninth into another difcord, when the fame
feventh and ninth may happen in every one of the three parts which compofe the original
fimple harmony, fometimes may be continued one or both parts, which begins with the
octave, or with the fifth in a long progreffion of the bafs, without changing the fcale,
becaufe being both the octaves of the principal, and its guide, as immoveables, and
ftable fundamental, which, as has been demonftrated in the antecedent book, may both
continue under all combinations in fimple progreffion : In regard to the harmonic third
major of the fimple combination, it cannot be ufed freely, being too much fenfible, and
confequently it will confound the fimple combination, which belongs to the fucceeding
note of the progreffion of the bafs ; but in folemn mufic, where all the fimple combinations
are tripled, and the compound doubled, may be ufed on fome occafions, as in the canon.

Article IV. Of full Combination.

CANON X. Plate 20,

TH H E full combination by which this canon is compofed, is derived from the union of
-*- almoft all the antecedent canons. The firft three parts are the fame as in the ante-
cedent ninth canon, compofing the fimple combination to the loweft principal, immoveable,
fundamental baffes, and all together with the following parts, the fulL combination to the
other bafles. The two following parts, marked 4 and 5, are the two parts in the firft
canon, which doubles the two confonant fifth, and octave. The next eight parts, the
fixth, feventh, eight, ninth, tenth, eleventh, twelfth, and with the firft following bafs,
are the fame which compofe the eighth canon of the compound combination. The two
baiTes numbred 13 and 14, proceed betwixt one another from the unifon to the octave,
which in full combination are accounted two different parts, becaufe, ftrictly fpeaking, the
unifons are not the fame found as the octaves > but in compofitions of lefs than eight parts,
they are accounted only as one part, becaufe they have the fame combination, and confe-
quently

Part I. 0/ /fe Composition 0/ MUSIC, 51

quently the fame figures : Thefe two baffes are the fundamentals of the progrefTibil of every
harmonic combination, fo called to diftinguifh thenV from the laft two ftable and unmove-
able fundamental baffes, which continue firm to the end of the canon j the loweft is the
principal, and the other the guide, as mentioned in the firft book. In this canon all the
founds of the octave are continually combined in full or general harmony, in fimple and
natural progreffion of the perfect confonant fkip of cadence, which fkip is the principal
of all the progreffions, and to which every other movement are fubfervientand fubordinate.
It comprehends all the more natural and common proper preparations and refolutions,
as has been explained by the antecedent canons : But becaufe the full Combination is con-
tinued fucceffively all thro' the canon, it cannot be of any ufe in compositions of figurate
harmony, or common mufic, in which the fimple, or compound combination, muft be
mixed with the full combination, as will be explained in the laft book. Therefore this
canon is put here only to know the derivation of the full harmony, and as an epilogue,
or a fummary of all the antecedent canons, confequently it may ferve for a memorandum
of all the natural and common rules concerning the different combinations to this funda-
mental fkip of cadence.

Article V. Of the Seventh and JVinth paffing to another Difcord^ as

commonly ufed.

CANON XL Plate 21.

IN the ninth canon it was fhewn in what manner a found may be continued palling
from one difcord to another through all the octave, being at laft refolved by the bafs ;
but in this canon is fhewn the paffage of one difcord to another, and afterwards their proper
refolution in the fecond time, or in the fame note of the bafs in the following meafure,
the notes of the bafs being all doubled for this purpofe. The two firft parts make the
feventh and ninth in the fecond meafure ; and the third and fourth parts the fame feventh
and ninth in the third meafure ; each palling to the following meafure keeps firm the fame
notes which are changed by the progreffion of the bafs from the feventh and ninth into the
fourth and fixth, which are immediately refolved in the middle of the fame meafure, the
fourth defcending into the third, and the fixth into the fifth. The firft part which gives
the ninth fo the bafs proceeds with the fecond part by thirds, and with the third part by
thirds refolved into fifths, and the fame firft part proceeds with the fourth part by fixths
and fevenths, which fevenths are refolved fucceffively into fixths ; the fecond part with the
third, proceeds by a fecond refolved into a third, and with the fourth part proceeds from
third to third, as appears in the canon : Thefe fort of falfes may be called falfes of poftpofition,
becaufe the refolution is prolonged or poftponed.

How to refolve the Seventh a?id Nmth in afceitdmg.

CANON XII. Plate 21.

*T* H E refolution of the feventh and ninth in afcending muft be done as in the above
•*■ canon, to the fame note of the bafs, the notes being doubled to the purpofe, the
difcord, or falfe, falling in the firft note of the meafure, and their refolution in the fecond
note of the fame meafure, in that manner the falfes notes and their refolutions are diftinctly
and clearly perceived. In this canon all the parts proceed with the fame fucceffion of
notes : The fifth prepares the ninth to the firft note of the following meafure, and the
ninth is refolved by afcending to the third in the fecond note of the fame meafure ; the fame
third ferves for a preparation to the feventh in the next meafure, and in its firft note ; and
the fame feventh is refolved afcending to the octave in the fecond note of the fame meafure :
The octave paffes to the fifth in the following meafure, which fifth prepares again the ninth
in the next meafure, which is refolved by afcending to the third in the fame meafure,
continuing in this manner, as it is apparent from the canon. It muft be obferved in this

kind

52 0/ /Zv Compositio n of M U S I C. Book II.

kind of refolution of thefe falfes afcending, that the difcords derived from thefe preparations,
being the fame notes continued, inftead of afcending or defcending for the timple com-
bination to the motion of the bafs, by which they are changed in difcord, they ought
to be confidered as appogiatures in afcending ; but the belt appogiatures are thofe performed
in defcending than afcending, as being more natural, and confequently more pleafant.
Notwithstanding that the feventh when it properly is a fundamental indicative note defcending,
belonging to the fundamental guide, and when the fundamental guide keeps firm, it may
afcend to the octave of the fame guide, being its principal note, from whence it derives,
fo the refolution afcending may be equally good and pleafant : But the ninth refolving
afcending to the third it returns far from its principal note, viz. the octave, with a contrary
motion ; for this reafon it muft be ufed only upon fome particular occafions, as in grand
mufic, where all the parts are doubled and tripled.

Article VI. Of feme uncommon Combinations ', and firft ^ of Falfes by

Anticipation afcending.

CANONS XIII, XIV, XV. Plates 21, 22. .

A Nticipation is the contrary of the poftpofition, the notes which makes the firft combina-
***- tion to the bafs move afcending to the following combination, before the bafs moves
itfelf ; and this anticipation being the combination of the next note of the bafs, confequently
is a difcord to the exiftent bafs note, which difcord is refolved by the note of the following
motion df the bafs, as in the canons. In the thirteenth canon the note which makes the
third palfes to the fourth afcending, confequently the bafs has over it the combination
of the fourth and fifth, and the fourth ferves by way of anticipation of the octave of the
following note of the bafs ; and the part which makes the fifth, afcends to the third, which
prepares the fourth, which again is refolved by the motion of the bafs into the octave.

The fourteenth canon mews the manner of forming the anticipation with the fourth
joined with the fixth to the third and octave, which is done, as the above anticipation of
the octave by the fourth^ the fixth making the anticipation of the third, as in the canon.

The fifteenth canon is compounded of the thirteenth canon joined with the firft canon,
by which the two confonants are doubled, and the fame firft canon may be added to the
fourteenth in order alfo to double the confonants.

Of the Anticipations in defcending.
CANONS XVI, XVII. Plates 22, 23.

*~jn H E fixteenth canon is almoft the fame as the fifth canon, the only difference is, that
■* the fifth in canon V. defcends directly to the octave in the next meafure ; and in
this fixteenth canon it defcends into the fourth in the fame meafure, becoming the antici-
pation of the octave in the next meafure, confequently the combination in the firft part of
the meafure is the fifth and feventh, and in the fecond Part of the fame meafure it is the
fourth and feventh. The feventeenth canon is the fixteenth, with this difference, that the
feventh defcends to the fixth in the fame meafure, which fixth becomes the anticipation to
the third, as it appears in the above canon ; the bafs having the combination of the fifth
and feventh to the firft note of the meafure, and the fourth and fixth to the fecond note of
the fame meafure, which fourth and fixth are the anticipations of the third and octave.

N. B. It muft be obferved, that the anticipations in defcending arifes from the compound
harmony, where all the parts defcend with the bafs ; on the contrary, on the fimple
combination, as the parts afcend, and the bafs defcends, the anticipations muft .afcend with
the parts.

. Second

Part I. 0/ /& Composition 5/ MUSIC, 53

Second N. B. Thefe anticipations are only ufed in grand mufic of churches, where all the
principal parts are doubled, tripled and quadrapled ; and particularly, and almoft only, in
the full combination of long cadences ; and more particularly in the final and laft cadence,
which generally holds long for two, three, or more meafures ; and every meafure having
at leaft two accented times 3 we muft take care that the anticipation fall not upon the
accent time, but upon the part of the meafure which is nearefl to the conclusion, and
muft ufe them alfo very feldom, and with judgment, all thefe fort of difcords being of
unnatural preparation and refolution.

Article VII. Of the Difcords called by the Italian Maflers Falfes by

Change.

CANON XVIII. Plate 23.

~ ? H I S canon is compofed of ten real Parts to two chorufes, from which appears the
**■ rule and manner of changing the fuperior thirds or difcords, called falfes by change,
and their refolutions from one to another part.

The fecond part of the firft chorus makes in the fecond meafure the third, which is A
to the fundamental bafs, and in the fame fecond meafure, marked thus (A *) j defcend
from the third A in G, making the ninth to the fame bafs, which ninth is refolved into
the fifth to the bafs in the following meafure. The fecond part of the fecond chorus in
the fame fecond meafure, whofe firft note is G, ninth to the fundamental bafs of the fecond
chorus, and in the fecond time of the fame meafure, alfo marked thus (A *), afcends to
the note A, refolving the ninth into the third to the fame note of the bafs of the fecond
chorus : By this means the two fecond parts of the firft and fecond chorus change each
other their founds, and notwithftanding this change, both continuing the fame combination
to the bafs. The third part of the firft chorus in the fecond meafure, is in the Note F,
which is the octave of the bafs in the fame firft chorus, and this octave prepares the feventh
in the fecond note of the fame meafure, marked ( *) ; and the third part in the fecond
chorus in the fame fecond meafure, which alfo is marked (B *), has the note E, which
is the feventh to its bafs, which feventh is immediately refolved in the fame meafure by
afcending to F the. octave of the bafs, with the fecond note of the fame meafure : Thefe
two parts of the A fecond chorus change alfo their notes, without changing the compound
combination of their bafs ; only that the bafs of the firft chorus has the fimple combination
in the firft note of the meafure, and the compound in the fecond note of the fame meafure :
On the contrary, the fecond bafs of the fecond chorus hath its compound combination
in the firft note of the meafure, and the fimple in the fecond note of the fame meafure,
which difference changes not the order of the harmony, the total combination being ftill
continued notwithftanding the above change.

CHAP.

j 4 Of the Composition j/.M'.US I'C. Book II,

CHAP. II.

Of the Progreffion by the imperfect Confbnant Skip of the
Guide, with all its Combinations ; and firft with the
Confonant Combination.

Article I.

pS§tR§N this natural and fimple progreffion of the imperfect confonant fkip of guide,
Sj M defcribed in this chapter, the bafs from the principal note of the natural fcaie C,
1&& afcends to the fifth note G, which is its fundamental guide, but immediately
the fame note G changes the quality of guide, becoming the principal note of its own
relative fcale, becaufe it afcends fucceffively to the note D, which is its fifth note, and
confequently its relative guide j and by afcending the fcale with the progreffion of the fame
imperfecl; confonant fkip of guide, the harmony paries fucceffively through all the divers
guides of the fcales relative to the firft principal fcale, preventing by this manner the final
cadence, and by this means deceiving the expectation of the ear. The bafs, by this
progreffion, afcends the fcale, together with its two confonant notes, the fifth and octave,
alfo with the compound harmony ; but the fimple combination defcends in contrary
motion of the bafs, and of the confonant, and compound combination ; which proceeding
is the oppofite of the proceeding by the perfect fkip of cadence, by which the bafs,
joined with the confonant, on compound combination, defcends the fcale, and the fimple
afcends the fcale on the contrary motion of the bafs. In this progreffion of the guide, the
harmony can only proceed to the note E, becaufe the following note of this progreffion
is the note B, which is deprived of its confonant fifth in the natural fcale, having the falfe
fifth, which cannot be prepared in the antecedent combination of this progreffion. This is
the firft reafon which fhews the imperfection of the fame imperfect confonant motion, or
fkip of guide j and another reafon is, that it cannot be compounded immediately with the
two firft fuperior thirds, the feventh and ninth, becaufe they cannot be prepared in the
antecedent combination, which feventh and ninth, being the neareft difcord to the
principal note of the fcale, confequently are the propereft founds of the compound
combination.

CANON XIX. Plate 24.

TH HIS canon has the octave, which afcends to the fifth in the next note, and the
-*■ fifth keeping firm in the next meafure, is changed into the octave, proceeding in this
manner all along the canon, afcending with the bafs, without paffing the note E, for the
reafon above-mentioned.

"Article II. Of the fimple Harmonic Combination.
CANON XX. Plate 24.

r T* H E progreffion in this canon differs from that of the antecedent canon, (as mentioned
**• above) in which the two confonant parts afcend with the bafs, but in this canon the
parts all defcend contrary to the bafs. The combination differs from that of the fecond
canon of the antecedent chapter 5 in which fecond canon, by the motion of the perfect
confonant fkip of cadence, the fifth afcends to the third ; this paffes afcending to the
octave, and this keeping firm, is changed into the fifth ; but in this progreffion of the
imperfect confonant ikip of guide, the octave muft defcend to the third, and the third

defcends

Part I. 0/ A Composition 5/ MUSIC. $5

defcends to the fifth ; this fifth refting firm, is changed into the octave, by the motion
of the bafs.

CANON XXI. Plate 24.

'TPHIS canon mews the manner of doubling the two confonant notes, the fifth
-*■ and octave, which is done in the fame manner as the third canon, that is, by joining
the confonant combination of canon xix. with the following canon xx. becoming a
compofition of fix parts.

Article III. Of the Compound Combination,
CANONS XXII, XXIII. Plates 24, 25.

I N this progreffion there cannot be introduced the feventh and ninth, thefe not being
■*• comprehended in the antecedent combination, as mentioned before 3 but inftead of the
feventh and ninth, may be added the two fuperior thirds, the eleventh and thirteenth,
commonly called the fourth and fixth, which being far diftant from the fimple combi-
notion, are confidered as difcords j therefore thefe two founds, being part of the preceding
combination, may fubfift in the following combination, as in the two canons xxii. and
xxiii.

The canon xxii. fhews the manner of introducing the eleventh or fourth with the fifth,
the eleventh being prepared in the octave, and refolved into the third in the fame meafure.
The canon xxiii. fhews the preparation and refolution of the thirteenth or fixteenth, joined
with the eleventh, as it is expreffed in the canon. In this fort of fundamental combination,
the notes of the bafs, and of the parts, muft all be doubled, becaufe the refolution of thofe
difcords muft be done to the fame note of the bafs, which is the fame note as the firft,
and becomes a principal relative, which afcending to the fifth in the next meafure, the bafs
paries into its following relative guide, the fame order continuing in all the progreffion of
this canon. Thefe falfes in both thefe canons are properly falfes of poftpofitions.

Article IV. Of the Anticipations,

CANONS XXIV, XXV. Plate 25.

H E anticipation in this progreffion arifes from the feventh to the third, as in canon
xxiv. and from the ninth the anticipation of the fifth, as in canon xxv. The
1 feventh is prepared by defcending from the o6lave in the fame meafure, and afterwards it is
refolved by the motion of the bafs into the third. The ninth is alfo prepared in defcending
from the third in the fame meafure ; and in the next meafure it is refolved into the fifth,
by the motion of the bafs. The firft of thefe two canons has only the combination of the
. feventh, and the fecond canon is combined with both the feventh and the ninth ; the feventh
is the anticipation of the third, and the ninth to the fifth, as it is clearly defcribed in the
above canons.

N. B. Befides what has been faid in the fecond note, after canon xvii. at the end of
the article VI. chap. I. of this book, it muft be obferved, that thefe anticipations are
refolved contrary to the rule of refolutions, which is, that the difcord or falfes muft be
refolved by the fame parts, which makes the fame falfes in fyncoping, or moving. This
general rule has fome exceptions, but thefe exceptions feem not applicable to the anticipa-
tions in this progreffion of the prefent imperfect confonant fkip of guide j therefore the befr.
way is never to make ufe of them.

CHAP.

$& 0/ A Composition f MUSIC. Book II.

CHAP. III.

Of the perfe£t Auxiliar Skip of a Third low.

Article I.

H E perfect confonant fkip of cadence, by its proper motion, cannot gradually
afcend the fcale ; but by the help of this harmonic auxiliar fkip of a th.rd low, it
may afcend continually by tones and femitones.

CANON XXVI. Plate 26.

/ TpHIS canon only mews, that this perfect auxiliar harmonic fkip is not properly
■*■ fundamental in continual progreflion, but derived from the perfect confonant fkip of
cadence, to which it is particularly fubordinate, notwithftanding it bears all fundamental *"
combination, as its true fundamental bafs, which appears by the following canons.

Article II. Of the Simple Combination to the fuppo fed fundamental
Ba/s, which Combination is compounded i?i the true fundamental Ba/s.

CANONS XXVII, XXVIII, XXIX, XXX. Plates 26, 27.

*TP H E following four canons have every one two bafTes ; the firft, which is the fuppofed
-■• fundamental bafs, defcends continually by thirds, but the loweftis the true one.

The canon xxvii. is with fimple combination to the fuppofed fundamental bafs, but the
fame combination becomes compound to the true fundamental bafs, becaufe the note which
makes the fifth to the firft bafs, is the feventh to the fecond, the very fundamental bafs ;
and this feventh is refolved into the octave, by afcending to the fame note of the fecond
bafs, its octave; which octave keeping firm, it changes into the third of the fuppofed
fundamental bafs, but is the fifth to the true fundamental bafs. This manner of reiblving
the feventh, in afcending to the octave of the bafs, is always good, as mentioned in the
explanation of canon xii. plate 2 1 .

The canon xxviii. fhews the rule for adding the feventh to the fuppofed fundamental
bafs, which feventh is the ninth to the true fundamental with its refolution in defcending ;
the refolution of the feventh into the octave, is a refolution by fuppofition, becaufe the
feventh is in the place of the ninth to the true fundamental bafs, and this refolution into
the octave in defcending together with the fuppofed bafs, pafies for good, for being the
proper refolution of the ninth, notwithftanding that the firft bafs defcending a third in the
fame time that the part defcends a fecond, the fame bafs muft neceffarily proceed by two
octaves, not explicit, but implicit : Moreover the fame refolution is not only fupported,
as being by fuppofition, but alfo becaufe the combination of the founds is complete, in
which the two Octaves, or two fifths following each other, are confidered as double parts.

In canon xxix. the firft bafs has the feventh and octave combined in the firft notes
of the fecond and the following meafure, and the feventh and ninth to the fecond note of
the fame meafure ; but the two notes in every meafure of the fundamental bafs being the
fame notes, they have continually the combination of the feventh and ninth. The deriva-
tion of thefe falfes, and their refolutions, appear very clearly by their canons. The fuppofed
fundamental bafs defcending a third, and the part which gives the feventh keeping firm
the fame note all the meafure, the fame feventh is changed into the ninth in the iecond
part of the fame meafure by the motion of the fuppofed fundamental bafs ; as likevvife the

fifth

Part I. 0/ /& Composition c/ MUSIC. $j

fifth into the feventh, and the third into the fifth ; therefore both the notes of the meafure,
being part of the proper combination to the fame bafs, confequently the firft notes of every
meafure are falfes of fuppofition, which by the motion of the fame bafs in the fame meafure
are changed into the proper fundamental falfes in the fecond notes, which after are refolved
by fuppofition of the fuppofed fundamental bafs with the firft note of the following meafure,
as it is clearly apparent in the canon.

The canon xxx. has the refolutions of all the compound combination in afcending,
before the fundamental bafs moves j confequently in the fuppofed fundamental bafs all the
falfes and their refolutions are by fuppofition.

N. B. The refolution of the ninth afcending a full tone to ihe true fundamental bafs,
becomes a little harfh, as its proper refolution is in defcending to the octave, which is its
principal note; therefore the refolution of the ninth afcending, when the hses fundamental
baffes fubfift, muft only be ufed in full harmony, where all the notes are doubled and tripled.

CHAP. IV.

Of the perfect Auxiliar Skip of Third low joined with the
perfect Confonant Skip of Cadence.

Article I.

H E perfect auxiliar harmonic fkip becomes fundamental, when it is followed by
the two confonant perfect and imperfect flaps, but properly with the perfect
confonant fkip of Cadence, which is the fubject of this article.

CANON XXXI. Plate ij\ ~

TH E bafs in this canon defcending by its firft motion a third in the fecond part of
the meafure, becomes the relative guide to the following note in the next meafure
to which following note in the next meafure it moves with the fundamental fkip of cadence.
The octave, and the third in the fecond and third parts, keeping firrn all the meafure
are changed, the octave into the third, and the third into the fifth, by the fecond note of
the bafs in the fame meafure, and in the next meafure the fifth afcends to the third, and
the third in the lower part afcends to the octave. The firft part, which begins with the
fifth to the bafs, paries to the octave in the fame meafure ; and the octave in the next
meafure is changed into the fifth by the motion of the bafs.

N. B. It muft be obferved in thefe canons, that as the progreflion of the bafs is made
with different fkips, confequently the combinations muft be different. In the auxiliar fkip
the octaves and the third keep firm, and in the confonant fkip of cadence the third paffes
into the octave, the octave is changed into the fifth, and the fifth afcends to the third as
has been fhewn in the canons of the progreflion of the fame perfect fkip of cadence in
the firft chapter.

Q~ Article

5 8 Of the Composition 0/ MUSIC. Book II.

Article II. Of the Compound Combination to the fame Progrefion.

CANONS XXXII, XXXIII, XXXIV. Plates 27, 28.

TH E principal thing to be obferved in thefe three canons is the manner of preparing
and refolving the fuperior thirds or difcords, which manner differs in the auxiiiar fkip
from that of the confonant fkip of cadence, as above-mentioned. In the fkip of cadence
the feventh is always prepared by the third, and refolved into the third, as may be feen in
the canons of the third article, chap. I. But when the bafs fkips a third low, or a fixth
high, as in the canons of this fecond article, the fifth keeping firm, prepares and becomes
the feventh, which is refolved into the third, becaufe the bafs then moves with the fkip of
cadence -, but when the fame feventh is prepared by the third in the fkip of cadence,
as in canon xxxiii. the fame feventh becomes the ninth by the bafs note failing a third,
which ninth is refolved into a fifth by the fkip of cadence, according to the rules for the
refclutions in the fame fkip. Likewife the ninth when prepared by the fifth in the fkip of
cadence, inftead of being refolved into the fifth, it is refolved into the third by the auxiiiar
fkip : Alfo the feventh, when it is not joined with the ninth, is refolved into the octave
by the fame auxiiiar fkip, as in canon xxxii. In the fame canon xxxii. is the rule for
joining the feventh with the o&ave ; and in canon xxxiii. is fhewn the rule for joining the
feventh with the ninth only in the fkip of cadence ; and in the following canon xxxiv. is
the rule for joining the feventh and ninth to both the fkips of the progrefTion in the com-
pound combination of eight real parts, which is made by joining the canon xxxi. with
any one of the two following canons.

C H A P. V.

Of the fame Harmonic Skip joined with the imperfect

Confonant Skip of Guide.

CANONS XXXV, XXXVI. Plate 28.

H E canon xxxv. fhews, that this fkip, joined with the fkip of guide, cannot be
continued, but only for a few meafures, becaufe the note B has not its perfect
fifth in fimple and natural progreflionj and the canon xxxvi. fhews, that the
perfect auxiiiar fkip is improper with the fkip of guide, becaufe there is another better
fundamental bafs, which is the propereft fundamental - 3 therefore it is evident, that this
harmonic fkip a third low, or a fixth high, can only properly be joined with the perfect
confonant fkip of cadence, from whence it derives, and to which it is its proper auxiiiar
fkip.

C PI A P.

Part I. 0/ /& Composition c/ MUSIC. 59

CHAP. VI.

Of the imperfect Auxiliar Harmonic Skip of a Third high,
or a Sixth low, in continual Progreffion.

CANONS XXXVII, XXXVIII. Plate 29.

H E lower bafs is added to both thefe two canons, in order to fhew, that the
firft bafs, which afcends by thirds, is not fundamental, but derived from the
imperfect confonant fkip of guide, by which fkip of guide the lower true
fundamental bafs moves, notwithftanding that the firft bafs, which proceeds
by the perfect auxiliar fkip, may be treated as fundamental, namely, joined with the
fundamental combination of founds, but cannot be long continued in fimple and natural
progreffion, for the imperfect fifth to the note B.

In canon xxxvii. the third part, which begins with the octave to the bafs notes,
defcends in the fame meafure, and gives the fifth to the fecond note of the firft fuppofed
fundamental bafs, which fkips a third high, which fifth is the feventh to the lower true
fundamental bafs ; and this feventh, which is the fifth to the firft bafs, fuppofed funda-
mental (as above-mentioned) properly is an anticipation of the third, in the next meafure
to both the banes. Alio in canon xxxviii. the feventh to the fuppofed fundamental bafs,
which is the ninth to the lower true fundamental bafs, is an anticipation to the fifth, in the
next meafure; and really eveiy note in both thefe two canons, are all anticipations, and very
difagreeable to the ear ; and if they can be fuffered, muft be only in quick movements,
as paffing notes.

Of the fame Auxiliar Skip, joined with the perfeSi Skip of Cadence*

CANONS XXXIX, XL, XLI. Plates 29, 30.

fP ~T % H E canon xxxix. is with fimple combination, and the canon xl. with the compound
-*■ combination, which combinations are fufficiently explained by looking on the faid
canons.

The canon xli. fhews, that the other two antecedent canons are improper, and confe-
quently cannot give any pleafure, having the fame improper foundation.

N. B. It muft be obferved, that in this progreffion of the firft note of the bafs,
fkipping a third high to the fecond note in the fame meafure, the combination paffes by
the guide, with the fkip of cadence, into the firft notes of the following meafures,
confequently all the firft notes of each meafure may be confidered as principal, and the
fecond notes of the fame meafure, as relative guides ; and as all thefe principal firft notes are
diftant a third between themfelves, in defcending a third low, the progreffion becomes
improper, becaufe it cannot be fundamental, as has been demonftrated by canon xxvi. with
this difference, that the progreffion in the faid canon xxvi. defcends directly and fucceffively
by thirds, and the proper foundation of the fame progreffion is the fimple natural fkip of
cadence ; but in this prefent canon, as in the two antecedent canons, the progreffion being
made by two different fkips, confequently its true fundamental bafs muft be different from
that of the faid 26th canon, as it is in this canon ; from which it appears, that the three
following notes defcending by thirds, notwithftanding they are joined with another fkip,
cannot Jae all fundamental, but one or two ; the fundamental bafs cannot conftantly fubfift
in a like progreffion, as it appears in the two above canons xxxix, and xl.

CHAP.

60 Of the Composition c/ MUSIC. Book II.

CHAP. VII.

The fame Auxiliar Skip joined with the Skip of Guide.

CANON XLII. Plate 30.

HIS canon is added here to demonftrate, that the progreflion of the imperfect
auxiliar flcip, joined with the imperfect confonant fkip of guide, is improper for
many reafons ; the firft is, that in the courfe of the progreflion, the harmony will
fall upon the note B, the falfe fifth of which cannot be prepared ; fecondly,
that all the firft notes of every meafure paffing by the fecond skip of guide into the firft note
of the following meafure, only diftant a fecond below the firft note of the antecedent
meafure, and becaufe, that the fame progreflion may more properly be made by the
Ample procefs of the perfect confonant skip of cadence, in which procefs the falfe fifth to
the note B, is prepared, as has been explained in the firft and fecond canons of chapter I.
confequently the skip of third high, joined with the skip of guide, becomes unnatural,
and improper in its progreflion ; therefore, from what has been faid, this skip of third
high, joined with the skip of guide, is of little ufe in fimple, natural progreflion ; and it
muft be ufed with moderation upon fome occafions, but never in continued progreflion.

— \ — _

C HA P. VIII.

Of the divers Combinations to the fimple and natural Pro-
greffion, with all the four Skips of the fundamental Bafs.

CANONS XLIII, XLIV, XLV. Plates 31, 32.

; H E S E three canons contained in this laft chapter of the firft part of this
Harmonic Code, are compofed by the four fundamental skips, the two confonant,
and the two harmonic auxiliar j confequently the preparations, and the refolutions
of the difcords become different, every one being relative to its particular skip of the
bafs, as has been explained in their refpective canons.

The canon xliii. is in fimple combination, and the xlivth in compound. The canon
xlv. fhews the manner of introducing the full combination, according to the particular rules
to every fundamental skip. To the fame laft canon xlv. of full combination, is put under
the firft bafs, a fecond bafs ; the firft is the fundamental bafs of progreflion, the fecond is the
fundamental, ftable, and immoveable bafs, which has in its firft note the principal note
of the fcale, joined with its fifth, which is its fundamental ftable guide, into which it paries
immediately with the following note in the next meafure, and continues firm to the laft
meafure, in which it refolves, returning in the firft note of the fcale, which is the principal
ftable foundation of the fame fcale, as has been explained in chapter IV. article I. firft book.
In the firft meafure of the fame canon, the bafs has the firft principal fundamental note of
the fcale, which has its fifth joined above it; in the fecond meafure it partes directly,
joining its fifth, which is its fundamental ftable guide, at the fame time that the fuperior
fundamental bafs of progreflion, moving with the skip of cadence, pafl'es to the note F,
which is the fubprincipal relative of the fcale natural : Thefe two different motions happen-
ing at the fame time, may at firft fight be fuppofed a difcord, becaufe the note F was not
in the antecedent combination, but was the note G, as fifth, and fundamental guide, which
as fimple fifth was joined in the firft meafure to its principal, which, as before faid,

becomes.

Parti. Of the Composition c/ MUSIC. 61

becomes, in the fecond meafure, the ftable fundamental guide, which by the fame note in
the firft meafure, upon the fame bafs, prepares the note F, in which the firft bafs of
progreffion has parted ; alfo its third, which becomes the ninth to the under bafs ftable ;
and in regard of the other fuperior thirds to the fame note F, as the fifth and feventh, which
are alfo prepared by the antecedent combination ; thefe become the eleventh and thirteenth
to the ftable fundamental bafs, which in this manner has the full combination of the
feventh, ninth, eleventh and thirteenth, as is exprefled in the canon. The following meafure,
in which the fundamental bafs of progreffion paffes to the note D, with the compound
combination of 3, 4, 5, 6, 7, 8, 9, the combination of the ftable fundamental bafs is
augmented with the fifth, which properly is the twelfth ; and in the following fourth
meafure, where both baiTes are united, both have the fame full combination, which is
refolved into the fimple combination in the next meafure, paffing with the fame fimple
combination into the final note of the cadence. From this canon it appears, that the
fundamental feventh fometimes may be ufed without apparent preparation in final
cadences, fuppofing the principal note doubled j but in this cafe the harmony muft be
complete, confequently it cannot be ufed in lefs than four parts. The other feventh, which
is not fundamental, but relative, muft be always prepared.

Here is the end of the explanation of the canons relative to all forts of combination of
founds belonging to the fimple and natural progreffion j therefore we fhall pafs to the
fecond part, which contains in its canons all the laws and rules of the combination of
founds belonging to the mixed and varied progreffion in its fucceffive order, and fhewing the
proper manner of tranfpofing the two principal fcales, natural and artificial, in every femi-
tone of the fcales of tranfpofition.

THE

Of the Composition vf MUSIC

Book II.

THE

HARMONIC CODE.

PART II.

N the firft part of the Harmonic Code has been fhewn all the laws and rules
of all pofiible combinations of founds belonging to every one of the funda-
mental motions of the bafs in the fimple and natural progreflion, through all
the eight original founds. And in this fecond part will be fhewn the fame
laws and rules of every combination of founds belonging to all the fame
different fundamental motions of the bafs, but in mixed and varied progremon, namely,
the bafs pafling through all the thirteen founds of the fcale of tranfpofition.

Firft N. B. In the mixed progreflion all tranfpofed fcales become principal of their
own fcale, confequently every one has its {even relative fcales, in which the progreflion may
pafs at pleafure with its proper harmony.

Second iV. B. The founds of the tranfpofed fcales muft be in the fame order of the
principal fcale, from which they are derived ; if derived from the natural fcale, the third
mufl be major, the fourth, fifth, and octave, all perfect; and the fixth, feventh, and
ninth all major; the feventh to the guide, which in general muft be flat, but on fbme
>occafions may be major, and the tranfpofed fcales from the artificial fcale, the third mufl: be
minor, the fourth, fifth, and octave, all perfect: ; the fixth and feventh in defcending the
fcale muft be flat, but both fharp in afcending ; the feventh to the fundamental guide mufl:
be flat, as alfo the ninth, but on fome occafions the ninth may be ufed fharp, as will appear
from the canons,

"Third N. B. The beft and moft pleafant manner of compofitions, is not only derived
from the perfect knowledge of all combinations of founds, and their propereft and
natural progreflion, but alfo from the good tafte of the compofer, in regard to the juft and
beft application of the fame combinations and progreflions to the different expreflions, as
gay, or pathetic, from which arifes many particular rules ; between thefe rules the
harmony requires an eafy and proper variety, by which the human fenfation is extremely
delighted ; confequently the progreflion of all thefe canons defcribed in the Harmonic Code,
being continued all along the whole octave, in the firft part, and all along the femitones in
the fecond part, becomes improper and tirefome, and many, particularly in the fecond
part, impracticable, becaufe the bafs moving continually with perfect fifths defcending or
afcending, fome parts in the combination are obliged to proceed continually by full tones,
contrary to the order of the gradual progreflion of the natural fcale, which proceeds by
tones and femitones ; and this order muft be followed in all forts of progreflions, and their
combinations ; therefore all thefe canons contained in this Harmonic Code, muft be
confidered, not in their continual progreflion, but only in their feparate particular pro-
greflion, as only in three or four motions, having been compofed all along the octave,
and all along the femitones only, to fhew all the particular combinations and progreflions'
in pafling from every tone and femitone to their nearer tone and femitone by the different
motions or fkips of the fundamental bafs; and not for an example of a long progreflion,
which muft always be avoided.

C H A P.

Part II. 0/ /fe Composition c/ MUSIC. 63

CHAP. I.

Of the perfect Confonant Skip of Cadence tranfpofing the
Natural Scale into all the Semitones, with only the
Confonant Combination.

Article I.
CANON XL VI. Plate 33.

ps§|^GHIS canon fhews in what manner the fundamental bafs, joined only with the two
«$) T |p confonant fifth, and octave, paffes through all the twelve intervals of the fcale of
-"t^SS&tlS tranfpofition, tranfpofing the natural fcale into all the thirteen founds of the fame
fcale by its perfect confonant fkip of cadence : By this means there arifes thirteen fcales, all
principal ; but the laft being the fame as the firft, is excluded, twelve remaining only,
which are different in their founds, but not in the order of their intervals : The fifth note
of every fcale is always the fundamental guide to the fame fcale, and its principal note
becomes alfo the fundamental guide to the next tranfpofed fcale, confequently the bafs
proceeding continually with its fkip of cadence, every note muft be confidered as principal
of their own fcale and guide fundamental to the next note.

£T

Firjl N. B. In fimple prpgrefiion the bafs cannot go out of the eight original founds
of the natural fcale ; and this is the reafon that one of its fifths muft be falfe, which is
that from B to F afcending, or from F to B defcending, as has been explained by the
fecond note, at the end of article I. chap. I. of the firft part j but in mixed progreflion,
where the bafs can have its perfect fifth, by uiing the femitones of the fcale of tranfpo-
fition, it paffes fuccefiively through all the thirteen founds of the fame fcale of
tranfpofition.

Second N. B. It muft be obferved, that in the feventh meafure of this confonant canon,
the bafs paffes from G flat to B natural ; this may be taken for a falfe fkip of cadence, but
G flat being the fame found as F fharp, both which are diftant from B natural {even
femitones, confequently is a perfect confonant fifth defcending ; alfo the fifth of G flat is
D flat ; from this D flat defcending to B natural, as it is done by the fuperior firft part of
the canon, may feem a fkip of a third low ; but D flat being the fame found as C fharp,
diftant a tone from the fame B, confequently it defcends only a fecond, and not a third ;
alfo the octave of the fame G flat in the fecond part, pafling to F fharp, changes the name,
but not the found, which conftitute the fame. All which fhews clearly, that the different
denominations cannot alter the founds, which are always the fame ; and alfo fhews, that
the diftinction of the major arid minor femitone is incompetent to the melody and
harmony.

'Third N. B. When in the beginning of a compofition next the key, is found a diefes, in
Engli/h called a fharp, this diefes, or fharp, augments a femitone all notes comprehending
its octaves grave and acute, which belong to the fame place where the diefes is put ; and
when it happens in the courfe of the compofition to augment the fame notes of another
femitone higher, is put this mark ( x ) called improperly diefes enharmonic, but better in
Engli/b, extreme fharp, as mentioned in article VIII. chap. VI. likewife the b mole, which
diminifhes the natural note of a femitone, when this b mole, or flat, is put at the beginning
of the compofition next the key, in this cafe, another b flat being put to the note, which
has the flat at the key, the fame note muft be diminifhed another femitone ; as for
example, the iign b, in the place of the found called B natural, at the key, all the notes of

the

64 Of the Composition «/ MUSIC. Book II.

the fame B natural, comprehending its. Octave, grave and acute, are tranfpofed in B flat,
which is a femitone lower ; and when, in the progrefs of the compofition another b mole,
or flat, happens to the fame b flat, this diminishes it another femitone, and becomes A
natural, which is called B extreme flat, as may be found in fome of the canons.

Article II. Of the fame Iranfpoftiony with tloe fimple Harmonic

Combination. .,

CANON XLVII. Plate 33. /

^"T^ HIS canon being in fimple combination, and as the natural fcale is formed with a
■*■ major third, fifth and octave both perfecl:, fo likewife in all the tranfpofed leaks, by
which the bafs pafTes, the fimple combination muft be in the fame order with the third
major, perfect fifth and ocfave, as in the canon.

Article III. The fame Tranfpofition with the compound Combination of

the Seventh.

CANON XLVIII. Plate 33.

T N the firft chapter of the firft part of this code, Articles iv. and vi. it has been (hewn,
■*■ that in the perfect confonant fkip of cadence the feventh is always prepared by the third,
and the ninth by the fifth, and refolved into the fifth ; but as in the firft part of this code
the harmony proceeds only from one found to another of the natural fcale, in which the
principal note, its fourth, and its fifth, have all their thirds major ; and the others, as the
fecond, third, fixth and feventh, have all their thirds minor j confequently when the funda-
mental bafs proceeds with the fkip of guide in the fame natural fcale, the feventh will be
major, or minor, according to the antecedent third from which it is prepared ; alfo the ninth,
if the fifth by which it is prepared is falfe, will likewife be minor ; as when the bafs pafTes
from B to E the ninth is minor, becaufe the fifth to B is F natural, which is a falfe fifth
from which it is prepared, and confequently the ninth being alfo diftant a femitone from
the octave, and the above preparation by the falfe fifth, is fupported, as has been demonftrated
in the fecond N. B. of the firft article, firft chapter, in the firft part of this code. But in
the mixt progreflion with the fame ikip of cadence, as all the notes which the bafs pafTes
through are principal of a new tranfpofed fcale, and at the fame time fundamental guide of
the next note, into the fcale is fucceflively tranfpofed, and having, as fundamental guide
the major third its indicative note, confequently this fame third mult prepare the following
feventh, which is fundamental and indicative note, becaufe a principal note of a new fcale
follows ; therefore the fame feventh as fundamental indicative defcending, muft be minor,
or flat j for this reafon the major third, which muft ferve as preparation of the above feventh
in the antecedent meafure, muft be diminifhed in the next meafure of a femitone, to make
the flat feventh, as may be feen in this canon. JB% this feventh being diminifhed a femi-
tone from the note by which it has been prepared, confequently it has been prepared by
a different found, the third major being not the fame found of the third minor ; therefore
the preparation is improper, and rigoroufly falfe,, #Qtwithftanding that this fort of prepa-
ration are fuppofed good by almoft all the cpmpofers of mufic, becaufe they make no
diftinction betwixt the major and the minor third, when they ferve for the preparation of
any difcord ; but a better reafon is, that the major third, is the fundamental indicative
afcending note, and changing from the major into a minor, it becomes the fundamental
feventh, and it is changed in this manner from the indicative note afcending into the indi-
cative defcending note, and the bafs note is alfo changed from the principal note into the
fundamental guide j this kind of feventh may be fupported without preparation, being
fundamental.

N.B. This

as.

Part II. 0/ /& Composition «/ MUSIC. 65

N. B. This fort of combination may pafs for a few meafures in fome pathetic expreffions ;
but in a long progreffion, as in the canon, it becomes tedious and tirefome ; for which
reafon it is better not to change the major third into a minor third for the preparation of
the feventh, by which means all the notes preferve the quality of principals of their own
fcales ; but the quality of the fundamental guide is changed into a relative guide to the next
note, as it is in the "following canon.

Of the fame Tranfpofition with the Seventh and Ninth », both natural^ as in

their refpe&ive Scales.

CANON XLIX. Plate 34.

IN this canon becaufe the feventh is not minor, but natural, as it is in its proper fcale,
confequently it is not fundamental, but only a relative guide ; the ninth which is added,
becomes alfo relative, notwithstanding it may fubfift as fundamental, being the tranfpofition
of the natural fcale, and the whole progreffion is made by perfect fifths from which they
are prepared, and into which they are refolved.

Of tranfpofing the artificial Scale with fimple Accord.

CANON L. Plate 34.

HP HIS cannon mews the manner of tranfpofing the artificial fcale with fimple com-
**■ bination, namely the minor third, fifth, and octave, by the above fame progreffion ;
which combination muft be ufed in every found where the fame fcale may be tranfpofed.
All the notes in this canon are principal of their own fcale, and at the fame time guides, but
relative to their fucceeding note, and not fundamental, becaufe their firft third is not major,
as it muft be major in the combination belonging to all fundamental guides, as has been
explained.

Article IV. 'The fame Tranfpofition with the compound Accord of the Seventh.

CANON LI. Plate 34.

T"* HIS canon wants no explication ; the feventh being very well prepared by the minor
-*• third, and very well refolved into the minor third : All notes are principal of their own
fcale, and guides relative to the next tranfpofed fcale.

Of the fame Tranfpofition with the Ninth inflead of the O&ave.
CANON LII. Plate 35.

THERE are two different ways of joining the ninth to the feventh inftead of the
eighth, that is, either with the major or minor ninth. It was mentioned in the fixth
Chapter, Article iv. of Book I. that the artificial fcale had two fcales, one for afcending,
the other for defcending ; in afcending the fixth and feventh are major in all fcales
tranfpofed from the artificial ; but in defcending, the fixth and feventh muft be minor ;
the major fixth in afcending belongs properly to the order of melody; becaufe, as men-
tioned, the melody cannot gradually pafs to the next feventh, which muft necelfarily be
lharp to afcend to the octave of the principal note; confequently this major fixth can
only belong by accident to the bafs note in the fundamental guides of the artificial fcales,
in changing the fame fundamental guides into relative guides, which fundamental guides
muft have the combination of the major third, fifth, and octave ; and when the fame
accord is joined with the feventh and ninth, thefe muft both be flat, or minor : but in this

S prefent

66 Of the Composition of MUSIC. Book II.

prefent canon, the guide being deprived of its (harp third, which is the neceffary indicative
note of the fucceffive fcale, confequently it cannot be fundamental, but • only relative,
which relative guides are always improper in tranfpofing the fcale ; and when the guide is
fundamental, the fifth of the antecedent note muft be diminifhed a femitone for the flat
ninth belonging to the fundamental guide, which ninth becomes a minor fecond to the
©clave of the fame guide ; and this fecond to the octave note, or minor ninth to the bafs,
being done in moving both parts, confequently is not properly prepared, notwithftanding it
derives from the fifth of the antecedent note, but derives from the fame name, and not
from the fame found. For example, the fifth to the firft principal note C, as in the canon,
is G natural, the bafs pafhng into F, the fame note G fifth muft be diminifhed one
femitone for the minor ninth to the bafs note F, and G natural becomes flat ; it is the
fame G, but being, flat, the found is changed, and altered one femitone : Befides the
fame combination of the fifth pafiing into the ninth proceeds always by falfe filths one
with another, which together become not very pleafant to the ear ; for thefe reafons the
major ninth becomes lefs unpleafant, being prepared by the perfect filth without any altera-
tion in the founds, and in the progreflion the fifth and ninth move by the fourth and fifth,
notwithftanding that it is always improper in a long progrefiion, becaufe the tranfpofition
of the fcaies muft be done by the fundamental guides, and not by the relatives : Therefore
the beft way of proceeding with the combination of the ninth, in changing the fcale, is in
doubling all the notes of the parts and the bafs 5 in this manner may be diftinguifhed the
principal notes from the guides, as it is done in the following canon.

N. B. Here is put only a canon with the major, or natural ninth, which canon may be
eafily changed in puting to every ninth a flat, to have both the canons of the two
manners of imploying the ninth.

Article V. Of the fame Tranfpofition in the heft Maimer.

CANON LIII. Plate 35.

' I "" HIS canon fhews the beft manner of fucce0ively tranfpofing the artificial fcale, with
* and by the proper fundamental guide in compound combination with its major third,
perfect fifth, feventh and ninth both flat; this muft be done by doubling the notes of every
part, and the bafs in all the meafures, as it is in the canon. The firft bafs note of every
meafure is a principal note of its own fcale joined with its fimple combination of minor
third, fifth and octave. The fecond note in the fame meafure, which is the fame as the
firft note, is the fundamental guide to the next principal note in the following meafure j
which note being tranfpofed from the antecedent artificial fcale has the fame combination
of the minor third, fifth and odtave, proceeding in the fame manner through the canon.
All the firft notes are principal, and the fecond notes of every meafure all fundamental
guides, with their proper compound combination of the indicative afcending major third,
fifth, feventh, and the indicative defcending ninth. The firft part in the canon, which
gives the minor third to the bafs principal note, this minor third is changed in the fecond
note of the fame meafure into the major third indicative of the following firft principal
note of the tranfpofed fcale in the next meafure, in which meafure the fame indicative
third major afcends to the octave of the principal note in the bafs ; and this octave defcends
into the feventh with the fecond note of the fame meafure ; which feventh is refolved into
a minor third of the next meafure, and this minor third being again changed in the
indicative major third, afcends as before to the octave, proceeding continually in the fame
manner. The fecond part, which gives the octave to the bafs in the firft meafure, and in
the fecond meafure it is changed in the fifth from which it paries in the following meafure
to the minor third, in the fecond note of the fame meafure defcends to the ninth, which is
the indicative defcending note of the fundamental guide of the artificial fcale, and in the
following meafure defcending a femitone it refolves into the fifth ; which fifth keeping firm
all the meafure, in the next meafure afcends to the minor third, which defcending a full

tone
%

Part II. Of the. Composition j/ MUSIC. 6y

tone paries to the ninth, as before, proceeding always in the fame manner : All the others
proceed alfo in the fame manner as the above two firft. By this means the fimple com-
bination belonging to the artificial, and its tranfpofed fcales, paries into the compound
accord with its fecond note, the bafs keeping firm its proper fundamental note, and the
compound combination is refolved again into the fimple combination in the next meafure,
as it clearly appears in the canon ; in which are fome notes with double flats, as has been
mentioned in the third N. B. at the end of the firft article of this chapter, to which double
flats we muft take care ; and to avoid miftakes, the fame note has been abundantly marked
with a crofs under the double flat note, as it is in this canon.

Article VI. Of tranfpofing the 7tatural Scale with the Refolution of the

Compound Combination afcendi?zy.

CANON LIV. Plate 36.

THIS canon is alfo formed by dividing the notes of every meafure. The feventh
arifmg from the third in the antecedent meafure, is refolved by the fecond note of the
meafure in afcending to the octave ; and the fifth prepares the ninth which is the firft note
in the next meafure, which ninth is refolved by afcending to the third in the fecond note
of the meafure ; the third prepares again the feventh as above, and as above it is refolved,
proceeding always in the fame manner, afcending in contrary motion to the bafs.

Firft N. B. The feventh is properly prepared and refolved, but the ninth would be better
refolved by defcending to the octave, for the reafon mentioned at the end of the explanation
of canon xii. in the firft part of this code ; but in fome cafes it may be refolved in afcending,
as in the canon.

Second N. B. In this canon all the firft notes of every meafure are deprived of their
thirds, which are the principal harmonic founds ; and that happens from the uncommon
refolution by afcending, which properly are appogiatures, but fomewhat improper, as men-
tioned before : Therefore this canon has been put here only to fhew the manner of pre-
paring and refolving the fuperior thirds (called falfes) by afcending, when on fome occafions
it becomes neceffary in compofitions in five parts.

'Third N. B. The fame canon may be augmented to more parts in the fame manner as
has been done in cannon xviii. which , is in ten real parts in two chorufes in the firft part
of this code, and by the addition of the parts all the compound combination will be full
of the falfes alfo of change, as in the above canon xviii.

CHAP.

68 Of the Composition of MUSIC. Book II.

CHAR ir.

Of tranfpofing both the Scales, natural and artificial, by the
imperfect confonant Skip of Guide in fimple Combination.

CANONS LV, LVI. Plate 36.

N fimple progreflion this imperfect confonant fkip to the guide cannot go through
all the founds of the octave, as has been fhewn in the firft part of this code :
But in this mixt progreflion, as the bafs may have all its perfect fifths, it may pafs
through all the thirteen founds of the fcale of tranfpofition.

Canon lv. has the tranfpofition of the natural fcale ; and canon lvi. has the tranipofition
of the artificial fcale ; both with fimple combinations. The harmony in the progreflion
by the fkip to the guide, cannot be compounded with the feventh and ninth as explained
in the firft part of this code, but only with the eleventh and thirteenth, or fourth and
'fixth, the fame as in this mixed progreflion by the fame fkip ; therefore when the compound
combination in this progreflion is wanted, we muft have regard to the canons, and their
explanation relating to the fame confonant imperfect fkip in the firft part of this code :
The only difference between the fimple progreflion and the mixt by the fame fkip, is the
accidental figns fharp, or flat, to be put in their proper places, the combination being the
fame.

CHAP. III.

Of tranfpofing the two Scales, by the auxiliar perfe& Skip of
Third low, or Sixth high, in continual Progreflion.

CANONS LVII, LVIII, LIX, LX. Plates 37, 38.

T has been demonftrated in the firfl part of this code that the continual progreflion
by the third low, or fixth high, which is the fame, is not fundamental, but derived
from the perfect confonant fkip of cadence, to which it is added as auxiliar. The
fame it is in the mixt progreflion, as it is apparent by obferving the true fundamental
bafs exprefsly put under the firft common bafs fuppofed fundamental in all thefe four
canons.

Canon lvii. is properly the tranfpofition of the natural fcale by the true fundamental
bafs ; but in regard to the fuppofed firft: bafs feems the tranfpofition of the artificial fcale,
becaufe in all meafures its firft thirds are all minor, as being the fecond third, which
compofes the perfect fifth in the natural fcale j the firft third which compofes the fame
fifth being major is occupied by the fame firft fundamental bafs, confequently it has for
its firft third, the fecond third, which is, as abovefaid, minor.

Canon lviii. on the contrary, feems by the firft common bafs, that pafling from the
firft meafure to the fecond, it tranfpofes the fcale artificial into the natural, becaufe defcending
a third low it defcends in the fecond third, which compofes the fifth, confequently it has
always the firft third fharp upon its firft note, but the tranfpofition is of the artificial fcale
the firft third of the two, which compofes the fifth, is minor to the combination of the

fundamental

Part II. 0/ /& Composition c/ MUSIC. 69

fundamental bafs : Therefore it is manifeft that the above auxiliar Ikip depends upon the
confonant ikip of cadence, but when it is joined with it, becomes itielf fundamental, as
will be feen in the following Chapter IV.

The harmony of the above two canons proceed in afcending in contrary motion to the
two bafTes, becaufe the harmony to the firft bafs is of fimple combination, notwithftanding
that is compound to the fundamental lower bafs.

Canon lix. is the tranfpofition of the natural fcale in the manner of the canon xvii. but
with the defcending harmony. Alfo the canon lx. which is the tranfpofition of the artificial
fcale with defcending harmony, both thefe two canons, lix. and lx. proceed with the
compound combination of feventh and ninth in defcending with the bafTes.

Firji N. B. In the above two canons lix. and lx. the fifth prepares, and is changed into
a feventh, which is refolved into the octave, in the common firft bafs, becaufe it defcends
only by thirds j fo the ninth into which the feventh is changed by the firft fkip in the
meafure of the firft common bafs ; the fame ninth into the third by the combination of the
fame fkip of a third low by the fame bafs ; but the fame feventh in the true fundamental
bafs, is refolved into the third, and the ninth into the fifth, according to the rules to be
obferved in the progreffion of the confonant perfect fkip of cadence.

Second N. B. The figures are marked over and under every part : The upper figures
belong to the firft bafs, and thofe under the fame part to the lower fundamental bafs ; as
alfo in all the canons compofed with two bafTes.

C H A P. IV.

Article I Of the Tranfpofition by the fame auxiliar Skip,
but joined with the perfeft Skip of Cadence in fimple
Combination.

CANON LXI. Plate 39.

S^if^f N this progreffion the bafs defcends a minor third, in order to tranfpofe the natural
H 1 %l fcale in the next note higher with the fkip of cadence, by which the fcale is
Ek3*£§! tranfpofed a tone higher in the next meafure. The firft notes of every meafure
may be confidered as principal of a new fcale, and the feeond notes principal, and, at the
fame time, relative guides to the next note.

Of the Tranfpofition of the artificial Scale with the fame Progreffion and

Combination.

CANON LXII. Plate 39.

*T S K E firft notes in every meafure in this canon are all principal notes of the fuccefilve
-*- tranfpofed fcales from the firft artificial fcale 5 and the feeond notes are all fundamental
guides to the following principal note of the new tranfpofed fcale. The bafs fkips a minor
third low, in order to afcend by the following fkip of cadence a full tone above the firft
note of the antecedent meafure. By the fkip of third low the octave paffes to the major
third in the feeond note of the meafure, which ferves as indicative note of the next fcale.

T The

yo Of the Composit 10 n e/ MUSIC. Book II,

The fifth afcends to the octave, and the third, which is minor, is changed into a perfect
fifth, and with this combination the firft fcale is tranfpofed by the fame fundamental fkip
of cadence a full tone higher, containing the fame combination and progreflion, to the end
of the canon.

Of the fame Iranfpojition and Progrejfion> but the Bafs flipping by major and

minor Thirds in the natural way.

CANON LXIII. Plate 39.

THIS canon is the fame as the antecedent canon, being only different in the fkipping
low by major and minor thirds j with the fkip of minor third the bafs afcends a full
tone, and with the major third it afcends only a femitone by the fucceffive fkip of cadence,
•which is always fundamental.

Of the Tranjpofition of the natural Scale with the fame Progreffon and
Combination^ but with the fundamental Guide.

CANON LXIV. Plate 40.

H E difference betwixt this canon and canon lxi. is only in the combination of the
fecond note of every meafure, which notes in canon lxi. are all relative guides, but
in this canon are all fundamental guides ; confequently the octave to the firft bafs note
muft pafs to the third in the fecond note of the fame meafure, as indicative of the fame
fundamental guide to the next tranfpofed fcale.

The Manner of tranfpofng the artificial Scale by the fame Progrejfion and

Combination^ a Semitone higher.

CANON LXV. Plate 40.

"'g ' H E auxiliar fkip, when it defcends a major third, or afcends a minor fixth, which
-*• in combinations harmonic is the fame, tranfpofes the fcale by the fucceeding perfect
fifth of cadence only a femitone higher. The firft notes in all the meafures are all prin-
cipals of the new tranfpofed fcale, and the fecond notes all fundamental guides; the
progreflion afcending continually by femitones.

Article II. Of the Tranfpofition of the natural Scale by the fame Progref-

feon^ but with compound Combination.

CANON LXVI. Plate 40.

THIS canon differs only in the combination from canon lxi. that has the perfect
fimple, this the compound combination, as is clear enough in looking on the canon.

CANONS LXVII. Plate 41.

* I v HIS canon alfo is the fame as ^the antecedent, the difference is only in the third -of
■* the combination to the fkip of cadence, which in the above canon Ixvi. it is minor,
and in this canon is major, as in the canon in which is the progreflion, and its combination,
is fufflciently clear.

Part II. 0/ /fc Composition c/ MUSIC. 71

Of the Tranfpojition of the artificial Scale by both the above two Skips in J even

real Parts,

CANON LXVIII. Plate 41.

TH E tranfpofition in this canon is of the artificial fcale, the bafs defcending a minor
third from the principal firft note, partes with compound combination into the funda-
mental guide of the next tranfpofed note by its fkip of cadence, which tranfpofed note
having only the fimple combination, may be confidered as fimple principal of terminate
harmony in a new tranfpofed fcale ; which principal defcending into a fundamental guide
for tranfpofing again the fcale, continually afcends the octave by full tones. This canon
fhews at the fame time the manner of doubling the two confonant fifth and octave, which
is done by adding the fimple combination to the compound ; the fimple combination
afcends with the bafs, and the compound defcends in contrary motion to the bafs, as it is
explained in the canon.

N. B. When the harmonic progreflion is continually done by the perfect confonant fkip
of cadence, or by the imperfect confonant fkip of guide, the fimple combination proceeds
always in contrary motion to the fundamental bafs ; and on the contrary, the compound
combination proceeds defcending together with the bafs; but the fame two fkips being joined
with the auxiliar fkip of third low, or fixth high, the fimple combination goes with the
bafs, and the compound on contrary motion to the fame bafs.

Article III. Of the fame Tranfpofition and Progrejfion^ but in Compound

and full Combination in eight Parts,

CANON LXIX. Plate 42.

THIS canon is the fame as the above Ixviiith, only with this difference, that all the
firft notes of the meafures in the fame Ixviiith canon, being principal notes with fimple
combination, confequently are all of terminate harmony : But in this canon its firft notes
being with compound combination becomes indeterminate harmony, and they muft be
confidered as principal notes of indeterminate harmony, and the bafs fkipping continually a
minor third low in the fecond note of the meafure, which fecond note is the fundamental
guide to the next tranfpofed fcale, to which it paffes with the fkip of cadence. The firft
fcale is continually tranfpofed a full tone higher ; and the bafs paffes with both its fkips
through all the femitones of the divifion of the natural octave. This canon is in compound
and full harmony compofed by eight real parts, in which the combination of the feventh
inftead of refolving into the minor third in the next meafure, keeps firm for the full com-
bination, in which it is changed into the eleventh, or fourth, refolving into the perfect fifth
in the fecond note of the fame meafure. If the compofer will not ufe the full combination,
the fourth muft be fuppreffed in refolving directly the feventh into the minor third, which
in the next note muft be changed into a perfect fifth, by putting a fharp to the antecedent
note ; and if he fuppreffes the ninth, he muft defcend directly to the octave, which alfo
muft be altered with a fharp to give the major third indicative in the fecond note of the
fame meafure to the fundamental bafs, which is the fundamental guide to the following
new trafpofed fcale in the next meafure.

N. B. When the bafs, with its confonant fkip of cadence, defcends continually a perfect
fifth, or afcends a perfect fourth, the parts which defcends with him muft proceed con-
tinually by full tones, as in the canons xlvi. xlviii. xlix. li. and lii. and when the fame
confonant fkip of cadence is joined with its perfect auxiliar fkip, defcending only a minor
third low, the bafs afcends continually by a full tone, the parts alio which alcend with him

muft

72 0/ /& Composition 0/ MUSIC. Book II.

muft afcend continually a full tone, as it is done by fimple combination in canon lxi.
and in compound combination only by thofe parts which afcends with the bafs by fifths
and octaves, as in canons lxii. and lxiv. by their third parts, and in canon lxviii. by its fixth
part, and in this prefent canon lxix. by the feventh part. This progreflion, by afcendino-
or defcending continual ly^jscontrary to the convenience of the voice, and to the order of
the two fcales natural and artificial, which both proceed by tones and femitones : Therefore
all progreffions which afcend or defcend continually a full tone, cannot be ufed in a long
and fucceffive progreffion, as has been mentioned in the third N. B. at the beginning of
this fecond part ; and in regard to the auxiliar fkips, the beft way of ufing them is defcend-
ing or afcending, by fkipping fometimes by minor thirds and fometimes by major thirds, as
it is proper to the fcales in which the harmony proceeds.

CHAP. V.

Article I. Of tranfpofing the natural Scale by the fame
auxiliar Skip of Third low, joined with the imperfect Skip
to the Guide.

CANON LXX. Plate 42.

N this canon the bafs defcending a minor third low with the auxiliar fkip, and
afterwards afcending by the fkip of guide, tranfpofes the fcale a major third higher j
- , therefore cannot pafs through all the founds of the octave, to which it rifes in
three fkips of guide ; the octave being equally divided by three major thirds. This pro-
greffion can only ferve for tranfpofing the fcale only one time, and very feldom for two,
but never for three times fucceffively, as in the canon.

Article II. Of the Tranfpofition of both the natural and artificial Scales^
as they happen in their Order ^ by the two joined Skips as above,

CANON LXXI. Plate 43.

IN this canon, by the two motions of the bafs, the harmony paffes fucceffively all the
founds of both the afcending and defcending fcales of tranfpofition ; fucceffively tran-
fpofing the natural and artificial fcales a major or a minor third high, which is done by
the bafs defcending continually a perfect fifth from the third note of the firft principal note,
and afterwards afcending a perfect fifth ; which third note of the principal note, when it
is minor, as in the firft meafure by the fucceffive fkip of the perfect fifth, tranfpofes the
fcale in the fame minor third j and when the third of the tranipofed fcale is major by the
fame fucceffive fkip of the perfect fifth, tranfpofes the fcale a major third higher, as is
apparent in the prefent canon : By this means the harmony pafles through all the twenty-
five founds, divided by twenty-four femitones of both the afcending and defcending fcales
of tranfpofition, proceeding always by major or minor third (as the perfect fifth of the
antecedent fcale requires) combined with its perfect fifth and feventh to the fkip of the
fifth in the fecond note of the meafure, and third, fifth, and octave, to the principal firft
note.

CHAP.

Part II. Of the Composition of MUSI C. y^

• CHAP. VI.

Articlle I- Of Tranfpofitions by the imperfect Skip auxiliar
of the Third high, joined with the confbnant Skip of Cadence.

CANON LXXII. Plate 44.

|pt#§£| H E S E imperfect auxiliar fkips of third high or fixth low, are always improper in
^T i fimple and mixt progreffion by fucceffion, as it is apparent by the canons of this
&&I3I& chapter ; in which canons the ill proceedings of the parts cannot be avoided j
befides, this fame fkip in a continual progreffion cannot be fundamental, as has been
explained by canon xli. therefore it can only be once ufed as fundamental ; and, as has
been mentioned in the third N. B. at the beginning of this fecond part of the code, all
the canons in this fame fecond part are made to fhew the manner of tranfpofing the fcales
by all the fkips of the fundamental bafs, with their proper but different combination of
founds. This canon lxxii. is of fimple combination, the bafs afcending by major and minor-
thirds with the auxiliar fkip, and defcending and tranfpoflng the fcale a major or minor
third low with the perfect fifth of the fkip of guide. The firft notes may be confidered as
principal in their own fcales, and the fecond following notes in its fame meafure as funda-
mental guides to their next tranfpofed fcales.

Article II. The Tranffofitton with compound Harmo7iy.

CANONS LXXIII, LXXIV. Plate 44.

/ "lp H E S E two canons are the fame, only the parts are difpofed in a different order, to
■* fhew the manner of changing the places of the fame parts. Both canons are com-
pounded with the feventh, which may feem as not prepared, being prepared by fuppofition ;
becaufe the part which begins giving the third to the bafs, defcends a full tone to give
the feventh to the next bafs note : Therefore this fame bafs note, notwithftandinf it has
not been in the antecedent meafure the firft principal note, but only its third, which by
the tranfpofition is changed into principal, confequently the feventh is prepared by the fame
which has fubfifted in the antecedent accord ; moreover, being a fundamental feventh, it
may on this occafion fubfifh without preparation, refolving the third into the next meafure.

CANONS LXXV; LXXVI. Plate 45.

I N canon lxxv. the bafs afcending a major third tranfpofes the natural fcale a minor third
-*■ low by the fkip of cadence, and proceeding in the fame manner it divides the fcale in
four parts, becaufe the octave contains only four minor thirds, and no more. But* the bafs
afcending a minor third, and afterwards defcending a perfect fifth with the fkip of cadence,
defcends always a major third ; and by this manner it divides the octave in three equal
parts, as has been done in canon lxx. but in contrary progreffion.

U CHAP,

74 Of the C c ' m p o s i T i o n of M U S I Co Book II,

CHAP. VII. o

Article I. Of the Tranfpofition of the fame Skip joined

with the Skip of Guide.

CANONS LXXVII, LXXVIII. Plate 46.

N canon lxxvii. the bafs rifes a natural third, in order to defcend with the lkip
of guide a perfect fourth low, which is the fame as afcending a perfect fifth
high.

Canon lxxviii. afcends a minor third, and afterwards defcends in like manner a perfect
fourth. In this canon the third part defcends continually a full tone contrary to the conve-
nience of the voice, and the bafs paifes through the octave by only fix intervals of a full tone,
two femitones being omitted contrary to the order of the fcale ; confequently the continual
progreffion, as in the canon, cannot well fublift.

Of tranffofing the natural Scale by the fame auxiliar Skip afcending a major
Third y joined with the fame Skip of Guide,

■ CANON LXXIX. Plate 46.

HP HIS canon fhews the manner of tranfpofing the natural fcale a femitone lower, and
•*■ this is done by the bafs afcending a major third, and then defcending a perfect fourth,
into which the antecedent fcale is tranipofed, and by the fame progreffion the harmony
paifes through all the femitones of the octave, as is clearly exprelfed in the canon.

CHAP.

Part II, 0/ ^ Composition «/ MUSIC. y$

CHAP. VIII.

Of the Tranfpofition of both the natural and artificial Scales,
proceeding by all the fundamental and auxiliar Skips in
compound Combination.

CANON LXXX. Plats 46.

N this laft canon the harmony, which is compound, proceeds with all the funda-
mental motions in tranfpofing the two principal fcales. The firft notes form the
principal fimple combination of the natural fcale j which combination is changed
into compound, by defcending the third part from the o6tave into the indicative feventh, at
the fame time of defcending the bafs into its proper oitave ; which o&ave is alfo changed
from the principal of the fcale into the fundamental guide, by which it tranfpofes the fcale
into F, and by defcending by the auxiliar fkip of third low, it paffes to G and to A, from
which changing the fkip of third low into the fkip of third high, it returns into the firft
natural fcale of C, paffing after to G, returning again to C, which becomes the relative
guide to F ; and from F defcending to D, relative guide of G, paffes to the fame G as
relative principal of indeterminate harmony -, but by defcending in its octave, becomes the
fundamental principal guide of the firft natural fcale, and the firft notes in every meafure are
all principals of indeterminate harmony ; and the fecond notes all guides to the next notes.
All preparations and refolutions are relative to the particular motions of the bafs, explained
in their particular canons. Here ends the harmonic code, in which have been explained all
the fundamental laws and rules belonging to the compofition of mufic. Now we fhall pafs
on to examine the relation and application of the fame fundamental laws and rules to the
figurate harmony, or common compofition of mufic, in the following book.

END of Book II.

DELL 1

DELL'

ARTE ARMONICA:

O R,

A Treatise of the Composition of M U S I C.

book III.

Containing the Figurate Harmony ; its Difference from the Fundamental ;
and the diverfe Motions of the Bafs, and Parts, with the Diminutions of
the fundamental Notes ; alfo its different Compositions and Divifions ;
with their particular Laws and Rules, over and above the Harmonic Laws.

C H A P. I.

Article I. Of the Figured Harmony.

,lG URED harmony is the ufual and common mufic, which may be compofed
in two, three, four, to fixteen or more parts or voices, with or without
inftruments. It is called figured mufic by muficians, becaufe different
figures are made ufe of, with variety to time and meafure at pleafure ;
confequently it differs from the fundamental harmony, not only in the diverfity
of figures and time, but alfo in the combination of founds, which becomes
inverted by the arbitrary motions of the bafs, and of the parts.

Article II. Of the different Situation of the Bafs in figured Mufic ', by
which the fundamental Combinations are inverted,

T^Undamental harmony is a compofition only harmonic, without any fort of melody,
A having the notes all equal, and the motions of the bafs and parts all limited, otherways
it would be impoffible to fhew, in a proper order, the original rules of combination and

X progremon

78 0/ /& Composition 5/ M U SIC. Book III.

progreflion of founds. But the figured harmony being almoft always joined with fome
particular melody, and as the melody arifes directly from nature, being the product of the
natural genius of the compofer, it cannot be limited to any particular movements, but only
to thofe which arife from its being joined by and proceeding with the harmony ; and as the
melody is the principal object in figured mufic, in which it may be introduced into anv
one of the parts, and bafs, therefore the parts and bafs muft follow the melody according
to its different notes, movement, and time ; confequentiy the bafs, and the parts, bv
following or repeating the fubject of the melody, cannot always proceed in a fundamental
manner j and becaufe the harmonic combinations are adapted and calculated to the divers
distances, or, as commonly called, intervals, betwixt the parts and the bafs, when the bafs
is not in the fundamental place, the combination of founds becomes lefs or more inverted,
as the fame bafs is far or near its fundamental place, as may diftinctly be feen in the
examples 1, 2, 3, 4, and 5. plate 47.

The firft example is of fimple fundamental combination : It is divided into three parts ;
the firft divifion mews the fundamental fimple combination to the principal note of the
natural fcale C, occupied by the bafs j the upper parts compofing the fame fimple accord
of 3d, 5th, and 8th, and the octaves of the 3d and 5th. The fecond divifion fhews the
firft inverfion of the fame fimple accord, which happens when the bafs occupies the third
note of the fimple fundamental accord, which is inverted in the 3d, 6th, and 8th j the 3d
of this inverted combination arifes from the fundamental 5th, the 6th from the fundamental
octave, and the 8th is the 8th of the fundamental 3d, occupied by the bafs. In the third
divifion, the bafs being in the place of the fundamental fifth note, the combination funda-
mental is inverted, and becomes the accord of 4th, 6th, and 8th.

N. B. This fimple fundamental combination ®Be» has no more inverfion than the two
above-mentioned.

The 2d, 3d, and 4th examples are of compound combination to die note G, which is
the fundamental guide to the principal note of the natural fcale.

The fecond example is divided into four parts ; the firft divifion has the fundamental
accord 3d, 5th,' 7th, and 8th. In the fecond divifion the bafs being in the 3d of the
fundamental accord, it becomes inverted into the 3d, 5th, and 6th. In the third divifion
the bafs is placed in the fundamental fifth, and the combination or accord is inverted into
the 3d, 4th, and 6th. In the laft divifion, the bafs being in the fundamental feventh, the
fundamental accord is inverted and changed into the 2d, 4th, and 6th.

The third example fhews the compound combination of the 3d, 5th, 7th, and 9th,
without the octave, and is divided into five parts. By the firft divifion is defcribed the
fundamental compound combination of the 3d, 5th, 7th, and 9th. In the fecond divifion,
the bafs being in the third note of the fundamental combination, this fame combination is
inverted into the 3d, 5th, and 7th ; the 3d of this inverted accord is the 5th in the funda-
mental, and the 5th and 7th are the 7th and 9th of the fame fundamental accord. The
fundamental combination is inverted in the third divifion into the combination of the
3d, 5th, and 6th, the bafs being in the fundamental 5th. In the fourth divifion the bafs is
in the fundamental 7th, and the inverfion is 3d, 4th, and 6th. The fifth divifion being
the bafs in the fundamental ninth, the inverfion becomes 2d, 4th, and 6 th.

The fourth example is compounded with the addition of the octave to the 7th and
9th, and is alfo divided into five parts. The firft divifion contains the fundamental
combination of 3d, 5th, 7th, 8th, and 9th ; in the fecond divifion, the bafs being in the
fundamental third, the inverfion is 3d, 5th, 6th, and 7th. The third divifion has the bafs
in the fundamental fifth note, and the inverfion becomes 3d, 4th, 5th, and 6th. In the
fourth divifion, the bafs being in the fundamental 7th, the fundamental combination is

inverted

Chap. I. 0/ /& Composition «/ MUSIC. 79

inverted into the 2d, 3d, 4th, and 6th; and in the laft divifion, the bafs being in the ninth
fundamental, the inverfion is 2d, 4th, 6th, and 7th. Thefe four examples, as they are
explained, mew all the general inverfion of the fundamental fimple and compound com-
bination of founds in the natural fcale, which may ferve alfo as examples for all the other
fcales.

The fifth example is in full combination, as being compofed by the eight original founds
difpofed by thirds, which may be infinitely protracted ; confequently the inverfion cannot
always be apparent, becaufe in whatfoever note of the fundamental true accord the bafs is,
it has a like accord difpofed in the fame order by fuccemVe thirds, as is to be feen in
example v. plate 47. Therefore it may appear difficult to diftinguifh the fundamental true
bafs from the common, both having the fame accord : But in obferving the movement and
iituation of the bafs, is ealily known the true fundamental. The fundamental bafs cannot
proceed by conjoint degree, but by its confonant and auxiliar fkips ; confequently when it
moves by conjoint degree, only one of the two joined notes can be fundamental. For
fuppofing the bafs in the note C palling into the nearer note D, if C is fundamental,
D cannot be fundamental, but only one of the notes belonging to the fimple fundamental
accord of its two confonant or two auxiliar fkips. In the confonant fimple accord of C,
as principal, it cannot fubfift, nor in its two auxiliar fkips of 3d low and high : The fkip of 3d
low from C is A, and the fkip of 3d high is E, to which D cannot be 3d, 5th, or 8th ; con-
fequently it is apparent, that it can only belong to the other confonant fkip of 5th high or 4th
low, which is G guide to the above principal C, and D is the fifth note of the fame guide G.
But if D is the fundamental note, C can only be the third note of A ; which A is the
relative guide to D, and by the order of the antecedent and following progreflion of the
fame bafs notes, is known which of the two joined notes is the true fundamental. The fame
muff, be obferved in regard to the two auxiliar fkips of third high or low. When the bafs
proceeds by thirds, only two can be fundamental ; for example, the bafs defcending from
C to A, and fucceffively from A to F, both C and A may be fundamental notes ; C as
principal, defcending in A by its defcending auxiliar fkip, which may be the relative guide
to the note D j in this cafe the following note F, into which the bafs defcends from A,
as above, can only be the third of the fimple combination belonging to the fame D its
principal relative note ; and being fundamental C and F, the note A can only be the third
to the note F as principal, and C as relative, or fundamental Guide. The fame happens
with the other auxiliar fkip, as has been demonflrated by the canons of the harmonic
code relating to the fame two auxiliar fkips, where has been fhewn, that the bafs, as fun-
damental, can only proceed with one fkip of third, but following another fkip of third,
muft be joined by one of the two confonant fkips, which properly are only the two true
principal fkips fundamental.

N. B. The inverfion of the eleventh note of the fundamental accord has been omitted
in this article, but it will be explained in the following fifth article.

Article III. Of the Inverfeofts by the Bafs Syncopes.

f T has been mentioned in the firft article of this prefent book, that the common bafs is
-*■ not always in the fundamental place, but very often in the place of one or another of
the fuperior parts j and that happens when the bafs has occafion to imitate or contraft fome
propoied melody, or to fill the harmony, or fome other purpofes as may ferve the genius of
the compofer ; which is the caufe that the fundamental notes are changed, many in fyncopes,
many in fimple or double, but different notes, and many other in diminifhed notes.
Syncopes, which is the fubject matter of this article, is fo called when two notes are tied
together as if they were only one, as is to be feen in example vi. plate 48. This example
is divided into two parts, the firft part contains in general the fecond part, but particularly
the two extreme ftaffs, namely the upper extreme ftaff, keeping in the notes which gives
die fimple combination to the fundamental bafs in the low extreme ftaff; and alio the

fame

8c Of A Composition ^ MUSIC. Book III.

fame notes ferve to the diverfe combinations with the fix baffes contained in the fecond
divifion fubdivided in three parts, every one having two baffes proceeding one after another,
the firft fubdivifion containing the baffes i. and 2. gives to the bafs fundamental, alterna-
tively, the fifth and octave, doubling the fame notes of the fuperior notes. In the fecond
divifion both baffes gives alternatively the ninth, and the two lair, in the third fub-divifion
the feventh. The two baffes in the firft fub-divifion fkip from the firft note one odave
higher for paffing into the fifth * The other two, in the fecond fub-divifion, fkip a fifth
higher, by which is prepared the ninth ; and the other two, in the laft fub-divifion, arife
a third high, preparing the feventh to the fundamental bafs ; and altogether the fix baffes,
with the three parts in the upper extreme, make the fimple combination of 3d, 5th, and
8th, all doubled and joined with the compound combination of the 7th and 9th, to every
note of the fundamental bafs. The two firft baffes 1. 2. are the fame as the two parts
upon the bafs in the firft canon of the code, doubling the fifths and octaves of the fuperior
parts, as is done in canon hi. The other two baffes 3. and 4. are the fame as the two parts
in canon vi. giving the ninth to the fundamental bafs, prepared by the fifth and refolved
into the fifth ; and the two laft baffes, 5. and 6. are the fame as the parts in canon iv.'
giving the feventh to the fame fundamental bafs ; which feventh is prepared by the third,
and refolved into the third, as it is in canon iv. But in regard to every bafs feparately, in
the three divifions, the fuperior fimple combination of the three parts in the firft ftafF,
become all inverted in different manners, namely in the firft divifion the inverfion to the
two baffes 1. 2. is the 4th and 6th refolving into the 3d and 5th: So the baffes in the
fecond fubdivifion, when they have changed alternatively the firft combination into the 4th
and 6th, by the skip of guides, this accord is changed by the next fyncope into the 2d,
4th and 7th. The fame in regard to the two baffes 5. and 6. in the third divifion, which
baffes afcending a third one after the other, change their firft combination of 3d and 6th,
which is inverted in the following meafure 2d, 4th, and 6th, and it is refolved again into
the 3d and 6th. All thefe different inverfions joined together with the upper three parts,
and the fix baffes, make the fundamental compound combination of 3d, 5th, 7th, and 9th,
to every note of the fundamental* bafs, as it is apparent in the above example vi. plate 48.
which fhews all the inverfions by fyncopes of the compound harmony belonging to the
perfect confonant skip -of cadence of indeterminate harmony.

N. B. It muft be obferved, that in a compofition where the bafs fyncope is a falfe, the
fame falfe cannot fubfift in the other parts, without proceeding by octaves, which is improper,
and not truly harmonic : And when there are two parts which proceed, one by the 7th
and the other by the 9th, over the fundamental bafs, as it happens in compofitions of eight
or more real parts, the fuperior parts muft proceed with only the fimple combination, as
in the above example. But when the eight parts are all doubled and tripled, the 7th and
9th may fubfift alio in the fuperior parts, provided the refolution be done on the contrary
motion, namely, one afcending the other defcending j or elfe by change, as has been fhewn,
by their refpective canons in the firft part of the code.

Article IV. Of the varied and diminished Bafs Notes.

r T^ H E fimple doubled varied notes are expreffed in example vii. plate 49, which fhews
■*• the inverfion of the fundamental notes in fimple combination, and example viii. in
the fame plate, fhews the inverfion of the compound accord by the 7th and 9th. The
firft example is compofed by the fimple combination of the three fuperior parts at the top,
to the fundamental bafs at the bottom of the example, and the four inclofed baffes made
the inverfion. The other example viii. which alfo has the fimple combination betwixt the
upper parts and the fundamental, but the four inclofed baffes afcending one third, and
after defcending gradually, make the compound combination of the 7th and 9th to the
fundamental, inverting in that manner the fimple combination, as is clearly fhewn by the
figures at every one of the fame four baffes.

The

Chap. I. Of the Composition of MUSIC. 8*

The following plate 50, has the example ix. which is divided into four parts. The firft,
part has five ftarfs ; in the firft ftaff is the fundamental bafs, and the more common
djvilions and diminutions of the fundamental notes are in the following four baffes, namely
in the firft common bafs the fundamental notes are diminifhed every one into four, pro-
ceeding from the firft note to the third, and returning to the firft. The fccond common
bafs diminishes the above four notes of the firft common bafs. The third common bafs
has its diminifhed notes by skips, and the laft bafs has the diminifhed notes of the fame third
bafs. The fecond divifion contains a continual progreflion defcending by thirds, fhewing
that the fame progreflion is fubordinate to the perfect confonant fkip of cadence, as has been
demonstrated in the canons of the auxiliar fkip of third low ; and the fame progreflion
may ferve for augmenting two parts more to the fix parts, with which is formed the third
canon, making eight real parts in fnnple combination, but in figured harmony.

The third part or divifion, contains the diminutions of the fundamental notes diftributed
in four different common baffes ; the firft afcending a third, and the fecond a fifth, de-
fending together by fixths gradually to the notes of every following meafure : The third
and fourth baffes proceed in the fame manner, but beginning a meafure after the firft two.
The fourth divifion contains two baffes, which proceed one after the other, by the fkip of
an octave falling into the fifth of the principal in the middle of the fame meafure, and
paflmg to the third of the principal note in the following meafure, as is clearly expreffed
in the fame example. The inverfions of all the common baffes are expreffed by the figures
marked to every one, and all their diminifhed notes come from the fundamental notes in
the firft ftaff, which needs no further explanation.

N. B. It muft be obferved, that when a common bafs paffes particularly in accented
time, with its varied and diminifhed notes, by the fifth of the fundamental combination,
which fifth has its proper fundamental combination when it is the guide, but in the
diminutions of the principal notes, being confidered only as a fimple fifth of the fame
principal note, as in the above example ix. it is in the baffes 4, and 5, of the firft divifion,
in which they defcend a fourth from C to G, which G may be fuppofed the fundamental
guide, but in the fame diminution it is only a fimple fifth belonging to the principal note C,
and not its Guide ; therefore the compofer is obliged to put the proper figures of 4, and 6,
which is the inverfion of the principal note by the fimple fifth, for avoiding miftakes in the
accompanyment in the organ or harpficord ; as has been done in the fame example in the
firft meafure of the above baffes, and in the following meafure by a line over the fame
meafure, which fignifies the continuation of the firft accord.

Second N. B. In the above four example's, 6, 7, 8, and 9, all the bafles are expreffed,
two by two, which two bafles may be joined into one ; the fame difpofition in two bafles
being only done for fhewing the manner of dividing one bafs into two, when it is wanted,
as in compofitions in eight or more parts ; the fame manner may be applied to the parts,
and particularly, as it is done by the four bafles in the third divifion of example ix. plate 50.
but in the firft divifion of the fame example, is only expreffed the diminutions and fub-
dtminutions of the fame diminutions. Thefe diminutions and fubdiminutions of the prin-
cipal notes arifing properlv from the melody, which being arbitrary to every one, may be
produced in diverfe and infinite manners, confequently may be alio done in diverfe and
aimoft infinite manners at the pleafure and according to the genius of the compofer.

Third N. B. The refolution of the ninth, which is refolved into the fifth of the funda-
mental note, as has been fhewn in its proper canons, when it is inverted by the common
bafs, may feem improperly and falfely refolved, becaufe the bafs forming the falfe major
fecond with the indicative afcending third, which afcending a tone, and the bafs defcending
a tone in the following meafure, the fecond is refolved into a fourth, which may be con-
fidered as falfe, or difcord ; but the fame fourth is the octave of the principal note, and
the bafs in defcending a tone paffes into the guide of the fame principal note ; which two

Y notes

82 Of the Composition of M U S I C. Book III.

notes may fubfift together, as immoveable fundamental baffes of its own fcale : Moreover,
the fame note of the guide, "in which is refolved the bafs, has fubfifted in the preceedino-
combination in the fuperior part, as feventh to the fame common bafs, and as octave to
the fundamental bafs, refolving the feventh in defcending to the fame note, which is the
octave betwixt the upper part and the common bafs, giving both together the fifth to the
fundamental bafs ; confequently the bafs refolves the fecond with the .upper part, which
gives the octave to the fundamental into the fourth, this being the fifth fundamental. This
manner of refolving the ninth, when it is occupied by the common bafs, is not commonly
underftood or known by many compofers, which ordinarily refolves the fuperfluous fecond
or ninth into the fundamental bafs by afcending a femitone together with the parts, or
defcending into the fame fundamental note, which is a fundamental guide, before the
parts and the fundamental bafs moves, which refolution makes the accord fundamental in
the fame common bafs ; but the beft way is the refolution, as it has been done in the canons
of the harmonic code; notwithftanding the other two' common manners of refolving the
fame ninth may alfo fubfift, being the fame ninth or fecond inverted, refolved in afcending
with the parts a femitone or a tone, becomes a deceptive cadence, and refolving in defcending
a tone before the moving of the parts, by this means paffes into the guide of the next note,
and in both manners the refolution is made by a third; therefore it is arbitrary to the
compofers.

Fourth N. B. In this article is only explained the reverfion of the fimple and compound
combination by the common bafs, with the {kip of cadence, and the other fkip to the
guide is omitted, becaufe when the reverfion of the perfect confonant fkip of cadence is
known, the order of the reverfion of the other fundamental and auxiliar fkips will be
underftood ; only it muft be obferved, that the imperfect confonant fkip to the guide has
no proper reverfions, only by the fourth and fixth, and this reverfion cannot be done
naturally from the bafs, without proceeding by falfes of anticipations, which may be only
fupported once or in the perfect cadences. For that which regards the diminutions of the
fundamental notes, is the fame, as it has been explained alfo for dividing the baffes ; only
it muft be obferved in the fkip of cadence, the fecond bafs, or part, repeats the fubject into
the fourth high, or fifth low ; but in the fkip to the guide, the repetition muft be done by
the fifth high or fourth low ; alfo in the divifion of the parts, or baffes proceeding by the
auxiliar fkips, the repetition muft be by the third high, or low, as it is the auxiliar fkip,
but this rule may be changed in the tranfpofition of the fcale by imitations.

Article V. Of t&e-fs&se Equivocal Combinations.

*~T^ H E S E equivocal combinations muft be diftinguifhed into two different forts or man-
■T ners. In one manner the founds are equivocal, it not being pofiible to know where,
or in what fcale, the fame combination may pafs by only hearing it ; but when the founds
are properly denominated in their notes, and figured under the bafs note, immediately is
known the next combination. The other fort of equivocal combinations are equivocal not
only in their founds, but alfo in their proper denomination. The above firft fort will
be explained by two following articles vi. and vii. Now in this article we fhall explain
the fecond fort of thefe equivocal combinations, which are derived from the fyncopes of
the common bafs, by which are tied two, three, or more notes. Thefe two, three, or
more notes, may be one of the two principal ftable and immoveable fundamental baffes,
both of which have the right of fupporting all combinations of the fimple harmonic pro-
greffion, which may be made by the original founds of its own fcale, without moving from
their ftable places, as mentioned in the firft article of the fourth chapter, book the firft :
Confequently the different combinations of the fuperior parts are not confidered as inverted,
but as proceeding naturally in their own fcale, fucceffively refolving their combination by
their own motions, as it is expreffed in example x. plate 51. which example is divided by
three bars, making three meafures ; in the firft meafure is defcribed the fimple combination

Chap. I. 0/ /& Composition «/ MUSIC. 83

to the fundamental bafs C j in the fecond meafure, the parts moving, change the fimple
combination into the compound accord 2d, 4th, 5th, and 7th, which properly belong to
G as fundamental guide in the fcale of C, as 3d, 5th, and 7th ; in the following meafure,
the parts moving again, refolve the falfe accord done to the bafs in the antecedent meafure,
reftoring the firft fimple combination to the bafs, which has continued firm in the principal
note C. The following example xi. in the fame plate, is alfo divided by three bars or
meafures ; in the firft and fecond meafure is the fame combination as in the firft example x.
but in the third meafure, the parts keeping firm the combination of the fundamental
guide G made in the antecedent meafure, the bafs refolves the falfe accord of the fecond
meafure, defcending one note, which is the third found to the combination of the guide G.
In the firft of thefe two examples the bafs being always firm in the principal note C, and
the parts moving, makes the falfe combination in the fecond meafure ; which falfe or difcord
is refolved in the third meafure by the fame parts ; the bafs rauft be confidered as liable and
immoveable foundation of all the original founds of its octave or its own fcale. In the
other example xi. of the fame plate 51, the bafs refolving in the third meafure the falfe
combination of the antecedent meafure, fhews that it is a common bafs, becaufe being fun-
damental in the firft meafure, and keeping firm the fame note in the fecond meafure, in
which the parts proceed from the firft combination of the principal to that of the guide,
and after in the third meafure the parts keeping firm, and the bafs refolving the falfe com-
bination of the fecond meafure in defcending as above-faid, fhews that the fame bafs that
has made the difcord, or falfe combination in keeping firm in the fecond meafure, and not
the parts in moving, to which movement the bafs fhould have followed flapping to the
guide , but in keeping firm the note in the fecond meafure, it is changed into the eleventh
note, which is the fifth third in the harmonic fyftem belonging to the full combination of
the guide, and in this manner makes the inversion in the fame eleventh note, which be-
comes a fecond below the fundamental fifth note D, and a fourth below the fundamental
indicative defcending 7th F, alfo a fifth with the octave of the fundamental guide G, and
a 7th major with the indicative fundamental afcending third ; all which is refolved by the
fame bafs, as common bafs defcending into the note B, namely the fecond into the third,
the 4th and 5th into the falfe 5th and 6th, and the major 7th into the odtave ; which all
together, the bafs with the parts, make the fundamental combination of the 3d, 5th, 7th,
and 9th, to the fundamental bafs G not expreffed.

This is the explanation of the eleventh note of the guide mentioned but not explained in
the N. B. at the end of article ii. of the fame chapter.

By the two above examples may be eafily known and diftinguifhed the fundamental bafs
from the common bafs, which confifts only in obferving the refolutions of the falfes, if
they are done by the bafs, or by the parts j it being a general rule, that the refolution of
all falfes, or difcords, muft be done by the fame parts which make the fame falfes ; which
general rule has fome exceptions, as has been feen in the canons of the harmonic code.

Article VI. Of fome particular Inverfio?ts arifeng from the artificial Scale.

■|N the fixth chapter and fourth article of the firft book, has been demonftrated, that the
"• artificial fcale is divided into two different fcales, one afcending, the other defcending.
In afcending the 6th and 7th founds are neceffarily major, or fharp, but in defcending are
both minor, or flat. This is the caufe that the inverfion of the compound combination
with the 7th and 9th to the fundamental guide, becomes fomewhat diverfe from the like
inverfion of the fame combination in the natural fcale. The figures which reprefent the
above falfe combination, are the fame in both fcales natural and artificial, but the founds
are not the fame ; and that is alfo the caufe that thefe inverfions are called equivocal

•accords, or combinations, as will be explained in the next article. When the common
bafs in the natural.fcale occupies the indicative 3d of the fundamental guide, the inverfion
becomes 3d, 5th, and 7th (as has been fhewn) the fame is in the artificial fcale j but

the

84 Of the Composition cf MUSIC. Book III.

the 7th derived from the defcending indicative minor 9th of the fundamental guide, rauft
be marked flat. When the fame bafs is in the fifth note of the fundamental guide, the
inverfion is 3d, 5th, and 6th, in the natural fcale, the fame as in the artificial fcale, but
the fifth of the common bafs derived from the minor or flat 9th, muft be diminifhed a
femitone, and figured as a falfe 5th j the fame alfo when it occupies the place of the 7th
of the fundamental guide, its 3d being the fame flat 9th, confequently muft be flat ; and
the accord is the fame in the natural fcale, namely 3d, 4th, and 6th, but the 3d in the
natural fcale is naturally major, derived from the 9th, which is major, and the 4th, derived
from the indicative (harp 3d, muft be marked iharp : The interval betwixt the above 3d
flat and 4th (harp in the combination of the artificial fcale, is compounded of one fecond,
but exceeding a femitone the major natural fecond ; confequently the found is the fame as the
flat third, being compofed of the fame interval, notwithftanding it is confidered as a fecond,
becaufe the mark, or fign of iharp, or flat, alters only the founds, but not the names of
the founds, as has been before-mentioned. It is the fame when the common bafs occupies
the fundamental indicative flat 9th, the inverfion is 2d, 4th, 6th, and 7th ; the interval
betwixt every one of thefe founds is of flat 3d, but it is not fo in the natural fcale, and
this difference derives becaufe the natural notes and figures in the natural fcale reprefent
the natural founds with their proper names ; but in the artificial fcale the figures and notes
reprefent the names of the fame notes, but not their proper founds. In the natural fcale
the found named A is diftant from the following note B the interval of a tone, which is
the fame as two femitones; but in the artificial fcale (fuppofing the fcale of 3d flat) the
fame A being flat in the fundamental combination of the guide G, as its defcending indica-
tive 9th, becomes diftant three femitones from the note B natural, which muft be major
or fharp, as indicative afcending 3d of the guide G j and the above interval, from A flat
to B natural, being three femitones, confequently the found correfponds to the flat third,
not to the fecond, as before told ; but B being the fucceflive fecond name of A, is called
a fecond ; and when the fame A flat ferves as 7th to B natural, this 7th being compofed
by nine femitones, which properly is the interval of a major 6th, but being the fame A flat,
the feven'th name from B, is named and marked as a 7th, which is diftinguifhed by the
the furname of 7th diminifhed. This is the difference of the combination of founds between
the natural and artificial fcale.

Article VII. Of the different Ufes arifrig from the Inverfion of the fun-
damental Accord of Guide in the artificial Scale.

T? R O M the explanation of the above article it is manifeft that the compound combination
■*• with the major 3d to the fundamental bafs note, joined to the 5th, 7th, and flat 9th,
in the artificial fcale, when the fundamental bafs note is abftracted, the following four notes,
namely the 3d, 5th, 7th, and 9th, make a combination of four fucceflive flat thirds, form-
ing an octave, divided into four equal parts, every one in the fame degree of harmony
with the other ; confequently all together joined, in whatfoever manner they may be in-
verted, are perfectly harmonic, therefore they need no preparation nor refolution ; and from
one of the faid combinations may be paffed to another like combination, compofed by four
different flat thirds, without refolving the antecedent combination : But thefe paffages with-
out refolution can only fubfift for two times, or at moft for three, becaufe the octave being
divided by twelve femitones, by which the octave becomes compofed of thirteen founds,
and the above combination confifting in five founds forming four intervals, each divided by
three femitones, every one of which is a fourth part of the faid twelve intervals, by which
the o&ave is divided, as above-faid j confequently when from the accord of the firft femi-
tone is tranlpofed the fame accord to the fecond femitone, and after to the third femitone,
proceeding to the other femitone, the progreflion of the fourth femitone becomes the fame,
as has been done by the firft femitone and alfo of the others refpectively one to another :
Moreover, being the fame accord of indeterminate combination and progreflion, it muft at
laft be refolved into one of the two confonant fkips fifth low or fifth high, otherwife the

fenfatiort

Chap. Ii 0/ ^ Composition 0/ MUSIC. $5

fenfation will be tired in prolonging the expected conclufion of the harmony promifed by
the firft of the above accords. Theie accords or combinations derives from three femi-
tones whatfoever may be, but following one another, as in example xii. plate 5 1 . Every
note of the above combinations may be conlidered as fundamental indicative afcending 3d,
leading in their next femitone, which is the principal note of the following fcale, confe-
quently every one muft have their proper fundamental bafs note a {harp 3d below as guide
to the fucceeding fcale, as may be feen in example xiii. of the fame plate 51, in which
example is fuppofed the fecond femitone C fharp, defcribed in example xii. the combina-
tion of which is C fharp, E natural, G natural, B flat, and C fharp, which accord forms a
combination of four fucceffive flat thirds. The common bafs in the fame example is fup-
pofed always in the indicative afcending 3d, in every one of the four divifions, by which it
is evident, that fuppofe C fharp the indicative afcending third leading into the next femi-
tone D, the fundamental guide muft be the note A diftant a major third from C fharp,
paffing together to D the principal note of the indicative fcale. If it is fuppofed that the note
E of the fame combination be the indicative afcending note leading in F 3d flat, C na-
tural muft be its fundamental guide, but C fharp becoming the 9th of the fundamental
combination, muft be changed into D flat, which is the fame found as C (harp, becaufe this
name of C fharp cannot fublift in the fcale of F 3d flat. If G natural in the fame accord
is confidered as being the afcending indicative 3d, leading in A flat with its 3d flat, the
fundamental note of its guide muft be E flat its indicative 3d to the above note G natural,
its fifth B, D flat is 7th, and F flat its indicative defcending 9th, which D flat and F flat
are the fame founds as C fharp and E natural. If at laft it is fuppofed that the note B flat
of the fame accord, fharp, E natural, G natural, and B flat, be the indicative afcending
3d leading in C flat, the fundamental guide muft be G flat ; but for the convenience of the
eafier fcale, the name of B flat muft be changed into A fharp, and C flat into B natural,
being the fame founds j confequently the fundamental guide G muft alfo be changed into
F fharp ; A fharp being its indicative note leading in B natural, fubfifting in the reft of the
combination, namely C fharp as fifth to the guide F fharp, and E, G, both natural,
as 7th and 9th flat to the fame guide F fharp, as is clearly defcribed in the above example
xii. from which it is apparent, that the combination compofed by four fucceffive flat 3ds,
may pafs into four different principal, but artificial fcales : Moreover, if thefe four artificial
fcales are changed into natural, namely, inftead of giving to them the flat third, is given
the major* 3d, the fame four fcales are changed from being principal of their own fcale into
guides to four other artificial fcales, as it is expreffed in example xiv. plate 52. the reafon
is, that paffing from the firft bafs note C fharp of the fame accord into the note D, this
fame D having its 3d fharp, cannot be a principal note of its own fcale, becaufe the feventh
to the antecedent note C fharp, being B flat, it cannot fubfift in the fcale of D 3d fharp,
where B muft be natural ; confequently the fame D muft only be confidered as fundamental
guide paffing into G flat 3d, which is the fame as the above B flat in the firft combination,
as it clearly appears in the above example xiv.

Firft N. B. The firft bafles in thefe two examples are both common, and not fundamental,
being in the indicative afcending 3d of the fundamental accord, but they may fubfift alfo
in every one of the notes of the above fame combination, namely in the 5th, 7th, and
9th, coniequently the combinations and the refolutions become inverted, and all different
one from another. For example, if the common bafs is in the fifth note of the fundamental
accord, which is E natural in the firft combination of both the examples, the firft accord
being the bafs in the note, C fharp is 3d, 5th, and 7th, flat ; the bafs in the fifth E being
the firft combination, is inverted into 3d, 5th flat, and 6th fharp ; and the refolution is
not afcending, but in defcending one note to the principal; and the bafs being in the
note G, which is the 7th flat of the fundamental accord, the inverfion is 3d flat, 4th fharp,
and 6th natural, and the refolution defcends a tone in the third note of the fcale. And the
bafs, when it is in the laft note of the combination which refers to the 9th of the funda-
mental accord, the inverfion is a fecond extreme fharp 4th and 6th natural, in the refolution
of which the common bafs defcending a note, the accord becomes the 4th and 5th, or the

Z 4th

86 0/ ^ Composition c/ MUSIC. Book III.

4th and 6th, which feems as a falfe refolution, but is the propereft and original refolution,
as has been explained in the third note of the fourth article of this chapter. The above
explained combination derived from three femitones following each other, as in example
xii. plate 51. may be called equivocals, becaufe they may pafs into different fcales, without
being known, by hearing the founds, where their refolution will be ; but when they are
properly known and figured, the fucceeding fcale is prefently known.

Secofid N. B. The above-faid combinations, refolutions, and arbitrary paffages in different
fcales, fhew evidently the impoflibility of that fo much celebrated divifion of the tone and iemi-
tone fubfifting in major and minor j which divifion never can have fubfifted in pract ce j but
if it has fubfifted, muft be only in the firft time of the Greeks, where was uied the lira of
the four firings. Notwithftanding the above diftinction of the tone and femitone into
major and minor, as it is now fuppofed true, certain, and unquestionable, not only by fo
many writers in mufic, which following the opinion of Ptolomy> and after of Boetins, have
fhewn their lkill in calculating the reafons of the fuppofed intervals betwixt thefe different
tones and femitones, to find out a juft manner of tranfpofing the Greek diatonic fcale,
knowing nothing, or very little, in the practice of the harmonic art ; but alfo by almoft
all the prefent practitioners and compofers in muiic, fhewing at the fame time that they
know nothing of the true harmonic theory, which muft be formed and calculated, not by
the mathematic rules, which have nothing to do with the human fenfation, but by practice ;
the faculty of forming perfectly the fame fcale has been provided according to the general
conftitution of mankind, by the fame nature, and confirmed by rules of practice derived
from phyfic, namely for the general conftitution of the common human hearing.

Article VIII. Of fome irregular Combinations, which happen in the

artificial Scale.

IN the firft note at the end of the fecond article in the third chapter of the firft book,
has been mentioned, that befides the intervals of the two feconds major and minor,
the two fifths perfect and falfe, the two fixths and fevenths major and minor, alfo of the
perfect octave j there is a fecond, which is compofed of three femitones, commonly called
the fuperfluous or extreme fharp fecond, being equal to a flat third, one 5th, and one 6th,
called fuperfluous, the 5th formed with a femitone more than the perfect fifth, alfo the
fuperfluous 6th a femitone more than the major 6th, the 5th fuperfluous being equal to
the minor 6th, and the fuperfluous 6th to the minor 7th. Alfo a 7th, called diminished,
compofed of nine femitones, being equal to the major 6th, and an octave, alfo called
fuperfluous, containing a' femitone more than the perfect octave, being equal to the minor
9th. The combinations with every one of thefe above intervals only happen in the
combinations of the founds of the artificial fcale, becaufe it has two fcales, one amend-
ing and the other defcending, as mentioned and explained in the firft bookj and
that happens when two founds of thefe different fcales are joined in one combination,
namely, one in the common bafs, the other in the fuperior parts. The extreme fharp 2d
derives by being joined to the flat 9th of the fundamental guide, with the tenth note, which
is the octave higher of the fharp indicative third ; for example, the 9th in the fundamental
combination of the guide of the artificial fcale C 3d flat, is A flat, and the octave of the
indicative 3d is B naturally fharp j from A flat to B natural is one interval of three femi-
tones, which is the fame as the interval of a minor, or flat 3d ; but becaufe the name of
the found B is the fecond after A, it is called a fecond, as mentioned before. The fame
of the fuperfluous fifth. For example, fuppofing the artificial A natural, its feventh note
which is G, is naturally minor in defcending from the octave of the principal A j but in
afcending from the principal A to its octave the fame G muft be fharp, forming a major
7th to the fame principal, and confequently altered with one more femitone, as has been
explained in its proper place ; and when it happens that the fame note G fharp is joined
with the bafs note C, which is the minor 3d of the principal, this combination makes the

fuperfluous

Chap. I. Of the Composition c/ MUSIC. 87

fuperfluous fifth j on the contrary, G being natural in defcending, gives the perfect fifth to
the fame bafs C, as in the example xv. plate 52. the interval of the fuperfluous fifth is
the fame as that of the minor 6th.

The fuperfluous 6th happens (fuppofing the fame above fcale A natural) when the
common bafs defcends gradually from A to G natural, and fucceflively from G to F alfo
natural, G being the feventh note and F the fixth of the principal note in the fcale, as
may be feen in the above example xv. in which the fecond part in the laft meafure but one
having continued the antecedent meafure in E, its fifth note of the fimple accord, giving
fucceflively to the common bafs the accord of 5th, 9th, and 7th, at laft it refolves the note
E in D fharp, which is computed a major 6th to the bafs note F natural, but the juft
interval betwixt thdfe two founds D fharp and F natural, is a minor 7th, which interval
reflectively to the name is called fixth with the furname of fuperfluous ; and the fame D
fharp being not compofed in either of the two fcales afcending or defcending, confequently
the falfe accord becomes of falfe relation j notwithstanding that the ear is not offended,
for the reafon of defcending the common bafs from the octave of the principal note A, in
which is combined with the fimple accord, paries gradually to F 3d below, which in the
defcending fcale muft be natural, and ftill remaining in the fame F which belongs to the
fame artificial defcending fcale A with the reft of its accord, it keeps firm in the fenfation
the remembrance of the fame fcale j and the bafs being in the bafis of the above combina-
tion covers partly the harfh found of the fuperfluous fixth, in . a manner, that by following
the refolution, when all the parts are properly combined with the fame fuperfluous fixth, it
becomes extremely pleafant, for the fame fuperfluous fixth afcending to the octave of the
fundamental guide of the fcale, and the bafs defcending into the fame fundamental guide,
both proceeding by femitones, which is the fhorter way, always ufed by nature, and con-
fequently the more agreeable. Seethe above example xv. plate 52. As to the fuperfluous
octave, it happens when the common bafs defcends in the fuppofed fcale of A natural, from
the octave of the fame A to G natural, which G muft be compounded with the octave
for the preparation of the 9th to F, into which the fame bafs defcends from G, and the
fame 9th is refolved into F fharp, which is the fuperfluous octave to F natural; this
fuperfluous octave F fharp is a minor 3d to D fharp, which is the above explained fixth
fuperfluous ; and the fame D fharp being the 3d fharp to B natural, which becomes the
guide to the following note E ; confequently F fharp is the perfect fifth to the above guide
B, by which accord it feems like a fundamental guide to E, but is only relative guide to
the principal fundamental guide of the fcale A natural ; and notwithftanding the above B
is only a relative guide, being the firft fucceeding guide of the principal guide E, may have
alfo arbitrarily its 3d fharp, inftead of its minor 3d; which B is diftinguifhed clearly for a
relative guide by the bafs fubfifting in the note F natural, which cannot be comprifed in
the fcale of E, but only in the defcending fcale of A, and the fuperfluous octave F fharp,,
muft fubfift in the other afcending fcale ; confequently it is evident that the note E is not
the principal fcale, but its fundamental guide, and the note B the relative guide of the fun-
damental guide E having the arbitrary privilege of natural minor 3d, to be changed at
pleafure into a major 3d, muft be feen in the above example xv. plate 52, where, in the
fecond meafure of the example, is defcribed the falfe combination of the fuperfluous fifth,
and in the fecond time of the fifth meafure both the fuperflous fixth and octave are all
marked with (*).

In regard to the feventh diminished, is the interval betwixt the afcending indicative
major third, and the defcending indicative flat 9th, which interval is the fame as that of
the major 6th, as has been before explained.

N.B. The combination with fifth, fixth, and octave fuperfluous, muft be ufed with
judgment, and very feldom, particularly the fuperfluous octave, which is the fame interval
of a minor 9th, becaufe being obliged to refolve itfelf by afcending a full tone for giving
the fharp 3d G to the fundamental guide E, this refolution becomes fomewhat improper,

and

88 0/ /^ Composition p/ MUSIC. Book III.

and a little harfh, for the reafon that all falfes exifting in the fecond octave, have their
proper refolution in defcending, and may be ufed in afcending only when all the parts are
doubled.

Article IX. Of the differ e7it Motions and Variations of the Parts.

AS the bafs in the figured harmony muft be considered as one middle part of the com-
bination, being obliged to proceed not only by fkip, but alio by conjoin'd degree,
for the reafons mentioned in the fecond article of this prefent chapter .; fo the parts are
obliged to proceed in the fame manner for the fame mentioned reafons ; therefore by pro-
ceeding not only gradually, but alfo by fkips, they pafs from the place of one part to the
place of another part, as it may be feen in the example xvi. plate 53. This example is
defcribed in five ftaffs, in the firft ftaff is the fuppofed melody, in the fecond ftaff is the
fame melody, but varied by the diminutions of the principal notes ; the third ftaff has the
principal notes of the propofed melody ; and the fourth ftaff contains the combination, which
is compound, belonging to the fundamental bafs in the laft ftaff: In the fame combination
the principal notes of the melody in their correfpondent notes, as they proceed in the third
ftaff, are marked thus (*), by which is fhewn the progreflion of the principal notes of the
melody pafling from one part to another in their combination by fkips. The diminutions
in the fecond ftaff may be varied gradually, or in fkips, in almoft infinite manners, not
only by all the upper parts, but alfo by the common bafs, as mentioned ; but in what-
foever manner thefe diminutions may be done, it muft always be correfpondent to the
fundamental combination fimple, or may be compound ; alfo the refolutions, when the
variation is made by fkips, muft be done from the note, which is neareft to the funda-
mental refolution. But for a better, and more diftinct explanation, not only for the different
variations and diminutions of the parts, but alfo of the bafs notes, we have chofen to examine
the beginning of the firft fonata, a violin folo in the fifth opera of Coreli (being generally
known in all countries) for explaining the divers manners of variations by fyncopes, fkips,
and all fort of paifages relating to the above purpofe.

This firft fonata which is compofed in the key of D 3d fharp, confequently is a tranfpo-
fition of the natural fcale a tone higher, begins in a kind of introduction in common time
grave, compofed in two meafures. The firft meafure has the upper part of the octave of
the note D, which is the principal confonant note of the fcale occupied by the bafs ; in the
middle of the fame meafure, after a little fyncope of the firft note, the part fkips to the
3d of the accord, from which immediately it defcends gradually to the firft note again,
pafling to the note B in the fecond meafure ; which B may belong to E, as its relative
guide, being its perfect fifth, or to the note G to which the note B is its 3d; but the
author in figuring 4th and 6th, inftead of 2d and 4th, has chofe G, being of the better
progreflion, particularly in the beginning of a compofition, becaufe the fame G is the im-
mediate fub-principal relative to the principal of the above fcale D, and confequently the
more natural, and pleafant progreflion or modulation ; and the bafs keeping firm the note
D at the beginning of the fecond meafure, makes the falfe accord to the part, which
paffing into B tranfpofes the harmony into the note G as fundamental relative, and the
inverfion is the fourth and fixth, the fourth is the octave of the fundamental bafs not
expreffed in the accord, and the fixth is the note B of the part; and becaufe the progreffion
paffes immediately to A by the motion of the part, which after the note B defcends to A
octave of the principal guide of the fcale, and the antecedent fundamental note G which
cannot gradually afcend to the fame note A in a fundamental progreflion, confequently
the fundamental muft defcend with its auxiliar fkip of 3d low into the note E, which is
the relative guide of the principal guide A, and the note B of the part becomes the fifth
of the fame relative guide E, defcending to A octave of the principal guide, and the bafs
with its relative fkip of cadence afcending to the fame note A principal guide, and the
continued note D in the common bafs, becomes the 7th to the relative guide E, reib'ving

Chap. I. 0/ & Composition c/ MUSIC. 89

in C fharp 3d of the fame principal guide A, and the part defcending with the following
note to F 3d of the octave of the principal firft note of the fcale, the bais alfo paries into
the principal firft note ; all according to the fame laws and rules explained by the
canons of the harmonic code. After the above two mcafures in grave time, the part moves
in quicker time, making a kind of intonation in efsfiigila, as it is called by the Italians, which
in EngUJJj fignifies flying, paffing fuccedively from one note to another, of the prin-
cipal iimple combination, afcending by three different tranfpofitions of the combined notes
to the higheft pitch of the inftrument, and after defcending in the fame manner to the loweft
octave where it begun. The above-faid efsfugita, or intonation, palTes from the notes of the
laft meafure into the note G fharp of the fucceeding meafure in adagio, or grave time,
which G fharp belonging to E fundamental guide to A as its indicative 3d, confequently
the firft fcale D is tranfpofed into A j and the bafs having always kept firm the note D of
the firft fcale, as immoveable fundamental bafs, at leaft inftead of paffing from its ftable
fundamental to the fundamental bafs note of progreflion E under its afcending indicative
3d occupied by the part, it continues firm in the fame firft note D, confequently in the
antecedent meafure before the adagio time, the fame bafs note D, which has been always 1
a ftable fundamental note, as mentioned, is changed into a common bafs in the middle
of the fame laft meafure, in which place it mould have paffed into the note B as relative
guide to E fundamental guide in the next meafure under the note G fharp of the part,
which G is the indicative 3d, leading into the principal note A ; but the note D, in which
the bafs ftill continues, becomes the 7th indicative defcending note into the 3d of the
principal note A3 and the fame D in the middle of the antecedent meafure becomes
the third of the note B relative guide to the fundamental guide E, as before-faid. After a
little paufe the part begins a melody in common time adagio in the fcale of A 3d major,
with the fifth note of the fcale, in the fame time the bafs note of D 7th of the fundamental
guide E refolves defcending in C fharp, which is the major 3d of the principal fcale A, as
may be feen in example xvii. plate 54. The fame melody is continued in four meafures,
making at their ends the perfect cadence in the fame fcale A, after which the part repeats
the firft little introduction in grave time tranfpofed in the fcale of the note A 3d fharp,
to which follows in the fame fcale the fame firft intonation in flying time, after which the
fame antecedent melody, but tranfpofed in the fcale E, and after the fourth meafure, in
which it makes the cadence in E, continues with its progreflion through the different
fcales of A and G, and at laft the melody, accompanied by the bafs, makej the laft cadence
in D, the firft chofen fcale.

In the above example is only tranferibed the firft gravej firft allegro, and the following
firft adagio, to which is added the fundamental bafs and its proper notes of the fundamental
combination in their reverfion.

The fecond grave allegro and adagio following in the beginning of the faid fonata, is
omitted, being only a tranfpofition of the firft grave allegro and adagio, the explanation of
which may be applied to the reft omitted ; which explanation, joined with the other
examples explained by the antecedent articles, feem more than enough to diftinguifh eafily
and clearly all forts of inverfions that may be done by fyncopes, diminutions 5 and other
forts of motions different from the fundamental, by the parts and baffes in figurative mufic,
with their proper relation to the fundamental harmony.

A a CHAP.

9 o Of the Composition »/ MUSIC Book III.

CHAP. II.

Article I. Of Compofitions in divers Parts.

H E figured mufic may be compofed for divers numbers of parts, namely for
H two, three, four, five, to fixteen or more real parts. The compofitions in two
parts, when only one part with a iimple bafs, as a cantata or fong for the
voice, is called a cantata or fong a voce fola by the Italians, and for a iimple
violin, or flute, or other inftrument with the common bafs, is called alio a fonata or folo.
When the compofitions are deiigned for two voices, or two inftruments accompanied with a
iimple bafs, they are called two, or duetti, by the fame Italians ; but when the bafs is concerted
with the two fuperior parts, with the addition of another common bafs for the organ, or
for the harpficord, are named terzetti in Italian, and trio by the French : The fame of the
quatuor, where four concerting parts with a bafs continues. The inftrumental compofi-
tions never pafs the number of four, or at moft five parts real. It may be obferved, that in
many compofitions for many different inftruments, as feven, eight, and fometimes for twenty
or more parts, they are not all real parts, but the fame principal notes of four or five real
parts diftributed in the others in fimple or different manners of diminutions, confequently
cannot -be called real parts, which figniiies that all are diverily concerned, not only in
the harmony, but alfo in the melody. The vocal compofitions pafs much over the
inftrumental, going from eight to fixteen, and more real parts ; thefe fort of compofitions
for eight or fixteen parts, ferve only for church mufic, on occafion of fome great folemnity,
which are performed by a great quantity of voices, joined alfo with inftruments, or without.
Thefe great compofitions are ordinarily divided into' two or four chorufes, difpofed in a
manner, that fometimes one anfwers to another, and are not always in fixteen real parts,
but divided in particular compofitions for two, three, or four voices, as in a particular concert ;
and fome little choruffes are fometimes mixed, formed by ten or more voices, which are
ordinarily fopranos or contraltos finging all together a melody at the unifons, with only
an organ playing with tafto folo the fame melody, or with only keeping firm continually
the principal note of the guide, or of the firft note of the fcale for to keep the voices in
tune ; which makes a very pleafant effect when it is done in a proper place, as betwixt two
choruffes in full harmony. But when all the choruffes are united, as in the beginning, and
at the end of the compofition, the full combination in eight or fixteen parts may be
introduced in its proper place. The greateft difficulty in thefe kinds of compofitions, is not
only in difpofing the parts in their beft and proper places, but alfo in the difpofition of the
different and particular concertos of voices ; not only reflectively as to the convenience
of the words, but alfo in the repartition of the above divers concertos of voices, in a
manner, that being intermixed with the full chorus, one concerto of two, three, or more
voices, relieves its following concerto or chorus. In regard to the difpofition of parts, care
muft be taken when the chorus proceeds in full harmony, of putting the triird fimple
combination in the middle of the full combination. And it muft be remembered that the full
harmony is compofed with all the notes of the harmonic fyftem, which notes are the three
different combinations joined together, belonging to the guides of their different fcales,
namely the firft harmony of the fame guide, which is compounded with 3d, 5th, and 7th,
to which follows in the iecond place the fimple harmony of its 7th, which is the fourth
note of its principal fcale, and confequently its fub-principal relative ; after which follows
the third harmony, which is that belonging to the octave of the principal note of the fcale,
ending in the double octave of the fundamental guide. This third and laft fimple harmony,
which makes the full harmony, is that which muft be diftributed into the middle parts
of the full combinations j particularly the third of the fame laft harmony, which is the
thirteenth in the full combination, being too much fenfible when it is a major 3d, and
confequently makes confufion in all the combination} for that reafon the fame 3d muft

Chap. II. 0/ /fe Composition 9/ MUSIC. 91

be in the middle, but the bed way is only to ufe it in fome cafes of neceffity. The
octave and the fifth, or twelfth, of the faid third combination, may be ufed fometimes in
the extreme high part of the combination, particularly to give fome ftrong expreffion to the
words when there is occafion ; but ordinarily in the high extreme muft be placed one
of the two afcending or defcending indicative notes, which are, as has been
explained, the 3d and 7th of the guide ; or in the artificial fcale inftead of the 7th, the
9th, which is properly the indicative defcending note of the artificial fcale : by this dif-
pofition, the principal parts being alfo doubled and tripled, the progrefiion into the different
fcalcs is fenfihly and clearly diftinguifhed without confufion. In thefe greateft compofitions
may be ufed all forts of falfes by fuppofition, by change, and fometimes by anticipation,
but thefe very feldom, and' only in the final cadences, as has been explained in the canons ;
alfo maybe ufed all uncommon refolutions afcending, together with the common in defcending,
but in the manner explained in the fame canons. But in compofitions of only eight parts, when
they are in lull combination, the uncommon falfes and refolutions afcending, mull: not be
ufed fo freely as in fixteen or more parts, becaufe ordinarily the parts are not doubled
enough, as in more parts, by which the notes, not only doubled, but tripled and quatripled,
ftrengthen the principal founds of the compound combination ; otherwife a composition
in five real parts will have a better effect. But when all the fixteen parts are doubled and
tripled, and all well difpofed in their proper places, with a progreffion gradually afcending,
and fucceffively defcending, make a wonderful impreffion, not fo eafily perceived by thofe
who never heard thefe fort of performances.

In the compofitions in two, three, and four parts, the obligation of following the principal
harmonic laws is very precife ; and particularly in two or three parts, which compofitions
being formed only by two or three founds, muft be chofen from the reft of the full com-
bination the propereft for the beft harmony. In two parts, viz. for one voice or inftrument,
with a Angle bafs ferving meerly for compliment, it is very eafy to be done, but when the
bafs muft follow the part with good tafte, intermixed with fome proper melody by imitation
or contraft, to the melody of the part helping them, and without the leaft confufion,
it is not fo eafy. The fame is in three parts, when the bafs under the two parts proceed
only for a fimple compliment, in which manner may be called a duetto or two, which
is eafier than when the bafs is obliged to anfwer to the melody of the two parts, in which
cafe are properly called trio or terzetti, with another bafs for the clavicord or organ, in
fimple compliment of the harmony, or without the fame. In like manner may be confidered
the quatuor, as before explained.

In compofitions for two or three parts, are abfolutely forbidden two perfect fifths or two
octaves following one another, for the reafon of being fimple confonant, and not harmonic,
as mentioned and explained in the firft canon of the harmonic code, lid book ; and, in
two parts, not only rigouroufly are forbidden the two fifths or two octaves explicit, but
alfo implicit ; confequently when the part proceeds not by thirds or fixths, or by the falfes,
as fecond and feventh, it muft always proceed by contrary motion, and this proceeding is a
general rule. In compofitions in three parts, muft be combined always the fundamental
third, in whatfocver denomination it may be, as a 2d, 4th, or 6th (harp or flat, in all the
combinations when it is poflible, and more proper for the harmony. In compofitions for
four parts, are permitted two fifths or octaves, but only in contrary motion, becaufe two
other parts may fupply the firft original harmony.

N. B. It muft be obferved, that in compofitions of fimple and compound combination,
the third of the fcale when it is fharp is better in the middle of the accord than in the
extreme acute ,; confequently the feventh, when it refolves into the fharp 3d, muft alfo be
covered with fome other found of the fame accord, and not be in the acute part, in which
manner the refolution into the fharp third, becomes in the middle of the following combination :
on the contrary, when the fcale has its 3d flat, this flat 3d is beft in the high extreme, and
confequently the fundamental 7th of the guide muft alfo be in the extreme high part. The
above rule in regard to the fcale of the fharp third, is diametrically oppofite to that, which

has

92 Of the Composition 0/ MUSIC Book III.

has been mentioned in regard to full harmony : the reafon is, that the full harmony being
compofed of all the three principal harmonies of the fcale, as in the fcale of C, are G, F, C,
muft neceffarily have their indicative notes into the higheft place of the combination for
to diftinguifh their fundamental and principal harmony, otherways they may be confounded.
But the fimple and compound harmony cannot be confounded by the above three harmonies,
one of which is excluded, and the acute found being in the acute part, confequently the
more fenfibly weakens the other founds, of the combination ; fo on the contrary, the flat
founds, which are in proportion of leffer fenfation, are always better in the higheft part.

Thefe general obfervations in the compofitions of divers numbers of parts, may be fubject
to fome exceptions on feveral occafions, particularly on account of the melody, alfo for
fome particular expreffions by the harmony ; all which the compofer may diftinguifh when
he has acquired a fufficient practice and knowledge of the compofitions.

Article II. Of Fugues and Imitations. \

'HpHOSE kinds of compofitions, in which one part begins a fubject of melody, and after
-*- fome paufe, or refts, another part follows in a like or the fame fubject, is called fuo-ue
by muficians : it is diftinguifhed in real fugue and imitation. The real fugue, as improperly
called, is when the part which follows the firft repeats the fame fubject, or near the fame
propofed by the firft part, at the unifon, or fourth, or fifth, or at the octave; but without
departing from the founds of the octave propofed by the firft fubject. The imitation is
called when the fubject of melody is repeated by the following part in whatfbver note of
the octave, at the pleafure of the compofer, as in the 2d, 3d, 4th, 5th, 6th, 7th, and octave,
without being obliged to keep the fame repeat or anfwer in the fame octave. The real
fugues are generally ufed in church-mufic ; but very improperly ufed, and very improperly
named ; becaufe the laid repeat or anfwer being obliged to be done in the limits of the
propofed octave, cannot be always like the propofed fubject, but it muft be altered in fome
notes for fake of the mode, as it is called by muficians, which we call fcale, or octave, in
which has been propofed the fubject by the firft part. On the cantrary, the imitation gives
always the anfwer very like the propofed fubject, being not conftrained to the fame mode
or octave ; confequently the imitations are in better right to be called real fugues, or real
imitations : but becaufe Guido Aretino in harmonizing the Cantus Gregorian applied to the
fervice of the church, which are divided in eight different modes, has followed the Greek
manner of finging thofe cantus without forting from their different modes or octaves ; fo
the fucceffive chorifters, and choir-mafters of thofe firft times, being better acquainted with
the Greek modes than with the different harmonic combinations, and knowing only the moft
fimple harmony introduced by Guido ; confequently they, with all fucceffive muficians to
this prefent time, have fuppofed and do fuppofe, that the fugues in the precife compafs of
the octave called modes, be the very proper fugues calling them reals ; and the
imitations, becaufe fometimes change the octave, paffing into the following octave of the
fifth afcending or defcending, are confidered as improper and irregular : but now, that the
harmony is arrived to its perfection, and the fame melody is come out of its old bondage,
and alfo arrived to its perfection, being totally changed, and the old manner only conferved
and practifed in the common fervices of the church, feem very convenient that
the old terms and names, when improperly applied to the prefent mufic, may be juftly
changed. The above-laid fugues and imitations are alfo very improper for the church, but
of that more will be fpoken in the article of the church-mufic. Thefe fugues, or imitations,
which feem as a mufical pedantry, notwithftanding they may be ufed with tafte and judg-
ment, and properly varied, which very feldom happens, are ordinarily, and not properly
fit for the general pleafure of the public : But the ftudy and practicing them are the beft and
neceffary means for acquiring a perfect knowledge of all forts of combinations and pro-
gressions of harmony, which renders very eafy the compofing in mufic : therefore, a
ftudent in the harnionic art muft never neglect practifing the compofition of all forts of

fugues,

Chap. II. 0/ /& Composition ^/ MUSIC. 93

fugues, not only in the limitted manner of thofe called real fugues, but alfo in all forts of
imitations, not for the public pleafure, but for his own ftudy. In this manner he will be
capable of compoling and adapting the harmony to all forts of melody as he pleafes, in
the manner which is called by the Italians fugato, or by imitation and by reverfion, or
adding together different melodies, without the oftentation of continuing the fame fubject
in a real fugue or imitation, fometimes more than an hundred meafures in a dry fugue or
imitation, only by rambling from one fcale or octave to another j and often with a bad
melody and harmony.

Article III. Of the Manner of comfofmg Fugues and Imitations*

*Hp H E art of compofing fugues and imitations, is not generally fo hard as it is fuppofed j
■*■ what may be a little hard for thofe particularly who are not furniflied with a good tafte,
is for a prompt invention of a good melody, which mud be for the bell: compalfed in leffer
meafures, as is poilibie. if the chofen fubject may be divided in two parts, it will be of
good ufe in the continuation of the compofition in fhortening them, by which the anfwer of
the fecond part coming iboner makes the greater variety. When the fubjecl: of melody is
chofen, it muft be obferved if the anfwer becomes proper, particularly if the fugue is what is
called real, as above-mentioned ; (it muft be remembered that the principal notes of the octave
are two, namely the firft note which is the principal of the fcale, and the fifth note which
is its guide) if the fubject is between the principal note and its guide, the anfwer which
follows muft be betwixt the guide and the octave of the principal. For example, fuppofing
the natural fcale C, the fubject beginning in C paffes to D, the anfwer is G to A ; if the
beginning is D 'palling to E, the anfwer is A to B ; alfo beginning in E to F, the anfwer
is B to C : but when the notes of the fubject proceed by fkip§, the refponce is fomewhat
different ; for inftance, if the fubject paffes directly from C to G, fkipping a fifth higher
or a fourth lower, the refponce is G to C, fkipping a fourth higher or a fifth lower ;
becaufe the note C is the extreme acute of the principal C its octave below, which in
the above fugue real is forbid the pafTing over j but in the imitation the refponce is from
G to D, and the fubject fkipping from D, or from E to C, muft repeat A C, or B C, if the
fubject deicends from C to B returning to C, the anfwer defcends from G to F, and from
F to E, becaufe F being diftant a full tone, which is the perfect fourth of the principal,
becomes the flat feventh of the guide G, the fame feventh being the indicative defcending
note of the fcale, confequently muft be naturally refolved into E, which is the third of the
principal C j but by imitation the juft refponce may be done by G to F fharp returning in
G, which cannot be done in real fugue, the fame F fharp being not comprized in the fcale of
C. This.fhort diftinction feems enough for the knowledge of the difference betwixt the
fugues called real, and the fimple imitations ; being the enumeration of the divers proceeding
of the various fubjects of melody of too large a defcription, and of very little ufefulnefs to
the modern practice of the belt compolitions of mufic. Now, returning to the compofition
of fugues, when the fubject is chofen to which the anfwers become juft, the fame anfwer
muft be introduced in the laft note of the propofed fubject, if that is pofllble, or nearer
the laft note ; and the anfwer being introduced, the firft part muft proceed upon the fame
anfwer, with fome different melody, which may correlpond to the proper harmony ; after
which, the refponce being compleat, if there follows more, of two or three parts, the
preceeding parts muft go on ftill with fome different melody upon the refponces of all
the following parts, which melody muft have fome little connexion to the firft fubject -
or, inftead of fimple melody, may be introduced what is called a contra fubject, upon or
near upon the fame propofed fubject ; and, after all the parts have done, and palled every
one the fubject and its contra fubject, they muft all together make a cadence ; which
ordinarily is in the fcale of the fifth note high of the firft propofed fcale, bein^r its nearer
fcale in the progreflion of harmony, and the fame cadence may be of terminate or indeter-
minate harmony at the pleafure of the compofer.

. B b j f

94 Of the Composition a/ MUSIC. Book III.

If the fame cadence is of terminate harmony, ordinarily the firft fubjedt is repeated, in
the middle of which, if it is poffible, muft follow the contra fubjecl: ; or, when there is
a contra fubjecl:, it may be propofed firft, and for its anfvver the firft fubjecl: ; but if the
anfwer cannot be introduced in the middle of the fame fubjecl:, or contra fubjecl:, the fubjecl:
may be fhortened to introduce the anfwer fooner than it was done in the beginning of the
fup-ue, or imitation. But the proceeding in thefe fugues and imitations, being made in al-
moft infinite manners at the pleafure of the compofer, and the defcription of thefe different
manners being not poffible to be "done in a fmall compafs, as before-faid, confequently an
example to be explained will be the fhorter way, and more profitable for knowing the
proceeding of the above fugues or imitations : for this purpofe we have chofen the firft
fugue, in the firft allegro of the firft fonata, a violino folo, opera 5th, of Corelli, the beginning
of which fonata was explained in the ninth article of the antecedent chapter. The above
fugue is compofed in the fcale of D, with its third fharp : the firft note begins in the
unaccented time of the meafure, afcending gradually from the third note of the fcale to the
fifth note, from which it defcends a fifth, which is the note D octave of the principal
D of the fcale' ; in which manner making a bafs cadence, the above note D is properly the
end of the fubjecl: ; but, for the fake of introducing the anfwer of the fecond part, the
above fubjecl: is augmented with another different fubjecl:, which ferves as an half part of
the total fubjecl, and alfo as a melody for uniting a contra fubjecl:, which forms the end
of the intire fubjecl: propofed, and the 'above contra fubjecl: lines the refponce of the
fecond part, which is done in repeating the propofed fubjecl: in the fourth note below,
which is C fharp, third note to A guide to the chofen fcale D, after the fame fecond part
has repeated the firft, and the fecond part of the fubjecl:, has been added fome notes in
half a meafure for returning in the accord of the principal note D, pafling into the third
part of the fubjecl, which makes the contra fubjecl:, giving at the fame time the opportu-
nity of introducing the third anfwer performed by the bafs, as a third part, beginning the
fame anfwer in the laft unaccented time of the fourth meafure, continuing as was done
by the firft part, at the end of which he makes a perfect cadence in D, repeating after the
Contra fubjecl: done by the fecond part; but, inftead of keeping the harmony in D, as was
done by the fame fecond part, he pafTes B as guide to the following note E, which, as
principal guide tranfpofes the harmony in A, having the fuperior part in the middle accord
as it were a fourth part, repeats the fubjecl: in the accord of the above relative guide B, pafling
immediately into the principal guide E, making the cadence in A, with only the firft part
of the fubjecl:; and, with the fecond part of the fame fubjecl:, continues in the fame accord
of A, not as principal, but as guide to D, in which they fall with the end of the fame
fecond part of the fubjecl:, after which immediately follows as before a fifth part, which
repeat all the fubjecl:, as has been done in the beginning by the firft part, but in the lower
octave; and the bafs, under the fecond part of the fubjecl:, makes the contra fubjecl:, joining
with the fame the beginning of the above fubjecl: in the accord of the guide A, as being
a fixth part ; and at the end of the fecond part of the fubjecl - , and under the third part of
the fame, the bafs, as being a feventh part ? repeats another time the fubjecl: in the accord «f
the principal note D, making the cadence in A, as guide to the fame principal, with the
firft part of the fubjecl: continuing with the fecond part of the fame; at the end of which
is repeated the fame fubjecl: in the accord of D, by the fame bafs, but at the lower octave,
as being done by an eighth part performed by a fuppofing contra bafs or organ, the fub-
jecl: being difpofed in the above manner as it were in eight parts, terminating with the cadence
in the principal note of the chofen fcale D. (See the fame fugue defcribed in example
xviii. plates 55, 56, 57, and 58.) After the above cadence in D principal, the firft part
begins another different fubjecl:, which indeed is the fame as the firft, but with diminifhed
notes, which is followed by a fecond part, and fucceftively by the bafs ; after which is an
interval of melody in imitation of the firft contra fubjecl:, continuing in the fame imitation
for two meafures and a half, after the repetition of the above diminifhed fubjecl: in the
accord of the guide A, accompanied by the firft part with the contra fubjecl:, which makes
the third part of the firft chofen fubjecl:, after which the fame part immediately anfwers
to the diminifhed fubjecl: of the bafs, in the octave of the fame accord of the guide ; and

directly

Chap. II. 0/ /& Composition «/ MUSIC. 95

directly the fecond part anfwers to the fame diminifhed fubject, but in the accord of the
principal note D at the lower octave, to which follows, as being two and three parts joined
together into the violino, giving the accord to the bafs, which moves by Ikips, of guide
and cadence, but diminished with cromas or quavers, all together making a perfect cadence
in B i after which follows an arpegio, by three fuperior parts joined into the violino, the
bafs continuing with its diminifhed fkips of cadence, or of guide, for above nine meafures,
at laft making the cadence in D j but the violino continuing the arpegio, the bafs accom-
panying it, but with fimple notes, 'till the fame cadence in D is repeated j after which
the bafs repeats the firfl beginning of the fubject, to which is anfwered by the fame bafs
as a tenor, but the violino begins a melody, as being divided in two parts ; the firfl pro-
pofes a fubject in the accented time of the meafure, and the fecond gives the anfwer into
the fecond quarter not accented of the fame meafure, continuing in this manner for four
meafures, after the two parts change the melody in a kind of arpegio performed by diflinct
fkips, which alfo may be fuppofed, divided in two parts, the firfl: part in the firfl divifion.
and the fecond part into the fecond divifion, making at laft the cadence in A, and imme-
diately, as a fimple part, the violino propofes the beginning of the fubject in the lower
part of the octave of the chord A, which, inflead of being anfwered, another upper part
propofes three fimple notes of the fame fubject diminifhed, to which directly is anfwered
by a fuppofed other fuperior part with the fame three notes, but tranfpofed into the chord
of D, to which the bafs inftantly follows with the fame intire fubject diminifhed, in the
chord of D paffing in G, and after in A as principal of indeterminate harmony, from
which it is changed by its relative guide E, into the guide A fundamental and liable, as a
pedal in the organ, keeping firm under the parts in the fiddle, which gradually paries in
arpegio the notes of the accord of the principal D, to that of the guide A, in compound
harmony, from which the firfl part pafles with an esfugita, as it is called in Italian, into
the fimple accord of the guide, making at laft the terminate final cadence, (fee the above
fugue in the mentioned example xviii.) The fundamental bafs has been added in the be-
ginning in two different manners to the common bafs of the above fugue, not only for to
mew directly the progreffion, and the conftruction of the fame, but alfo for a more abun-
dant inftruction of the different relations between the combinations of founds, and its pro-
greffion in figured and in fundamental harmony j fhewing the relation of all the fyncopes,
diminutions of notes, and fkips paffing from one part to another in the figured harmony.
In regard to the compofition of the fame fugue, it is evident, that not only the very fame
fubject, but alfo the progreffion, or (as commonly called) the modulation, is of a very dry
nature j the melody of the fubject being very indifferent, and its progreffion being repeated
above eight times fucceffively, continuing always only in the two principal chords of its
octave, furely it cannot be fuppofed that the fame progreffion be too much varied, and only
properly fit for church-mufic, but not for what is called mufic of camera, or other public
and. private diverfion. But, confidering the undertaking of putting two or more parts joined
into the compafs of one fiddle, and the variety which has been ufed in the management of
the fame fubject, in repeating them fometimes in the octave high and low, and fometimes
all the fubject, and fometimes only one part of the fame j all that made not only excufable,
but laudable, and prettily pleafant the above compofition ; in the middle of which has been
alfo intermixed fome different melody, and fome harmony with arpegio, all very proper to
the principal fubject.

From what has been faid, the ftudent of the harmonic art may know the conftruction and
continuation of fugues. It muft be obferved, that when the fubject of a fugue, or imitation,
is chofen, and followed by its proper anfwer, if the ftudent will put under the fame fubject
and anfwer its fundamental bafs, with all the combinations fimple, compound, or full, which
can be afforded by the bafs, in obferving all the different accords, and in diminifhing their
principal notes in divers manners, he will certainly find fome melody which may ferve as a
contra fubject proper to be intermixed with the compofition, or follow the fame firfl fubject,
as we have feen in the above explained fugue of Corelli, in which the contra fubject follows
directly the fubject, and the fame contra fubject may be under me fame fubject, being

compofed

96 Vf the Composition of M U S I C. Book III.

compofed in its fundamental accord, muft alfo be obferved the manner with which has
teen diminiihed the fame firft fubject producing a different fubject, and may be alfo obferved
the laft allegro of the fame fonata, which is compofed by the fame fubject in fugue, only
differently diminiihed, and put in the proper order reflectively to the difference of the meafure,
^vhich in the laft above fugue is in triple time. And for a lure praclife of the management
of the fugues and imitations, it muft obferve not only one, but many of the beft authors
compdfitions, examining attentively their manner of proceeding in their fubjects, contra fub-
jedts, combinations, and progreflions, in fugues and imitations, and their divers melodies
introduced betwixt them, particularly in what is called fugue real, as the anfwers to the fub~
jects of the fame fugues are not always regular. In the above manner, and with a competent
practice of the management of all forts of fugues and imitations, the ftudent in the har-
monic art will in time find very eafy all forts of compofitions harmonic.

N. B. It muft be obferved that the fundamental bafs may be put in divers manners,

under and to the fame fimple melody, with its proper and different accords, by which the

progreffion or modulation is changed, as may be feen in example xix. plate 59. in which

the natural fcaie is expreffed in aicending and defcending with different lundamental baffes ;

it muft alfo be obfei ved, that the fundamental bafs proceeding with the auxiiiar perfect: fkip,

joined with the perfect conionant fkip of cadence (as it is expreffed in the third bafs of the

fame example xix.) is not the proper progreffion for only two parts, becaufe with the fame

progreffion the combination is formed by unifons or octaves in the accented time, and

divided only by the third in the time not accented (as it is between the bafs and the notes

of the afcending fcale) without the third in the accented time, and always without the

fifth, the harmony becomes empty in the accented time, which is the beft and moft fenfible

in the progreffion : but, in three and four parts, as it is in the faid above example, in

which in three parts always the third fubfifts in the accented time, and the fifth in

the unaccented, and better in four parts, where the combination is complete, confequently

the fame proceeding of the above third bafs may be ufed at pleafure. The proceeding alfo

with the (kip of cadence, as it is done by the fourth fundamental bafs under the fame

natural fcale defcending, expreffed in the above example xix. plate 59. is improper under

the fimple notes of the defcending fcale, being the combination only by fifth and octave,

without third, and confequently unharmonic, but when it is joined with all fimple accord,

may alfo be ufed freely.

Article IV. Of Canons,

g* ANONS may be called perpetual fugues, or imitations, becaufe they are compofed upon
^-^ a fimple fubject of melody, without being mixed with any other melody, which fubject
being introduced and terminated by a firft part, the fecond part follows immediately
with the fame melody, and the firft continues in the fame time another melody, which
may be proper to the fame firft melody, and the fecond part continues the fame in its
progrefiicns : if the canon is performed by many other parts, all proceed in the fame
manner, confequently the melody or fubject: being introduced by the parts, one after another,
all the parts cannot but end together all the fubject. The compofition of thefe canons
confift in chufing a melodious fubject, at the end of which muft be introduced the fame
fubject by a fecond part, with the fame notes at the unifons, or tranfpofed in whatfoever
founds of the chofen octave, as at the fecond, third, fourth, &e. at the pleafure of the
compofer ; upon the notes of this fecond part muft be continued, by the firft part, a proper
melody forming the continuation of the propofed fubject, which melody is after repeated
by the fecond part ; under which, if another following part is introduced another time, the
firft beginning propofed by the firft part, to which the fame third part follows always the
firft and fecond part in the fame proceeding with their melody ; and the firft part compofing
always a new proper melody upon the under part till at the end of the fong or tune,

after

Chap; IL 0/ /& Composition c/ MUSIC. 97

after which the fame firft part immediately begins another time the propofed tune cr
long at the time that the other part continues its refpective tune or long till finifhed,
at the end of which it begins the fame again. For to find out the proper harmonic
melody to the following notes of every one of the parts* the fame beginning of the tune
propofed mud be united with all the compound, or full harmony, which can be fupported
by the beginning of the fame tune or long propofed ; and from this compofition and
reverfion, will be found out all the changes that may be done in the propofed fubject.
It has been mentioned that fugues and imitations are only proper for inftrumental, and not
for vocal mufic, as will be clearly fhewn by the reafon that will be produced in the article
of vocal mufic. On the contrary, the canons are only proper for a fimple diveriion in
Vocal mufic, and not for inftrumental j thefe canons being ordinarily extremely dry, confe-
ouently they cannot afford great pleafure to the fenfation ; but in the vocal, the fame words,
which ordinarily are comic, fupply the dry progreflion of the canons. The canons only
in two parts are more eafy and pleafant, becaufe they may be compofed with fome varied
progreflion, as it is to be feen in example xxi. plate 61. but in four parts are always dry
and the words confounded. The example xx. plate 60. is in four parts at the unifon in
the fcale of D natural third, divided in time alia breve, as called by muficians. The firft
part begins a melody in the firft meafure, and the fecond part anfwers the fame melody
at the unifons in its firft meafure, which is the fecond meafure of the firft part: The third
part alfo in its firft meafure (which is the third meafure of the firft, and the fecond of the
fecond part) repeats the antecedent melody propofed by the firft part in the beginning,
following after the fame melody at the unifons, as it has done in the fecond part : The fourth
part follows in the fame manner as the other antecedent parts has done, following fuccef-
fively the fame melody propofed by the firft part, and every one terminating their melody
before every one of the fucceflive following parts j every one repeats immediately the fame
melody one after another, as they have begun, continuing repeating the fame at pleafure,
putting at laft the end, as it is marked in the fame example xxi. plate 61. In this example
it muft. be obfefved, that the melody of the canon has no other progreflion but only fuc-
c'eflively pafling from the notes of the accord of the principal note of the fcale D to thofe
of its fundamental guide A, every firft half part of all the meafures belonging to the accord
of the principal, and the other fecond part to the notes of the guide ; the fundamental bafs
pafling in every meafure from the principal to the fame guide. That has been done exprefsly
for an eafy and clear explanation of that, which muft always be obferved in continuing the
compofition of the melody with its proper reference to the following parts, and to the
fundamental bafs ; and by this obfervation is known how many changes may be fupported
by every note of whatfoever propofed combination, as it is apparent in the fame canon.
It muft alfo be obferved, that a canon in four parts at the unifon, the progreflion cannot
be altered till paft the laft meafure, in which the laft part puts an end to its melody, but
after all the parts have terminated their melody or fong, the progreflion may be changed, -
and continued in another fcale with a different melody, which may properly be united with
the beginning of the firft melody ; but that brings the canon very long and improper for a
compofition, which ferves only as a tune, or fong by memory, for a fimple diverfion in a
garden, room, or ftreet.

C c Article

98 Of the Composition 9/ MUSIC. Book III.

Article V. Of Cadences.

IN the firft book, chapter iv. articles i. and ii. it has been explained, that all progrefTion?
in mufic mull be done by the harmonic combination of the founds belonging to the firft
principal notes of the fcales, and to their fifth notes, which are the fundamental guides
of the fame principal notes. To thefe two principal notes have been added two other notes,
which ferve both as auxiliar to the two other above-mentioned, and thefe added notes are
two thirds, one below, the other above their firft principal notes. From the motions of
thefe above four notes, the two principal, and the two auxiliar, which are the places of the
fundamental bafs, all progreflions in mufic are made by continuall cadences, as it is clearly
apparent by all the canons of the harmonic code j therefore the compofition of mufic may
be defined an harmonic progreflion of divers cadences, viz. fimple, compound, and broken,
and are diftinguifhed in different manners ; firft, in perfect and imperfect j the perfect
cadences are the product of the perfect confonant fkip of a fifth low ; and the imperfect
cadences are produced from the other confonant imperfect fkip of fifth high. Secondly,
in terminate and indeterminate harmony : The two above perfect and imperfect fkips, may
be both of terminate and indeterminate harmony. The cadences arifing from the two
auxiliar /kips are all of indeterminate harmony. The terminate harmony compofes the
final and middle cadences. The final cadences are thofe which put an end to the compo-
fition, and the middle thofe which terminate fome particular periods in the courfe of the
compofition. The final cadences muft be done in the principal note of the fcale, in which
was begun the compofition, accompanied only by the more fimple accord, namely in. two
and three parts, with only the unifon or octave - y in four parts the unifon, fifth and octave ;
in five parts may be added the third j and in fix or more parts may be doubled the fifth
and octave, preferable to the third, particularly if it is major, being by its own nature more
fenfible than the two confonants, as before-mentioned. The manner of doubling the two
confonant notes has been fhewn by the third canon of the harmonic code. In the number
of the final cadences is one, which is imperfect, and it is particularly ufed in church
mufic for diftinction of the old eight Greek modes in authentic and plagal, as has been
explained in the introduction. This imperfect final cadence, inftead of defcending from
the fundamental guide, defcends from the fourth note to the principal ; but this final
cadence, which is done ordinarily immediately after the perfect cadence, muft be in a very
(low manner, by which is fhewn that it is a final cadence. The middle cadences are the fame
as the final, and may be done in three and four parts, with the addition of the third, when
it may ferve for the progrefs of the harmony. Sometimes thefe middle cadences may be
imperfect, deriving from the confonant imperfect fkip of a fifth high, and are called
fufpended cadences, becaufe they ftop at the fundamental guide, without defcending into
the principal note of the octave. Thefe fort of fufpended cadences are ufed and applied to
fome particular expreflions, as points of interrogations, admirations, or exclamations, and
more frequently in the recitative manner; which fort of cadences being of terminate
harmony, muft alfb be done with fimple combination, which is with the major third,
perfect fifth, and octave. All other cadences, perfect and imperfect, which are compounded
with the 7th, 9th, or other fuperior thirds, are all of indeterminate harmony, which
fuppoles the continuation of the harmony for the refolutions of the fuperior thirds, called
difcords by muficians, as has been mentioned in the above chapter iv. article i. By thefe
diverfe cadences is done all forts of fundamental progreffions, as before-mentioned ; but is
not fo clearly perceived in figurate mufic as it is by the fundamental, becaufe the parts and
the bafs moving in different manners, inverts the original fundamental combination, as it
is explained in the firft chapter of this prefent book, and by this means breaks alfb the
order of the fundamental cadences, in which order of the fame fundamental cadences the
common bafs muft be at laft united ; but it happens fooner or later, according to the pleafure
of the compofer : Therefore all inverted cadences may be called broken cadences j between
thefe broken cadences is one which apparently differs from the others, and is broken by

the

Chap. II. 0/ /& Composition a/ MUSIC. 99

the motion of the bafs, when is formed the combination limple or compound, upon one
of the fundamental guides of whatfoever fcale j which guide, inftead of paffing into the
principal note of its oftave a fifth low, or a fourth high, paries immediately to the
next fucceffive acute note, breaking in this manner the true cadence ; which kind of
cadences may be called deceptive cadences, derived from the fuppofed motions of the
auxiliar fkip of third low. As for example, the bafs being in G, which, fuppofing the
natural fcale of C is its fundamental guide, and inftead of paffing and making the cadence
in its principal note C, panes, afcending a note to A, as a relative fcale ; but as a funda-
mental bafs cannot proceed by joint degree, muft fuppofe that the latter end of the bafs
note G is changed into a common bafs, as being in the third note of the relative guide E
to A, and the fundamental bafs as defcended from G to the fame relative guide E for
paffing to A, with the proper and juft fkip of cadence.

Thefe deceiving cadences are like the broken cadences, which derive all from the
gradual motion of the common bafs, all depending from the auxiliar fkips; only the
ordinary broken cadences pafs fucceffively from one note to another, without keeping the
antecedent note in one accented time as it is done by the guide : But the defcending perfect
cadences keep the antecedent note, as properly a fundamental guide divided in two, the
one accented, the other not accented, paffing after into the next note, which alio is in
accented time. See the examples i. ii. iii. iv. and v. plate 62. by which are delineated and
exprefTed all the above forts of cadences. For compofing the fame cadences, the final
cadences muft have the guide in two times, one accented the other unaccented, as above-
mentioned, particularly in grave or adagio time, the accented part may be in compound
harmony, and in the other following unaccented part it muft for the better being relblved
the compound into the fimple harmony, paffing after into the fimple note, as it is exprefTed
in the firft example, plate 62. The middle cadences may be fometimes done in a manner
which may be called a flying cadence (as thofe which may be feen in the fecond example
of plate 62.) but very feldom, particularly in vocal mufic, becaufe when the cadence is at
the end of a terminate period, this cadence muft be regularly and fenfibly done, obferving
the expreffion of the fong and the value of fyllables. The broken cadences properly are
made by all the notes which compofe the harmony, when thofe notes inftead of paffing
with their following notes into their proper fundamental places, fyncopes the firft note, or
panes into thofe of a different fcale, relative, or principal may be, as may be feen in the
third example of the above plate. The fourth example fhews the deceptive cadences,
and the fifth the other cadences, called fufpended, as above explained.

Article VI. Of Accents.

TV/rUSIC has its proper accents as well as difcourfe. The accent in fpeaking, may be diftin-
guifhed into three principal fignifications ; one in regard to the fenfe of the words and
periods, the other to the pronunciation of fyllables j and the laft to the diftinclion of the pe-
riods. The firft is performed by the flexibility of the voice, in changing the founds a little from
the grave to the acute, or vice verfd, according to the diverfe fenfe of the words and periods,
and conformable to the cuftom of the diverfe particular languages ; and this flexibility of
the voice, being diverfe, and in almoft every language, cannot be exprefTed in writing.
The fecond fignification regarding the pronunciation of the fyllables in fhort or long, as-
every one knows the language of his own country by common habitude, confequently only Tome
equivocal fyllables are marked in writing by fome accent, which are called acute, grave,
and circumflex. The third fignification, which regards the divifion and diftin&ion of periods,
muft necefTarily be exprefTed in writing by fome points, columns, commas, and points, by
which the different little refts, which in fpeaking muft be ufed between the different pe-
riods, are perfectly known. Befides thefe figns referring to the diftinction of periods,
fome others are ufed, which not only ferve to the fame diftin&ion of periods, but to di-
ftinguifh their particular fenfe, and they are called points of interrogation, admiration, and

exclamation,

fed X)f the Composition of MUSIC Book lit.

exclamation, by which, in fpeaking, the flexion of the voice is appropriated to their particular
fenfe, in a little different manner from that which commonly ferves to the fenfe of the other
periods. The fame may be confidered in mufic ; but in a manner fome-what diverfe, but
more juft and perfect. All the above different fignifications are diftin&ly and properly
indicated by the divers notes, and other different figns, which notes and figns are all
delineated in the plates 4 and 5, explained at the end of the introduction ; to which notes
and figns .the flexibility of the voice, the pronunciation of fyllables, and the different
diftinction of periods, mufl exactly be conformed. The notes, with their value in the
meafure of time, are all expreffed in plate 4, and defcribed in ten figures. The firft figure
has the longeft in time, and the tenth, which is the laft, mews the fhorteft. To every-
one of the fame notes, immediately follows the number of meafures, or parts of the meafure,
which fhews the value of the fame notes, and under them the different figns, which indicates
their refpective refts. The afcending, and defcending of the above notes, as it is exprefied
in the examples iii. iv. and v. plate 5. denotes the diverfe flexibility of the voice, done in
■its proper time, which time is denoted at the beginning of the compofition with its proper
figns, as are exprefied by the firft and fecond figures, plate 5. and in regard of explaining
the notes, as allegro, grave, or adagio, the fame fenfe of the words gives the direction of
•it j but the inftrumental mufic being deprived of words, the terms adagio, grave, and
prefto, which belongs to the meafure of the time, and the others which relates to the
expreflion, as affetuofo, allegro, or vivace, andante, fciolto, or legato, mufl be always noted
at the beginning of the compofition under the fign of time. In regard to the pronunciation
of the fyllables, long, or breve, the fame notes which divides the meafure of time, mufl be
put in one proper order, by which the pronunciation may be done in a proper and eafy
manner for exprefling the long and breve, and at laft, for expreflion of the diftinction and
divifions of periods, are the diverfe fort of cadences, as are explained by the antecedent
article; or, inftead of them, the divers refts as are noted under every note defcribed in the
above plate 4. which indicates the paufes, or refts, which muft be betwixt one period to
another. We have feen in its proper place, that time in mufic, and their refpective meafures,
may be divided in equal and unequal parts. The time alia breve, a capella, or common
time, and their other derivations, as *, f, &c. are all divided in meafures, which may be
fub-divided by equal parts j on the contrary, the meafures of triple time are divided by
unequal parts. The meafures which may be divided in two equal parts, have their firft
part accented, and the fecond part unaccented ; when the fame meafures are divided in four
parts, by four equal notes, the firft note and the third are accented, and the fecond and
fourth not accented, as it is diftinguifhed in example vii. plate 62. but when the fecond
^note, which is unaccented, being 1 imipiYlnl in two notes, the firft of the two becomes
accented, the fecond unaccented ; and the firft part of the meafure being divided by four
equal notes, the firft and the third are accented, the fecond and fourth notes not accented,
as it is expreffed in the above plate 62. example viii. where every note is marked with their
particular fign long, or breve, expreffed thus ( — long, o breve) and the general rule is
this, that all notes of whatfoever but like value, joined together, the firft is the accented,
and the fecond unaccented, computing in the fame manner the following notes, fo far as
they continue compofed by the fame value ; but the principal accents are always two, the
firft is in the firft note of the meafure, which may be confidered as the very firft principal,
and the fecond accent which alfo may be confidered at the fecono' principal, is in the firft
note of the fecond part of the fame meafure. In triple time the accent falls fomewhat
different into the notes of their relative meafures. In the times divided by the figns of
equality before fpoken, being the accent principally confidered in the firft note of the
meafure, and alfo in the firft note of the fecond part of the fame meafure j confequently all
the middle and final cadences may be alternately in both of the fame two principal accents,
but in time of triples, the firft accent, when the meafure is divided by three equal notes,
is in the firft note, and the fecond accent is the laft ; the middle note being confequently
unaccented, as it is expreffed in example ix. of the above plate 62. The middle, and
particularly the final perfect cadences muft have their laft and final notes in the firft accent
of the next meafure j and this is a general rule which has an exception when the tune or air

Chap. II. 0/ /& Composition «/ MUSIC. 1$ t

•

is compofed for the dance ; in which, beginning the tune by the firft note of the meafure.,
conicquently the laft cadence being obliged to pafs immediately to the fame beginning of
the tune, is alfo obliged to have the laft cadence in the fecond accent of the meafure for
repeating immediately the tune ; and in this cafe, the above general rule is facrifked to the
dance, as has been formerly and commonly done, and it is to be feen in fome triples of
CorcIIi's operas : But in rigour of mufical accent, it is always abufively done. In the fame
triple time, the fecond accent -is not enough for a perfect cadence, and at leaft muft be
employed the fecond note of the meafure joined with the third note of the meafure following
the laft note of the cadence in the firft accented note of the next meafure ; and for final
cadence, the beft is when all the three notes of the meafure are occupied by the fundamental
guide. The perfect cadences are the more pleafant after an harmonic progreflion, which is
done (as has been feen in the antecedent article) by a continuation of broken, flying, and
other divers cadences, confequently in all forts of time they/ muft be done in a very fenfible
and melodious manner. In vocal mafic, its accent muft be conformed and joined to that
of the words ; but in instrumental muiic, being deprived of words, the accent is eaiily
miftaken and mifplaced, particularly by the compolers who has had no better mafter than
his own genius, or practice of the harpficord. It has been repeated that mulick is compofed
by way of diverfe forts of cadences. Thefe divers forts of cadences are to be coniidered in fome
gradual order. The principal cadences, the perfect and imperfect, confonant and fundamental
cadences muft be placed in the firft order ; to which may be added the fufpended cadences,
and the deceptive, or falfe cadences j the flying cadences may follow as fecond in the fame
order, after maybe continued the fame order for the divers broken cadences, giving always
the preference to the bafs note, which is nearer the fundamental, as it is the third note
following the fifth, the feventh, and the other fuperior thirds, by which are broken the
perfect cadences j and in this manner the accent cannot be mifplaced.

D d CHAP.

$e3 W $* Composition of MUSIC. Book III.

CHAP. III.

Article I. The Divifion of figured Harmonv.

HE figured harmony, or common mufic, may be divided, and diftinctly confidered
under three different denominations ; namely, vocal, inftrumental, and local.
Without voices, or inftruments, harmony cannot fubfift. A written compofition
of mufic may ferve for the eyes, not for the ears: Confequently the voices and
inftruments are the neceffary productions of harmony, bad or good. The vocal mufic may
he called natural, becaufe the power of it has been implanted in men by the very fame nature,
as mentioned in the beginning of the introduction ; and the inftrumental may be diftinguifhed
and called artificial, being invented by art. The local .mufic comprehends both vocal and
-inftrumental feparately, or joined together, efpecially applied to the property, decorum, and
'tafte belonging to the different places in which the mufic is to be performed, as will diftinctly
be fhewn in its proper place.

Articie II. Of Vocal Mufic.

WE have juft above mentioned, that the power of ringing, cultivating, and performing
mufic, has been implanted in men by the very fame nature : But this power was
proportioned to the particular conftitution of every one, from whence it happens, that one
has a better voice, difpofition, tafte, and more love to mufic than another : Notwithftanding
every one poffeftes the fame general power of making mufic with his own voice, bad or good.
The mufic produced by a good and proper voice for mufic, is infinitely fuperior to all mufic
that may be produced by any inftrument whatibever j becaufe the beft inftrument can only
produce founds, but a voice may join his mufical founds to the difcourfe ; and when it is
properly adapted, both together acquiring an extraordinary power, becomes abfolute arbitra-
tor of the human paffions, and made wonder and miracles as it is reported by lb many old
and modern hiftorians. But this power falls very fhort when mufic is not well, and properly
applied to the expreflion and fenfe of the words ; and notwithftanding that the mufic may
be compofed by an excellent artift, but indifferently adapted to the words, may be only
confidered as fimple inftrumental mufic, fit for pleafure, but not for affecting and moving
the human paffions, becaufe the excellence and fuperiority of the vocal mufic confifts only
in giving weight to the fpeech, which cannot be done without the excellence of the harmo-
nic art being properly joined to the expreflion of the words ; and this (if we will diftinguiih
the art) is what may be called the only fcience of mufic : Therefore in this k\\k mufic mav
be defined a perfect emphatical expreflion produced by an excellent combination of founds
and words : Confequently to poffefs this fcience of mufic, it is neceffary not only to poflefs
.perfectly all rules of combinations and progreflions harmonic, but all the different impreflions
which may be done to fenfation by the various motions, combinations, and progreflions
gradually, or by flaps ; to diftinguiih the propereft airs which are to be applied to the
■different fenfes, as pathetic, brifk, or languid, in their proper time, flow, or quick ; for
example, a fkip of the fifth high, in quick time, is more proper for fome lively expreflions,
than flapping a fourth low, which is the fame confonant found at the octave low, which
ikip may better ferve for pathetic and doleful expreflions in flow time : And becaufe the
vocal mufic is performed by different voices, as Sopranos, Contraltos, tenors and baftes, every
one of which have a different propriety ; confequently are not of a little advantage, when it
•is in the power of the compofer to make choice of the moft proper voice for exprefling
different compofitions of the words. The Sopranos being of the acute voice, are the more
proper for the quick movements, and thefe for the expreflions, merry and agreeable. The
Contraltos having ■ their voices Jefs acute, and of fwcet tone, may be imployei in the

pathetic

Chap. III.' Of the Composition of MUSIC 103

pathetic and amorous ftile, and other flow movements. The Tenor partaking of all
particularity of the other voices, may ferve in all gay, brifk, grave, and refolute movements,
and particularly in fimple narratives which are done under the terme, or moto andante,
by the Italians called arie perlanti ; which ifj Englijh fignifies a manner of fpeaking. The
Bafs being a more grave voice, is not proper for quick movements, not in the very adagio
pathetic, but in the middle of thofetwo extremes, as largo, andante, rifoluto, andltaccato;
the propereft motions of melody for baffes are fkips, alfo by their gradual divifions, or
diminutions of notes. To the tenor voice all motions are proper. To the contraltos it is
the foftenuto and firm note?, alfo fome few fkips, but not too much diftant in accutenefs
or gravity ; on the contrary, the foftenuto, and firm notes, are not proper for the foprano
voice, but the moving and diminifhed notes are .more proper. Thefe may ferve for general
rules in diftributing the mufic to the voices, which may have fome exceptions on fome
occafions. After all that has been faid above, a little knowledge of the art oratoria, or
poetica, will certainly be of no little fervice for adapting the propereft founds, fimple or
combined, to the various expreffions, as narratives, interrogations, exclamations, lamentations,
conclufions, and all other forts of declamations. But at laft the compofer mould put him-
felf into the fame paflion into which he would move his auditors by his compofitions ; this
may ferve for a general rule to be depended on, becaufe the enumeration of all obfervations
in the divers applications of founds in melody, and combined in harmony to the jufl expref-
iion of words, is of fo much extenfion, and fubject to an infinity of distinctions, all which
cannot be comparted in a moderate fpace. But every one may take care of knowing them
by practice, and by his own private application. .•$

Article III. Of hiflrumental Mufic.

I * H E instrumental mufic cannot pretend to equal the vocal, to which it is only a copy,
•*■ and a copy in miniature, without any obligation of obferving the rules mentioned in
the antecedent article, belonging to the fame vocal mufic, as derived from the fcience
fuppofing the art divifible, all expreffions being arbitrary to the compofers : Neverthelefs
the inflrumental has an honourable prerogative, having been in fome manner the caufe of
the perfection of the vocal. With only the voice, and without inftruments, it would have
been almost impossible, not only to compofe a perfect fcale of mufical founds, but alfo of
repeating a like found which fome time before was pronounced ; becaufe founds are fimple
fenfations, produced by the motion of the air, which vanifhes away, the fenfation alfo
ceafing immediately, and the fame fenfation cannot be printed in the memory, but we may
have the remembrance of having heard a found, which cannot eafily be repeated in the
fame pitch after fome little time past.

We have feen in the Introduction, that not only the firft Greek poets, but alfo the "Roman
orator Gracchus, has been obliged to make ufe of inftruments, only to keep the voice in a
proper and juft tone. Now notwithstanding at this day the performance in mufic is arrived to its
neplus ultra, it is very difficult to. the performers to keep their voice in the fame pitch without
inftruments, as has been tried many times by three or four fingers beginning a fong in a »
fixed pitch, following ringing without inftruments ; after the fpace of three or four minutes,
in founding the firft pitch, they find the voices all fall down into the grave, and that in
proportion to the quantity of time they continued ringing. But not only the vocal mufic in
particular is obliged to the inftruments, but the whole harmonic art, it being evident, that
without a perfect fcale of founds, the melody mould have continued in its imperfect-
beginning, and the harmony never mould have been producted ; being more than probable,
that neither Guido nor others mould have been capable of finding out the fimple beginning
of harmony without the help of the organ, the performance of which has been known
not only by the fame Guido, but alfo by others before him. All that is admirable in the
ordinary disposition and oeconomy of providential nature, which has given to men the power
of producing and cultivating mufic. and to the lame power ha.s joined fome particular

instincts

*o4 Of the Composition of MUSIC. Book Iff.

inftincfs for invening inftmments to imitate the human voice in finging, without thefe
inftin&s mufic mould never have ripened to perfection. Now returning to the performance
of inftrumental 'mufic.

The compofer is abfolute mailer of chufing what melody or harmony he pleafes, but
always rigoroufly obferving the laws or rules of the harmonic art. The inftrumental
-mufic being fit only for pleafure, as before-faid, and not having occafion of fome greateft
performance, as the vocal mufic, confequently it requires not a fupreme flull in the
harmonic art ; the more fimple it is compofed, the better it pleafes the public. A good
melody, carried in four, or not more than five real parts, makes a better effect than full
harmony, in which rauft neceffarily be employed a prodigious quantity of performers for
its good elFedt. The harmonic progreffion of an allegro, when it is the more fimple and
natural, is beft received by the public, as may be oblerved in the compofitions of many
of the beft authors. The allegro, and alfo all quick movements, are not capable of
uncommon combination of founds, as thofe which by Italians are called acciacatures^ thefe
may better ferve in the grave and flow movements. All melody allegro, grave, or pathetic,
may be partaking a little of the tafte of thofe which ferve for dances, and thofe are the
molt pleafant to the public ; as for example, the movements of jig, borree, correntes, for
the brifk and lively ; of ficilianes farabandas for the adagio, or affetuofo ; and of minuettos
for the allegro gratiofo. Here muft be remembred what has been before-mentioned in
regard of the divers terms added to the compofitions, and particularly of the term allegro,
which generally is very little underftood, being confidered as of quick and lively movement,
but is very different ; this term allegro regards the manner of expreffing the notes, but not
to the meafure of the time j and when the faid term allegro is only put, it mull be under-
ftood as in common time, or, as it is called by the Italians^ a giufto time, with the
expreffion merry, but not bride : The fame of the other terms, as gratiofo, amorofo, vivace,
fpiritofo, andante, and fuch other like, all which regard only the expreffion of mufic ;
'only the term prefto, and adagio, and giufto time, regard the meafure of time ; and the
term grave regards both for the expreffion and time, as adagio with an expreffion grave.
It muff, alfo be obferved, that the inftrumental mufic may be performed not only for public
or private diverfion, but alfo in the church, as betwixt fome pfalms, or other vocal per-
formances j in which cafe the inftrumental muft be compofed in the teft proper to the
decorum of the facred place : For doing this it will be uieful to look into the compofitions
of thofe authors who have compofed concertos and fonates proper for the church : It muft
alfo be obferved, that the inftrumental mufic for churches may be compofed with a greater
and more full harmony, being moft proper for the grave and majeftic, which is indifpenfible
in all churches. But this is not proper when the mufic is not deftined for churches. The
more fimple mufic, with a pleafant melody, as before-mentioned, is always the beft for
public and particular diverfions, conforming to what may pleafe the public, which ordi-
narily are ignorant of the harmonic art ; and notwithstanding all pretend to be not only-
lovers of mufic, but alfo connoiffeurs therein, it frequently happens, that the learned and
acquainted with the fame art, which are generally the leffer number of the alTembly, find
themfelves obliged to follow the greateft part of the audience.

Article IV. Of local Mufic ; and> firfi^ of facred Mufic .

t ~T^ H E Compofition of mufic muft be always done not only according to the
■*■ quantity and ability of the performers, and to the genius and general talie of the
country, but alfo to the propriety of the different places where it is to be performed, as
church, heroic, and comic theatrical mufic, and chamber mufic,. which are all compre-
hended under the title of local mufic. Every one of the above kinds of mufic have ibme
different peculiar rules to be obferved, befides the common rules of harmony.

Sacred

Chap. III. Of the Composition c/ MUSIC. 105

Sacred mufic in the greateft churches, particularly of the Roman and Amhrojian com*
munion in Italy and in Germany, as metropolitans, cathedrals, and colleges, is commonly
divided in ferial or coral, in fimple and double feftivals and folemn. The coral or ferial
in fimple canto fermo, as it is called, is performed on every common day called ferie,
by all the affiftants to the great choir of the church, as canons, chaplains, and prebendaries.
The fimple feftival is fo called, when on fome ferial day happens the commemoration of a
common faint ; and the prayers, pfalms, &c. are fung partly by the affiftants of the great
choir, as above, in canto fermo, and partly by mulicians in canto Gregoriano harmonized,
in three, four, or more parts. The double feftival is performed in figured mufic, almoft
all the prayers by mulicians, with the addition of one motteto for one, two, or more voices,
in commemoration of the particular faint; and the folemn mufic is pra&ifed in almoft all
the churches on the occafion of fome particular great feaft, as for thankfgiving to the
Almighty with a folemn 'Te Deum y being a devout and religious cuftom for fome public
remarkable fuccefs, or for the dedication and confecration of tiie church, or on fome other
great occaiions, in which the compofition and performance of mufic is done in the moft
folemn manner poffible. To this great and folemn mufic may be added fome facred
poetic compofitions, commonly called oratorios, the mulic of which is ordinarily performed
by only four, five, or fix voices, with a number of inftruments of all forts, in a majeftic
manner. Thefe oratorios are compofed for a feaft of fome particular faint, and particularly
for the folemnity of Chrijimas-day. Thefe performances are continued for nine fucceflive
evenings before the day of the feaft, or for eight fucceflive evenings after the fame feaft.
The compofition of thefe kinds of mufic are not obliged fo rigoroufly to keep their melody
and harmony in a grave order, though very modeft and more natural ; but they may be
compofed in a way more free and expreffive, not only in the compofition of the diverfe
recitatives, but alfo of airs and chorufles, which ordinarily are compofed in a manner called
madrigal ; notwithstanding all muft be regulated to the decorum of the facred place,
particularly in the melody of airs, which muft always be very far from the tafte of the
dance; except the. mufic compofed for tne folemn day of CbriJImas, and its novenes or
octaves, in which may be introduced fome long, air or chorufes, compofed with the melodies
in imitation of fome dances commonly played by bagpipes, as it is generally the cuftom in
Roman churches, expreffing in that manner the mirth and chearfulnefs of the fhepherds in
receiving the annuntiation of the nativity of the Mefliah, and by this remembrance a
particular devotion is promoted in the congregation.

The particular rules for the application of the harmony convenient to the church, feem
that by the fame name of church mufic, there may be enough explained, and by all
compofers be well underftood. Every one knows that the church mufic is imployed in
finging' hymns and pfalms to the Almighty, begging help, grace, pardon, &c. for all the
congregation, confequently mufic being as a deputed orator, muft be correfpondent to the
above ends, and at the fame time proper for promoting an humble afTurance and devout
hope, with a perfect contrition among the congregated faithful. All this muft be always
prefent to the compofer in compofing church mufic, choofing the propereft harmony to be
applyed to the divers fignifications of hymns, pfalms, &c. which harmony, as before-faid,
muft always be grave, but humble and modeft ; therefore the combination of founds muft
be the more natural, alfo the progreflion or modulation, without waving from one fcale or
mode to another, but only paiTing by the more natural fcales, and not frequently ; avoiding
in this manner all ftrong expreflions, being directly contrary to the modefty, the humility,
and to the necefFary reverence of the facred place ; and as the principal rule of all above-
mentioned, not only the fenfe of the words, but alfo their pronunciation, muft be clearly
and diftindtly perceived, this rule belonging in common to the compofers and the fingers,
which in this particular the fimple fucceflive notes muft not be altered, but clearly pronounced,
and in the belt but fimple manner in regard to the expreflion of the words, without flourifh-
ing graces, which are all impertinent and indecent in facred mufic : But this rule is the
moft negie£led both by the fingers as well as the compofers ; every one is poflefled with an
itching humour of dif playing his good tafte, the mafters in their compofitions, and the

E e performers

^06 Of the Composition cf MUSIC. Book III.

performers in ringing, without confideration to the juft and eafy pronunciation of the words,
in a manner that the words become only lubfervient to the mufic, when it is the mufic
that ous;ht to be lubfervient to the words; and this is the molt neceffirv rule in all forts of
vocal muiic.

•

The matters take care of compofing the mod ftudious and laborious pieces, of muiic,
full of fugues, imitations, contrafugues, double fugues mixed with fimple and double
<:ontrapoint, with many long contiles, or divifions, and fuperfluous repetitions of words and
mufical paffagcs, but notwithstanding that the harmony may be excellent, and very well
adapted to the fenfe of the words, yet in the fame inftant of being performed the fame
good application of the compolition muft be deftroyed, when the pronunciation of the
words is confounded by three, four, or more voices, by which every one pronounces different
fyllables and words. This is the greatefl and mofl fcandalous error which has been' in
vogue from the fifteenth century to this very day. The pra&ice of fimple and double
contrapoint, with all kinds of fugues, canons, &c. are not only the beft, but alfo the
neceftary means to attain the perfect knowledge of all forts of combinations of founds, and
their different progreflions, as mentioned before ; and the above fugues, imitations, &c.
may be praclifed in public by the inflrumental mufic ; but generally for the vocal, as efpe-
cially in facred mufic, all the above forts of compolitions feem to be very improper and
indecent, for the reafon of the great difficulty of making them without confounding the
words. Sometimes the fugues and imitations may be ufed in the word Amen^ or A/k/ujab,
becaufe all the fenfe is comprifed in one fimple word, confequently it is underftood by the
firft pronunciation j but care muff be taken to keep fhort the fubjecT: and its progreffion,
avoiding always the repetition of the fame word as much as poffible, alfo the long contilenes
or divifions, compofed and performed for and by a fimple vowel, both thefe infignificant
repetitions and long contilenes being very indecent and irreverent in facred mufic. The
repetition of words becomes fometimes proper for a greater expreflion, particularly in begging
pardon, grace, or for fome admirations of the divine providence, but muft be ufed very
difcreetly. All thefe faults will furely be avoided if the matter in compofing facred mufic
will imagine himfelf to be prefent before God, as a profound humble fupplicant, praying
for grace, or forgivenefs of his fins, or other like, conformable to the words to be harmonized ;
and in this manner he will find the propereft expreffions from the general combination of
founds, and their progreffion to be applied in every fort of church muiic, particularly for
the chorufes, which for the beft, muft be fyllabic, all performers ringing and pronouncing
the fame fyllables, which performers may be divided into two, or four churches, when
they are enough for a folemn mufic : From this divifion, the two or four chorufes finging
fometimes all together, and fometimes alternately, in the order of their chorufes, arifes fome
variety, which may be alfo adapted to the fenfe of the words : Moreover there may be
compofed, in the middle of fome chorufes, a verfe for eight or ten fingers, all finging
together at the unifons, as fupranos or contraltos, in a little chorus, accompanied with the
organ at the unifon of the voices, or with the immoveable fundamental bafs in the pedal,
without other accord, ferving for keeping in tone the voices, which is extremely pleafant,
when it is in a proper place ; and when the vocal is joined with the inftrumental, a greater
diverfity may be introduced by fome divers melody for the inftrumental not conformable to
that of the vocal, as fome fugues, or immitations to be performed by the inftrumental for
the lame time that all the finging parts proceed with their fyllabic harmony -, which manner
makes an admirable effect, as I have obferved in a folemn compofition of a credo per-
formed by a great number of fingers, and all forts of inftruments, in which performance
all inftruments playing a proper melody in fugue in fix real parts, accompanying in this
manner the fyllabic harmony of the fingers till the verfe paffes fub Pontio Pilato ; for
which was changed the firfl harmony, and a grave one, and very pathetic was adapted,
and after in the following article the refurrexit, was repeated the firft fubjecT: in the fame
manner of the beginning by all chorufes, and continued to the end ; and was all performed
in a very little time, being deprived of all unmeaning repetitions, and tirefome contilenes
or divifions.

Article

Chap. III. Of tie Composition of MUSIC, i0

Article V. Of Theatrical Heroic Mujic.

r T" , Heatrical performances have been introduced for reprefenting to the public, and
-*• exalting with praifes, the heroic actions of fome great man, and by this means to
flimulate the audience, and particularly the young people, to a ftrong love of virtue and
noble actions ; confequently the theatre was formerly a pleafant and diverting fchool of
morals. But this fchool has been drawn very far from its original defign. The caufe of
this alteration is not fo eafy to determine. It may be fuppofed that the inconftancy of
time, which continually metamorphofes every thing, has changed the firft fettlement of
virtue (modeftly fpeaking) in a fimple divertifement : But that is a general caufe, which
comprehends many others immediate and particular ; the principal of which feems to be the
infipidity of the very fame performance, which alfo may be derived from other caufes, as
from the particular negligence or ignorance of the compofers of poetry or mufic ; it beiny
evident, that without a good and proper piece of poetry a moving mufic cannot be done ;
and the moll excellent piece of poetry may be deflroyed by a bad compoiition of mufic :
Alfo the difficulty of uniting a proper company of good actors and fingers, which is the
caufe that in an opera compofed by a perfect mailer fcarce is to be found a moving air or
recitativo; to which may be added the little recompence done to the compofers, beino-
ordinarily an inferior actor preferred to the compofer. All the above chain of caufes have
changed theatrical performances from their firft inftitution into a fimple cover to many other
diverfions, confequently is not now any more the cafe of compofing a perfect moving piece
of mufic. Therefore the compofer of mufic has nothing more to do, than to look over
the poetic piece to be let to mufic, and to take an exact information of the abilities of the
actors in- their manner of finging and acting, for compofing the mufic proper to their
particular abilities. The mailer, in compofing the mufic, muft remember that it is to be
performed by memory, confequently the melody of the airs, alfo the recitativo, or recital
pieces, muft be eafy, particularly in their progreffions or modulations, pairing into the
more natural fcales, relative to the principal, chufing the melody moil appropriated to the
fenfe of the words, and particularly the moft capable of a clear and diftinct pronunciation
of their iyllables. The invention of the melody to the different airs muft be varied one
from another, but always in a manner fuitable to the fenfe of the words j and in refpect
to the recital part, it muft be done in an acurate manner, as in fpeaking, but finging - f
which recitativos muft alfo be varied one from the other, in a manner that when the fame
accord of founds happen to be repeated, it muft be inverted in another manner, the hearing
often an accord falling in a like manner, as many compofers do, without regard to the
necefiary variety of the mufic being very difagreeable : Alfo the end of all recitativos muft
be conformable to the fcale of the following air, when its {enfe has relation to the ante-
cedent recitativo. But when the air, as it fometime happens, changes the fenfe of the
words from allegro to pathetic, or, vice verfa, may be palled in a ftranger fcale, but proper
to the expreffion of the words, notwithstanding that the fcale may be improper to the ante-
cedent fcale of the recitativo, obferving always (as beforc-faid) to give the proper expreffion
with the compofition of the mufic, but in an eafy manner, not only for fake of the
memory, but alio becaufe the greater expreffion muft be compleated by the action of the
finger, which adtion mav be leffened when the finger is obliged to be attentive to a hard
piece ol mufic. Alfo it muft be obferved in compofing airs of fome fpecial paffions, always
to chuie the beft actor when poflible ; becaufe very often the compofer is obliged to give
the part of the greater expreffion to a bad actor for being- the beft finger, or for being
protected by fome gentleman of authority} and this is another caufe of the juft negligence
of the compofers, who will not undertake an unfruitful trouble ; it being evident that
exprefiion only may change the beft mufic into one very bad ; but a proper mufic, when it
is well exprefied, produces a wonderful good effect, as I have obferved on divers occafions,
and particularly in the opera called La Meropc, fet to mufic the firft time in Italy bv the
famou- Gajpitrihi, where in one ' recitativo without mftrurnents, fung by Mcrcpe and her

ion,

So8 Vf the Composition of MUSIC. .III.

•

fon, which with a feigned name, appearing as a ftranger meffenger to give the fa he account
of having feen his fon afiaflinated, and before he expired, havin^prayed him to kits, in hi*
name, the hand of the queen Merope his mother, to this purpose, being come to the court :
But (he, from fome internal emotion, by which fhe was furprized at the firfl feeing him,
fuppofing her own fon a long time dead, and confequently her fame prefent fon a ftranger,
and the affaffin of him. This recitativo was full of interrogations, redargutions, exclama- 1
tions, and other like fort of moving and ftrong expreffions, with the mulic and the a&ion fb
well adapted, that the crouded affembly were all fo affected as to fried tears. Here, in
London, in the opera of Coriolanus, the mulic compofed by Attilio Ariojli, at the fcene of
the prifon, performed by Sene/ina, all the affembly was abforbed in extreme attention and
profound filence. Therefore it is evident, that theatrical performances may be reftored to its
firfl inftitution by the contrary means by which it was deftroyed, namely, by a good piece of
poetry, expreffive mufic, and proper actors.

Article VI. Of Theatrical Co??iic Mufic.

*TP H E comic mufic was formerly introduced between the theatrical ferious heroic mufic,
-*- as for a little merry diverfion. It was performed by a comic finger, as fellow-fervant
to one of the principal parts. Now this ufe is paft, and inftead of it, there has been introduced
-fome comical compofitions performed by two fingers, as before, for diverfion, betwixt the
feveral acts of the heroic opera ; and thefe comical compofitions are called intermedia, which
contains fome ridiculous and merry fubjedts, totally feparated from the principal fubjecr. of
the whole opera. This comical mufic muft be very eafy, and not obliged to the rigorous
meafure of time, to the end, that the fingers in charging their proper action, and the
expreffions of the words, may move the fpectators to laughter. The invention of the melody
mufl be proper for it. Not all compofers have a proper tafle for this kind of mufic : One
may be excellent in all other branches of vocal mufic ; but in comic mufic his imagination
cannot fubminiflrate to him an adequate invention to the comical fubjedt ; therefore, the
looking into fome of thefe forts of compofitions will be of good ufe, and of better ufe in
framing them, when it is poflible, that will fuggeft to his own imagination fome like
inventions.

Article VII. Of Chamber Mufic.

*~Y* y H E chamber mufic may be diflinguifhed in three different forts, namely, vocal, with
* inflruments, and vocal, without inflruments, and fimple inftrumental.

The vocal compofitions, with inflruments, are near the fame as the oratorios j only the
melody is not fubjected to neceffary local devotion and reverence j alfo the harmony,
particularly in the recitative part, which mult be very expreffive, and much varied, and
confequently it is more liberty to the compofer, who may difplay their good tafte without
being perplexed by particular rules. This fort of mufic is ordinarily called, in Italian,
ferenate, confifting of fix, eight, or more airs, with recitativoes, performed by four, five,
or fix of the beft fingers, accompanied by many of the beft and properefl forts of inftruments,
and are performed in fome great houfes, as of kings, princes, and eminent lords, and
ordinarily, in fummer time, in the gardens (from whence is derived the name of ferenata, as
played in an open ferene place) on occafion of fome nativity, or marriage of princeffes and
great lords, or other folemn rejoicing. The compofition muft be very majeflic, but merry,
and with the beft and greateft, or full harmony. The majefty of the compofion may be
expreffed by the vocal parts, particularly in the different melodic chorufes ; and the melody
of the inftrument may be merry, with flourifhing and diminifhed notes, or with different
iubjects united to the vocal melody, or by way of contract in the beft manner, all applicable
to the fenfe and pronunciation of the words, taking care that the inflrumental may not
deftroy, but help the vocal in the expreflion of the words, and their fyllables; this being a

general

Chap. III. Of the Composition 0/ MUSlt 109

general and indifpenfable rule for all the vocal mufic joined with the inftrumental. In
regard of the recitative, when the vocal part cannot be aflifted by the inflrumental in the
expreflion of the fenfe, as ordinarily happens, in this cafe the compoler muft give all the
more moving expreflion in the compofition of the vocal with the propereft and mofl
moving harmonic combinations of founds in their proper progreflion, by which the finger
may have the be ft expreflion.

The fimple vocal without inftruments is only ufed in Italy, and very feldom in other
countries j and it is ufed in fome particular affemblies of lords and ladies, who pafs the
long winter evenings in finging fome cantatas or duettos, only with the harpfichord and
violoncello, when the reft of the afferribly pafs the time in playing at cards or otherwife.
Thefe cantatas are performed only by the ladies of quality, and fometimes by fome young
lords, in which affembly are not admitted the profeffors of mufic, but only fome ftranger
of the beft fort, and that but very feldom. This fimple vocal mufic is of the beft fort,
compofed by the beft poets, and mafters of mufic ; and fometimes by the fame lords the
poetiy and mufic, or alfo the mufic by the ladies, among whom are many not onlv
excellent fingers, but alfo compofers. Thefe fort of compofitions being deprived of the
help of the inftrumental, and of all action, confequently there muft: be ufed all the moft
expreflive combinations, and propereft progreffions, in compofing not only the recitative
part, but alfo the airs ; the melody of which muft be extremely proper to the fenfe of the
words : The bafs for the violoncello, when it is feparated from that of the harpfichord, muft
be compofed in the beft and moft melodious manner, by imitation, or fome different
melody, proper to help the expreflion of the vocal part : The harmony of the harpfichord,
particularly in pathetic airs and recitativos, muft be in as full combination as poflible, with
its accicaturas, more proper for the ftrongeft expreflion. Thefe cantatas are very ftudious,
and give the greateft pleafure with their moving affections : But in fome ordinary cantatas,
a voice fola, compofed by an indifferent poetic ftyle, the mufic cannot be of the moving
fort, but only proper to the infignificant fenfe of the poetry ; and thefe fort of cantatas are
thofe which commonly run in every country, but the beft fort very feldom, becaufe the
perfons keep them zealoufly clofe for their own ufe.

The fimple inftrumental chamber mufic comprehends all forts of inftrumental mufic, and
fometimes intermixed with fome favourite air or fong of fome opera ; and this happens in
almoft all the countries of Europe, and it is often performed in public affemblies ; excepting
in Italy, where all forts of chamber mufic are performed in private, and in thofe particular
affemblies of young gentlemen, where the inftrumental mufic is practifed for pleafure and
for practice, every one, who is capable of compofing, expofes their mufical compofitions,
which are almoft all compofed for the violino, flute, or oboe folo, or in concertos with a
principal inftrumental part accompanied by the other inftruments j and never, or very
feldom, is performed any printed mufic, excepting fome concertos, when they newly appear
in public, every afTembiy being provided with many particular manufcript mufic.

The inftrumental mufic is only fubject to the general rules of harmony, and to that of
pleafing, and the beft are thofe which pleafes the moft and are beft approved by the public.

Thefe are all the particular rules which may belong to the different vocal, inftrumental,
and local mufic, as are expreffed in the articles of the prefent laft chapter, which puts an
end to the whole treatife of the harmonic art, or compofition of mufic.

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10.

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