To Music's sacred Temple, Mercury.  
And Orpheiis dedicate their Harmony  
From thence proceeding. Whose fair Handmaids an  
Myster'ous Numbers: which, if you compare.  
The Rat'on of proport'ons you will find.  
These please the Ear, and satisfy the mind.  
For nothing, more, the Soul and sense contents.  
Then Sounds expressed by voice, and Instruments.  
Io. Dir. john Chantry ●  
sold by Peter Dring at the Sun in the Poultry:   

TEMPLUM MUSICUM: OR THE MUSICAL SYNOPSIS, OF The Learned and Famous Johannes- Henricus- Alstedius, BEING A Compendium of the Rudiments both of the Mathematical and Practical Part of MUSIC: Of which Subject not any Book is extant in our English Tongue.  
Faithfully translated out of Latin By John Birchensha. Philomath.  
●mprimatur, Feb. 5. 1663. Roger L'Estrange.  
London, Printed by Will, Godbid for Peter Dring at 〈◊〉 Sun in the Poultry next Door to the Rose-Tavern. 1664.   

To the Right Honourable EDWARD Lord MONTAGU Earl of Sandwich, etc. Knight of the most Noble Order of the Garter, and One of His Majesty's most Honourable Privy-Council.  
SIR,  
WHen I considered the Excellency of the Subject of this Book, and deserved Fame of the learned Author, I thought it not necessary to crave a Protection for this Treatise by a Dedication of it unto any: being in itself far above the reach of detracting Calumniators. Yet I have made bold, humbly, to present it to your Honour as a pleasant and delightful Divertisement from your many and great Employments. In all Age's Music hath been acceptable to the wisest, greatest, and most Learned men, of whom many have been famous for their great Ability and Knowledge in this Science and Art. It was no dispraise to David that he played skilfully on the Harp, and Sang well: the Compositions of divers Germane Princes are extant: neither is it the least of those Virtues which are eminent in your Lordship, that you are both a Lover of Music, and a good Musician. The renowned Alstedius in this Compendium (not much differing in his Judgement from the Opinion of the Generality of modern musical Classic's) does present the world with a great Light and Discovery of this Art, with the Subject, Principle and Affections thereof, with the curious Symmetry of Proportions: the proportional Dimensions of Sounds: the Variety of Diastems: the admirable Series of musical Voices: the usefulness of Tetrachords: the several Genus' of Music: and harmonical Moods, which being expressed by Voice or Instrument or both, do operate ineredibly upon the Affections. Wherefore I hope that this Book will be accepted both by your Honour, and all ingenuous Lovers and Professors of this Art, and the Errors thereof favourably pardoned by your Lordship and them. The Reason which moved me to undertake this Translation, was, because I desired a Discovery might be made of some Principles of the Mathematical part of Music, unto those ingenuous Lovers of this Science, who understand only our own Language, to the End that by this means the transcendent Virtue and Excellency that is comprehended in the due proportions of musical Sounds may be known unto them; which will give Satisfaction unto their Reason aswell as to their Sense. I do not think this unworthy my labour, because that many skilful Musicians have not thought it any Disparagement to publish their Translations of the Works of famous Men, who did write of the Art which they themselves professed. As Meibomius Translated some Fragments of Baccheus, Alyppius, Nichomachus, and others: the never to be forgotten Franchinus, the Commentaries of Briennius, Aristides, Ptolemy, and others: and our English Douland, the Introduction of Ornithoparcus. In the Author's last Edition of his universal Encyclopaedia, I met with an Appendix to his Musical Synopsis, taken out of the writings of Erycius Puteanus; but not finding any thing new in it, only an ABCdary Repetition of the first Elements of Music, formerly but more judiciously and largely handled in this Compendium: and also some few Questions started by Cardanus, which are, for the most part more fully and Satisfactorily resolved by the Author; I did forbear the Translation thereof; not being willing to weary the Reader with the unnecessary recital of those things, nor your Lordship with too tedious an Epistle, which I here conclude, humbly craving pardon for my boldness, and your Honours favourable Acceptation of this Mite from your Lordship's  
Most humble and devoted Servant, JOHN BIRCHENSHA.   

To all ingenious LOVERS of MUSIC.  
GENTLEMEN,  
IT was for your Profit and Benefit that I undertook this Translation: and that you might thereby understand the Rudiments and Principles both of the Mathematical and Practical Parts of this Science. We know that there is some light into the Mathematical Part of all other Arts; but little discovery of that Part of the Theory of Music hath been made in our Language; therefore I did suppose that this work would be gratefully accepted by you, the Author having more fully discovered the Precepts, Rules, and Axioms of this Science, than any other whose Works I have seen.  
Since the Rumour of this Translation hath been spread abroad, I have by divers been demanded, What Benefit and Advantage the Knowledge of the Mathematical Part of Music does contribute to the completing of a Musician? To which I answer, That it is as necessary for a perfect and complete Musician to understand the Proportion of Sounds, as for a curious Painter, exactly to know the Symmetry of every part o● a Body: that so he may rightly understand the ground and foundation of the Art he does profess, which is, the nature of Sounds, and their due Proportion, in respect of their Ration, Habitude, Quality, Difference, Excess, Dimension, and Magnitude. For this I dare boldly affirm, and if ●ccasion be offered: undertake to prove it: That such Rules may be yet further, and are already, in part, contrived (drawn from the Mathematical Principles of Music, by which, musical Consonants and Dissonants (artificially applied and disposed, according to the nature of their Proportions, and by the forementioned Canons) may afford, in 2, 3, 4, 5, 6, 7, or more parts, as go●d Music, that is, as agreeable, artificial, and formal, as can be composed by the help of any Instrument. Yet until such Rules be known, it is commendable in any to use such helps as may Advantage their Compositions. But for any Musician to unde● value or speak slightly of the Mathematical part of Music, is to reproach the Common Parent from whom the Art h● professeth received a Being. I know that all Ingenuous persons who are Artists, will acknowledge that it is a more noble way to work by Rules and Precepts in any Art, then mechanically; And so to work in this Art. i. e. to compose regularly, will be found more advantageous than any other way in these Respects. For by such a way of Operation the Composer shall work more certain●y, firmly, readily, and with more facility then by any other way.  
If Music be an Art, than it may be contracted and collected into certain Rules which may discover all those Mysteries that are contained in that Science, by which a man may become an excellent Musician, and expert, both in the Theorical and Practical Parts thereof. To the Completeing of such forcible Rules I have contributed my Mite, whose Certainty and Reality has been Experienced by divers, and may likewise be further known unto others, if they please or desire to understand them.  
I know that all Virtuoso's will encourage those things which conduce to the Improvement of any ingenious Art: but what shall be spoken against such things by persons rude, envious, or that do pass their Judgement rashly upon things which they know not, having neither seen, heard, nor understood them, is not to be valued. And I do assure myself that there is not any person in this Nation, that is a true Lover of this Science; or a Professor thereof, who does truly honour and understand this Art, but could cordially wish such an Improvement thereof, that those things which in Music are concealed and mysterious, might be fully discovered: those which are imperfect, completed: those which are doubtful and disputable, cleared by evident Demonstration: those which are not to be done without great trouble, facilitated: those many Observations which burden the Memory, made few and plain: and those whose Operation and Experience does require the study and Expense of many years, might be performed without any difficulty in a few Weeks, or Months at the farthest. And that this way is found out and effected in a great measure, I say, many persons of Worth and Quality are able experimentally to testify.  
Music hath already flowed to a great height in this Nation, for I am persuaded that there is as much Excellency in the Music which hath been, and is now composed in England, as in any part of the World for Air, variety and Substance. ●ut I heartily wish, that af●er this great Spring and ●lood, there be not in our succ●eding Generations) as low an Ebb. For if the serious and substantial part of Harmony be neglected, and the mercurial only used: It will prove volatile, evaporate, and come to nothing. But, Gentlemen, I woul● not willingly weary your patience, and sinc●●he Temple is so small, I will not make the ●ate too big; But subscribe myself as it is known I am) a true Lover of Music, and  
Your Servant J. B.   

I Have endeavoured faithfully to translate the Original, in wh●ch I find some mistakes, which I dare not impute to the Author, of which I would have thee take no●ice. And also one Erratum in this Impression.  
1. Fol. 20. the greater Semitone exceedeth the lesser by the lesser Diesis: whereas it exceedeth it but by a Comma, as appeareth fol. 18. where the Author saith thus, The Comma is the difference between the Semitone mayor and minus.  
2. Fol. 31. almost ten parallel Lines; the Word almost should be left out, for the greater System is ten parallel Lines.  
3. Fol. 44 for d moll. read b moll.   

TEMPLUM MUSICUM.  

CHAP. I. Of the Subject of MUSIC.  

PRECEPTS.  
MUSIC is the Science of Singing well, otherwise called Harmonical: and Musathena.  
The parts thereof are two: the general and the special.  
The general part doth treat of the Subject of Music; and both of the Principles and Affections of the Subject.  
The Subject of Music is an harmonical Song. And this is the Subject of Tractation. The Subject of Information, is the Faculty of Singing: and the Subject of Operation, is the matter to which harmonical Music may be applied.   

RULES.  

1. Music is a Mathematical Science, subalternate to Arithmetic.  
For as Arithmetic doth treat of Number, so Music of the number of Sounds: Or as others of numerous Sound. For as the Optic Science is called a certain special Geometry, so Music may be called a certain special Arithmetic: But whereas some contend that Music is both a Science, Prudence, and Art, because it doth instruct both skilfully, or scientifically, and prudently, and artificially to compose an harmonical Song, it is not so accurate. For it is not here Queried, whether Science, Prudence, and Art may concur in Practice: but whether Music being considered as a Discipline either habitual or systematical, be a Science, Prudence, or Art. But that it is a Science it doth thus appear, because it hath Subject, Principles, and Affections; which three thin●s are required unto the complete Ration of a Science.   

2. An Harmonical Song, is a concinnous multitude of Sounds, rightly composed according to the Text.  
The Subject of Explication in Music is a Song, whose chief Force lieth in this, 〈◊〉 accommodated to the Text and Affections 〈◊〉  
But if the same Sound may be accommodated to divers and contrary things and Affections, than the Music is inept and irrational; because it is contrary to the Scope and Principle of that most laudable Discipline, which will, That Melody be applied both to Things and Affections.  
If therefore v. g. in any Psalm of David, three Parts do occur, viz. Lamentation, Consolation, and giving of Thanks: there, three Tones ought to be.   

3. The Subject of Operation in Music are Things sacred and liberal. By which it appeareth that the usefulness of it is very great.  
Things sacred, as the Psalms and Songs in the Bible, and of other things wholly Divine.  
Things liberal, as pathetical matters in things Philosophical, and which doth altogether concern the common Life of Man. For Music doth penetrate the Inferiors of the mind, it moveth Affections, promoveth Contemplation, expelleth ●orrow, dissolveth bad Humours, exhilerateth the animal Spirits: and so is beneficial to the Life of Men in general, to the Pious for Devotion, to the Contemplative Life for Science, to the Solitary for Recreation, to the domestic and public Life for Moderation of mind, to the Health 〈◊〉 the temperament of their Body, and to the 〈◊〉 for Delight; As excellently saith that famous Musician Lippius in his Musical Synopsis. Hence it is that the Devil hateth Music liberal, and on the contrary is delighted with filthy Music and illiberal, which he useth as his Vehicle, by which he slideth himself into the minds of men, who take Pleasure in such Diabolical Music. On the contrary, the holy Angels are delighted with Music liberal, not because corporal Harmony doth affect them, but because all Harmony, especially that which is conjoined with the Affection of a pious Will, is grateful to those chaste Spirits. Hence it is, that the Heroes, holy Men, and Lovers of Virtue of all times, have magnified Music: as appeareth by these Scriptures; Exod. 15. Judg. 5.1. 1 Sam. 16.23. 2 Sam. 6 5. 2 Kings 3.15. 1 Chron. 23.5. Judith 16.1, 2, etc. Syrach 23.5, 6, & 39.20. & 44.5. Matth. 26.30. Luke 1.46. & 2.13. Eph. 5.18, 19 Col. 3.16. Apoc. 5.9. & 14.2, ●.     

CHAP. II. Of the Principles of Cognition in Music.  

PRECEPTS.  
THE Principles of an Harmonical Song are those things upon which it doth depend: And those are either the Principles of the Cognition or Constitution thereof.  
Those be complex: these incomplex.  
The Principles of Cognition are those by which an harmonical Song is known. And they are either internal or external. Those are taken from the Science itself, these from Philosophy, partly theoretical, and partly practical.   

RULES.  

1. The internal or domestical Principles of Cognition are here and there spread through the whole Body of Music.  
Wherefore it were not worth while to treat of them in this place.   

2. The theoretical Principles which Music doth use, or is built upon, are either remote or proximate.  
The remote are such as are taken from the Metaphysics and Physics. And indeed from the Metaphysics, there are taken Principles of Unity, Goodness, Pulchritude, Perfection, Order, Opposition, Quantity, Quality, and the like. And from the Physics, tho●e that treat of the Quantity, Quality, Motion, Place, and Time of a natural Body: Al●o of Air, an● Sound, and of its propagation, multiplication, differences, and perception: And lastly of Affections, as Love, Joy, Sorrow, and the like. The proximate principles are Axioms, Assumptions, Questions, Theorems, Problems, and Consectaries mathematical; and those partly arithmetical, partly geometrical: but chiefly a●ithmatical; especially those which concern the Proprieties of Simple Numbers, and also their proportion; viz. dupla, tripla, sesquialtera, and the like, of which in my Arithmeticks: But here let these Axioms be observed. 1. That Proportion of Equality is radically between one and one: And this is the Radix of all Proportion. 2. Dupla Proportion is radically between two and one, tripla between three and one, quadrupla between four and one, and so forward. Observe, that radical proportio●s are in Nine Simple Numbers, from 1. to 9 because these are the Radixes of all Numbers. 3. Sesquialtera Proportion is between three and two, Sesquitertia between four and three, Superbipartiens tertias, is radically between five and three, and Supertripartiens quintas is between eight and five. And these are simple proportions, in which such an order of perfection is observed, that after a proportion of Equality, a proportion of inequality followeth: First Dupla, afterward Sesquialtera, then Sesquitertia, afterward Sesquiquarta, and Sesquiquinta, then Superbipartiens tertias, an● Supertripartiens quintas. To these succeed compounded P●opo●tions, as Dupla-Sesquialtera between 5, and 2. 〈◊〉 Sesquitertia between 10, and 3. Dupla-Superbipartiens tertias, as between 8, and 3. and so forward. 4. Proportions are numbered by Division logistical, as the proportion which is between 3, 2. appeareth by Division. For if 3. be divided by 2. it will produce 1. ½. 5. Proportions are added by vulgar multiplication, as 3/2: 2/1: make 6/2: 2/1: 6. Proportions are substracted by Multiplication crucial; as 7. Proportions are multiplied or coupled when they are written without Intermission, and the antecedent number of the latter proportion is multiplied into the Consequent of the former, or contrarily. Also when the Consequent of the former is multiplied into the Consequent of the latter. Or lastly, when the Antecedent of the former is multiplied into the antecedent of the posterior. As 2.1, 3, 2. Here, once three, give three: and once two, give two, and twice three, give six. 8. Proportions are radicated in greater numbers, and in numberss compounded one with another by Mediation logistical▪ as 16-8. First they are reduced to 8-4. then to 4-2. lastly to 2-1. And thus radical Proportions by course are easily reduced to their greater Terms by logistical Duplation; as 12. to 2-4. thence to 4-8. then to 8-16. and so forward. 9 Every Dupla Proportion doth consist of a Sesquialtera and Sesquitertia. 10. If a Sesquialtera be taken away from a Dupla, a Sesquitertia will only remain, and so consequently.   

3. Practical Principles which Music useth, are chiefly taken from the Ethics, Economics, Politics, and Poeticks.  
From the Ethics are taken Principles of Virtue, and moral Beatitude; from the Economics of Action's domestic; from Politics Principles of virtue, and civil Beatitude; and from Poetry Principles concerning Rhyme and Verse: which have ●uch Affinity with Music, that by some Music is divided into Harmonical, Rhythmical, and Metrical.     

CHAP. III. Of the Efficient and End of an Harmonical Song.  

PRECEPTS.  
THE Principles of Constitution are those by which an harmonical Song is constituted.  
And they are either external or internal.  
The external are the Efficient and End. The Efficient Cause of a Song is either the first or second.  
The first Cause is GOD the Author of all Symphony.  
The second is partly Nature, the Mother of all Sounds: partly Art perfecting the Rudiment of Nature.  
The ultimate End is GOD that Archetype of Harmony.  
The subordinate End is Motion, and the impulse of Man to the hatred of Vice, and study of Uirtue.   

RULES.  

1. God is the Author and Maintainer of all Harmony,  
Seeing Harmony is Order, and tendeth to Unity; for God is the Author and Maintainer of all Order, and the greatest Unity. Furthermore, God is the chief and unspeakable Joy, therefore they who rightly rejoice come nigher unto God. Hence the Rabbins say, the Holy Ghost doth sing by reason of Joy. And Philosophers say, That the Soul of a Wise man doth always rejoice; For joy as it is pure Harmony cannot but be excited and maintained by Musical Harmony.   

2. The Exemplary Cause of Harmonical Music; is that Music which is called mundane.  
This is discerned in the Order, Disposition, and admirable proportion which doth occur in the Celestial, and subcelestial Region; partly among the St●rs, partly among the Elements, partly among all things compounded of the Elements; and lastly, among all tho●e things which are compared one with another: of which Music and Harmony we have spoken in our Physics. This Harmony being such and so great, when ancient men did diligently consider it, they supposed that there was the like Proportion not only in Numbers and Lines, but also in the Voice; especially when they did discern that Proportion in the various Sound of various Bodies.   

3. Music receiveth his greatest Perfection from the End.  
That Perfection doth not only depend upon matter and Form, but also upon the ●nd we have formerly shown in our Metaphysics and Logicks. In Music certainly this is most manifest: for unless it be referred to the Glory of God, and the pious Recreation of Man it cannot but equivocally be called Music. Hence it is apparent that those simple men who abuse Vocal and Instrumental Music to nourish the pleasures of this World, whilst they si●g Songs highly obscene, are nothing less than Musicians. For although the Form of a Song occur there, yet the End which perfecteth the Instrument, is not there discerned: Therefore in such Music there is the first perfection but not the ultimate; which necessarily is required in an Instrument, because the Virtue thereof is placed in the use.     

CHAP. IU. Of the quantity of a Musical Song.  

PRECEPTS.  
THE internal Principles of an harmonical Song are Matter and Form.  
Matter comprehendeth the integral parts of which an Harmonical Song is made.  
Of the parts thereof, the one is Simple, and the other is compounded.  
The simple part is called Sound: also a Musical Monad. in Greek Tonos.  
A Musical Sound is considered in respect of his Quantity and Signs.  
The Doctrine of that is called theoretical Music, and of this Signatory.  
Quantity is threefold, Longitude, Latitude, and Crassitude.  
The Longitude of a Musical Sound, is that which is discerned in the motion and duration thereof: and measured by a Musical Touch or Tact.  
The Latitude of a Musical Sound is that which is discerned in the tenuous and asperous spirit.  
The Crassitude of a Musical Sound is that which is discerned in the Profundity and Altitude thereof.  
By reason of this Crassitude a Musical Sound is equal or unequal.  
The equal Sound is the Simple Unison.  
The unequal Sound doth bring forth a Distance or an Interval of a sonorous Crassitude: which is called a Musical Interval.  
A Musical Interval is seen in Proportion and Intention.  
By reason of Proportion, an Interval is simple or compounded: that is called radical, this radicated.  
A Simple Interval is either Just, or not Iust  
A Just Interval is that which is neither defective nor redundant: as an Octave Fifth, etc.  
An Interval not Just is that which is defective or redundant: as a Semioctave, etc.  
A compounded Interval is that which doth consist of simple Intervals: as a double Octave, a triple Octave, a quadruple Octave, and so ad infinitum.  
By reason of Intention it is a Scale, called Musical; and it is the various disposition of acute and grave Sounds.   

RULES.  

1. Every Sound is Quantus.  
For in every Body that hath Quantity, there is an audible Quality. That Quantity is numbered by Division, and not barely considered, as it is a magnitude. So that the most accurate Lippius might rightly say, every Sound is continual or discrete, or explainable by number. But a Sound is Quantus, by complete Quantity. i e. So that it have a trine Dimension, and therefore Longitude, Latitude, and Crassitude.   

2. Every Sound is long numerably.  
For seeing every Sound doth continue so long, or not so long, this temporal duration thereof may be numbered. And it is numbered by a Musical Touch, which, according to the motion of the Heart, in this Science ought to be observed. This Touch doth consist of Depression and Elevation, according to a certain Proportion, but especially a Dupla: And it is either more simple, more natural, and more ●ommon, which is finished in two equal parts, and may be called Spondaic, as 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉: or less simple, and more unusual, which doth consist of unequal parts, th● one greater, and the other lesser, and may be call●d Tr●chaic. as 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉   

3. Every Sound is numerably broad.  
For every Sound besides the length thereof, is also tenuous or gentle, flat, submi●s, small; or sharp, harsh, clear, full, as consisting of a tenuous and asperous Spirit.   

4. Every Sound is numerably thick.  
Besides the length and breadth, every Sound is al●o thick; and so it is either deep or high. That, is called grave, and this, acute. And we measure this magnitude of a Sound by Proportions of numbers, especially radical, as they are applied to the Monochord.   

5. The Simple Unison is the Principal and Radix of all Musical Intervals.  
As in numbers there is one proportion of Equality, and another of Inequality: So also in Sounds, one is equal, and another is unequal. And again as in numbers, the Proportion of equality is the Radix of all the rest: So in Sounds, the Simple Unison is the principal and Radix o● all Musical Intervals. For the Simple Unison doth consist of a proportion of Equality, which is radically between 1. and 1. as may be seen in a Monochord. Therefore a Simple Unison is not a musical Interval, but the original thereof.   

6. Unequal Sounds do make a Musical Interval.  
Unequal Sounds do make a Diastem or Distance, which is called a Musical Interval, in which the grave Sound is profound and greater: and the acute, high and lesser. Of this Interval these Theorems are noted. 1. He that knoweth a simple Interval, may easily know a compounded Interval. That, as they say, is radical: this, radicated. 2. There are seventeen simple Intervals or Diastems in this order. The first, an Octave, to wit, a voice, in Greek a Diapason, which is of a Dupla Proportion, between 2. and 1. where one Sound as the greater and graver, doth contain another, as the lesser and acuter, twice in itself; Therefore is the Unison composed from Letter to Letter, v. g. from G. to g. etc. The second, a Fifth, or Diapente, which is of a Sesquialtera Proportion; between 3. and 2. The third, a Fourth, or Diatessaron, which is of a Sesquitertian Proportion between 4. and 3. The fourth, a greater Third or Ditone, which is of Sesquiquarta Proportion, between 5. and 4. The fifth, a Third minor, or Hemiditone, which is of Sesquiquinta Proportion, between 6 a●d 5. The sixth, a ma●or●or ●or greater Sixth] or fourth with the greater thi●d, which is of a Superbipartiens tertias Proportion, as between 5. and 3 7. A Sexta minor or fourth with the lesser Third, which is of a Supertripartiens quintas Proportion, between 8. and 5. The vl, is the major Second, or whole Tone, which is of a Sesquioctave Proportion, between 9 and 8. The ninth, is the minor Second, or minor Tone, of a Sesquinona Proportion, between 10. and 9 The tenth, is the major Semitone, of the Proportion of 16. and 15. The eleventh, is the minor Semitone, of a Sesquivicefima quarta Proportion, between 25. and 24. The twelfth, the Diesis minor, of a supertripartiens centesimas vigesimas quintas Proportion between 128. and 125. The thirteenth, a Comma which is the difference between the Semitone majus, and minus, of a Sesqui●ctogesima Proportion, between 81. and 80. The fourteenth, a Schisma which is the half of a Comma, or half of the Difference between the Semitone majus and minus. The fifteenth, is the fifth with a tertia major, or greater Seventh, which is of a Superseptipartiens octavas Proportion, as between 15. and 8. The sixteenth, is the lesser Seventh, or quinta cum tertia minore, which is a Superquadripartiens quintas Proportion, between 9 and 5. The seventeenth, are intervals not just, which are either deficient or redundant, chiefly by the lesser Semitone, or Comma, or both together: as the Semioctave deficient and abounding Fifth: the minute and superfluous fourth which is named a Tritone, and such like. 3. Intervalls' compounded of simple Diastems may be infinite. But it is proper to Music to bond that Infinity of gross Sounds. (which is such only potentially.) Notwithstanding let us take notice of certain compounded intervals. First, such as are once compounded, as a Disdiapason, double Octave, or Fifteenth, which is of a quadrupla Proportion, between 4. and 1. Also a Diapason with a Diapente, an Octave, with a Fifth, or Twelfth, of a triple Proportion, between 3. and 1. Also a Diapason with a Diatessaron, an Octave with a Fourth, or Eleventh, of a dupla superbipartiens tertias Proportion, between 8. and 3. Al●o others are twice compounded, as a Trisdiapason, Triple Octave, or two and twentieth of an Octupla Proportion, between 8. and 1. etc. Thirdly, others are thrice compounded, as a Tetradiapason, quadrupla Octave, or nine and twentieth of a sedecupla Proportion, between 16. and 1. Others are four times compounded, and so ad infinitum. 4. An Octave is the most simple, perfect, and prime musical Interval. 5. An Octave divided be gets all other simple Diastems. Therefore from the Division of the 0ctave, the Harmonies of every Genus do flow. For every Octave being divided two ways, begetteth two Moods of itself. 6. An Octave is first divided into a fifth and fourth, of which it doth consist: and that either by harmonical or arithmetical Division. That is called the harmonical Medium of an Octave, when the fifth is beneath the fourth: and that the arithmetical, when the fourth is beneath the fifth. Let this be the Example of Harmonical Division.  
But I suppose the Author meaneth thus:  
Division Arithmetical is thus:  
Therefore in the harmonical Division of an Octave the fifth remaining immovable, the fourth is placed above the fifth: in the arithmetical Division, the fifth remaining immovable, the fourth is put beneath the fifth. 7. If a Fifth be taken from an Eighth, there remaineth a Fourth, and so on the contrary. 8. A Fifth is divided into a Ditone, and Semiditone. 9 A Ditone is compounded of the greater and lesser Tone 10. The Tonus major is disposed into the Semitone majus and minus. 11. The D●tone is more than the Semiditone by the Semitone minus. 12. A Fourth exceedeth a Ditone by the major Semitone. 13. A Fifth is more than a fourth by the greater Tone. 14. The lesser Tone is excceded by the greater by a Comma. 15. The greater Semitone exceedeth the lesser by 〈…〉. 16. A Sixth is made of a Fourth and a Th●rd, the greater of the greater, and lesser of the lesser, or the greater of a fifth and dat Tone, and the lesser of the Semitone major. 17. The seventh major, is made of a Fifth and greater Third, the minor, of the minor. 18. The greater Tone doth contain almost ten Commas, the lesser almost nine; the greater Semitone almost five, and the lesser a most four. 19 A fifth doth contain two greater T●nes, one lesser, and the Semitone majus: A fourth one greater and lesser Tone, and the Semitone majus. Therefore an Octave hath in itself six Tones three major, and three minor, with the lesser D●esis: to wit, five Tones, three greater, and two lesser, with two major Semitones, and so it doth comprehend more than fifty Commas. 20. Compounded intervals do imitate the nature of their simple. A Disdiapason ariseth from two Octaves, an Octave with a Fifth comprehendeth eight Tones, five major, three minor, and three greater Semitones. A Trisdiapason is divided into three Octaves, and so of the rest. These Propositions are demonstrated by propositions arithmetical of proportions added, substracted, coupled, etc. v. gr. An Octave is of a dupla proportion, a Fifth of a Sesquialtera, a Fourth of a Sesquitertia. Therefore an Octave doth consist of a Fifth and a Fourth. This whole matter is demonstrated in a Monochord: How these things may be vulgarly propounded, you may see hereafter in the last Chapter and last Rule.   

7. The Scale of Music is explained in these Theorems.  
1. The Series of Intention and Remission: or of Ascension from a grave Sound into an Acute, and of the Descension from an acute into a grave, is called the Scale of Music. 2. The Scale of Music doth vary both according to ancient and modern Musicians. For the Scale of the most ancient Musicians, was only of one Diapason for radical Simplicity. The Scale of the Pythagorians was of a Disdiapason, for the keeping of Mediocrity. And now it is of a Tris, and Tetra-Diapason, for the grateful variety of vocal and Instrumental Music. The Scale also is either Simple: and that either old as the enharmonic, chromatic, and diatonic; or new as the Syntonic: or mixed, which is compounded of simple [Intervalls] Of these the enharmonic and chromatic, in respect of their Difficulty and imperfection are not used in Solitary Music. 3. The Syntonian Scale is of all others the most harmonical, to which the Diaton Scale may aptly be mixed: as it may be seen in a Clavichord, and wind Instrument, i. e. an Organ; where the white Keys do proceed in the Syntonian Scale; which is somewhat moderated by the Diaton. The Syntonian Scale proceedeth by the great Tone, the lesser Tone, and the greater Semitone which ariseth from the minor Tone: the diatonic or diaton proceedeth by two Tones and a Semitone. To these the enharmonic Scale is added, proceeding by two Dieses, the greater and lesser, and an immediate Ditone in his Tetrachords. Also the chromatic proceedeth by two Semitones, the greater and the lesser, and an immediate Semiditone. So the black Keys proceed with the white in the chromatic: from whence they are called fict in the Syntonian. Hence also ariseth the Scale irregular or flat, which differeth not from the regular or dural, but by accidental Transposition, or by the fourth above, or by the fifth beneath. And this is the Disposition of the old diatonic Scale.  

1. The greater Tone. 9.8.  
2. The greater Tone. 9.8.  
3. The lesser Semitone from the greater Tone 256.243  
4. The greater Tone. 9.8.  
5. The greater Tone. 9.8.  
6. The greater Tone. 9.8.  
7. The lesser Semitone. 256.243.  
8. The greater Tone. 9.8. and so on through the Octaves below and above.   
But the Disposition of the new and perfect Syntonian Scale is as followeth; 

1. The greater Tone. 9.8.  
2. The lesser Tone. 10.9.  
3. The greater Semitone. 16.15.  
4. The greater Tone. 9.8.  
5. The lesser Tone. 10.9.  
6. The greater Tone. 9.8.  
7. The greater Semitone. 16.15.  
8. The greater Tone. 9.8. And so on through the Octaves above and below. Compare these things with the antecedent Rule, and following Chapters.       

CHAP. V. Of the Signs of a Musical Sound.  

PRECEPTS.  
THE Signs of a Musical Sound do follow.  
And those are of a Sound either broad, long, or thick.  
The signs of a long Sound do note the duration thereof: and they are either principal or less principal.  
The principal Signs are a Note and a Pause.  
A Note is a sign of a present and positive sound: and containeth Touch, and that either whole or not whole.  
It containeth the whole Touch either eight times as a Large, or four times as a Long, or twice as a Breve, or once as a Semibreve.  
The rest do contain not the whole, but part of a Touch, and that either the half part as a Minim, or the fourth part as a Crotchet, or the vl part as a Quaver, or the sixteenth part as a Semiquaver.  
A Pause is the Index of a privitive or absent Sound, that is of silence: and it answereth either to a Large, or Long, or Breve, etc.  
Signs less principal are a semicircle with a Centre, Custos, or the like.  
Signs of a broad sound, are a prick of Augmentation, breathing, and Syncope: of which, Syncope, is a certain losing of the Touch; Notes, or Pauses; breathing answereth a Semi Minim.  
The Signs of a Crasse Sound are parallel Lines, whereof the place and name do occur.  
The place is a Musical System, and that greater or lesser.  
The greater System for the most part doth consist of ten Lines: and serveth for the Composing of a Song, called otherwise a conjoined System.  
The lesser System doth consist of five Lines, and serveth chiefly to a Song pricked out. This is otherwise called a simple System.  
The Name is aswell a Letter as a Uoice, or as others will, a Musical Syllable.  
A Letter is as a Key by which the Song is opened, therefore called Clavis. Such letters are seven. A. B. C. D. E. F. G.  
The musical Voices or Syllables are six, ut, re, mi, fa, sol, la.  
These are found in a Musical Scale either continued or discontinued.  
There, there is no need of Mutation: but here otherwise.   

RULES.  

1. The most certain and ready Signs of Sounds are Ciphers of Numbers.  
Because a Sound can neither by any Man be written in Paper, nor kept in his Mind, neither only nor always; therefore it standeth in need of certain Signs, by which the Quantity and Quality thereof may be represented. For because in the Numbers and Proportions of these, all the Dimensions of Sound have their assigned Essence; the most sure and ready Signs are Ciphers of Numbers placed according to their Longitude, Latitude, and Profundity. For according to Longitude. 1.2.3.4.8. ½ 1/3 ¼ may note the stay of one Touch, two, three, or four, etc. According to Latitude in like manner; and according to Crassitude the greater Numbers may signify the grave Sound; and the lesser Numbers, the acute Sound. But it behoveth here to retain vulgar Signs, because they are most used.   

2. The Doctrine of Notes is contained in these Rules.  
1. Notes are either simple or compounded. And those are either whole or broken. These are called bound. Simple Notes are placed without any joining of either: Compounded, contrarily. Whole Notes are measured by whole Times; broken Notes, by parts of Time. Whole Sounds consist either of one Time, as a Semibreve: or of more, and those either of two, as a Breve: four, as a Long: or eight, as a Large. The broken Notes do contain either the second part of a Time, as a Minim: or the fourth, as a Crotchet: or the eighth, as a Quaver: or the Sixteenth, as a Semiquaver. According to the following Scheme.  
Names. Figure. Value. Large. 𝆶 Excessus. 8. Long. 𝆷 Excessus. 4. Breve. 𝆸 Excessus. 2. Semibreve. 𝆹 Medium. 1. Minim. 톹텥 톹텥 Defectus. ½ Crotchet. 톺텥 톺텥 Defectus. ¼ Quaver. 톼텮 톼텮 Defectus. ⅛ Semiquaver. 톼텯 톼텯 Defectus. 1/16  
Although more Notes of Longitude may be given, as well greater or lesser, potentially infinite: yet the●e notwithstanding do suffice, which were invented by Musicians of former Ages. 2. Notes are varied according to the Augmentation or Diminution of their value, or according to both together. Either all or some are augmented by the half part; and truly, all are augmented either by the Opposition of a Semicircle. 𝇋. 𝇍. and a Prick, of which this is the Rule: A Prick put after Notes doth add the half part of the time above their proper value, as 12. 6. 3. 3/2 ¾ 𝆶. 𝆷. 𝆸. 𝆹. 톹텥. Thus a Prick after a 𝆸. is a Monotone, or 𝆹. after a Semibreve is a Minim, or 톹텥. Some Notes are only augmented by prefixing a Circle 𝇈. as a Large, Long, Breve. Notes are diminished by a Trochaic Touch in a certain proportion, either Tripla or Sesquialtera. Where the Signs are either Number or Colour: as 3/1 is tripla, 3/2 is sesquialtera. Notes are partly augmented and partly diminished, chiefly by the ligation and obliquation of a Breve, which is done for the extending of one Syllable. And a Long also with a Breve is counted for a Semibreve; and also in like manner a Breve with a Breve. But this kind of ligation and obliquation is now wholly omitted, as not necessary in the least.   

3. Pauses measuring Silence do answer to those musical Notes whereof they are Privations.  
For a Pause (which is noted by a little Line) doth answer either to a Large, or Long, or Breve, or other Note: as in the Type. 8. 4. 2. 1. ½ ¼  
A double Breathing doth answer to a Quaver: a Triple to a Semiquaver. Hitherto do pertain the Neuma, Custos, and the like. As Neuma. Custos.   

4. Signs of a broad Sound are by Artists expressed less carefully.  
The Sign of a broad Sound ought to show the Latitude of it according to the asperous, harsh, clear, full, soft, flat, and small Spirit thereof, as the nature of the Text requireth. But Musicians do less weigh the Latitude of a Sound, and do leave it to the Text, and to the things themselves that are to be sung, and are content with few Signs, chiefly using breathing and Syncopation. Breathing doth answer to the Crotchet: Syncope or Syncopation is a certain Luxation, that is, a fraction, and Contraction of Touch, Notes, and Pauses. e. gr.   

5. The Sign of a Crass Sound is a crossed Line, as they call it.  
The Sign signifying Crassitude of gravity and acuteness measurable by proportionable Numbers, is a perpendicular Line, which a right line doth cut; thus, +. The●e Lines are called Seats of crass Sounds or Musical intervals. Also a Musical System which is twofold, the greater and the lesser. In both there are perpendicular and parallel Lines; indeed in the greater there are 〈◊〉 ten parallel Lines, in the lesser always five. The greater serveth for the composing of a Song; where the perpendicular Lines are cut by the distance of one or two Touches: But the lesser doth serve for Melody, which is to be extracted and noted.  
Let this be the Type of the greater System.  
Let this be the Type of the lesser System.  
Both these Systems are put in a Chart, or Melopoetick Abacus, or Compositary as they call it. The first is convenient to a young Beginner: the latter, for a longer Practitioner: but others would rather draw more simple Systems in an Abacus; Thus,   

6. Of Letters and Voices Musical, as they call them, these are the Theorems.  
1. The radical Letters are seven, in this order, a. b. c. d. e. f. g. which do moderate Sounds in the Diato●ic Scale of a Diapason. These are usually called Keys, because that by them a ●ong is, as it were, opened. They were invented by Guido Aretine; at this time they are insufficient. 2. Letters or Keys are either capital, minute, or geminate. Capital are they which are written with Capital, that is with great Letters. Thus Γ. A. B. C. D. E. F. G. of which Γ. A. B. C. are called grave, because they emit a grave Sound in respect of the rest: the rest, as D. E. F. G. are called finals, because every Song regularly doth end in these Keys. We have only Γ from the School of the Greeks. The minute Keys are in number seven, so called because they are written with little Letters. Of these a. b. c. d. are called asfinal, because in these Keys the transposed Song doth end: otherwise call●d acute, because they do emit a more acute Sound. The other are called Superacute because they are put above the acute, as e.f.g. The geminate Keys are commonly five in n●mber. aa bb. cc. dd. ee. So called because they are written with double Letters. Otherwise called excelling; because in their Sound they transcend all others. But because the number of Keys is not sufficient; therefore latter Musicians under the great Latin Letters have put seven Germane Letters: and the double Letters they do fully recite, and moreover they add unto them triplicated Letters. Thus 

1. A B C D E F G.  
2. A B C D E F G.  
3. a b c d e f g.  
4. aa bb cc dd ee ff gg.  
5. aaa bbb ccc ddd eee fff ggg.   3. Keys are signed, or understood, or not signed. The signed Keys are three which are distant one from another by a Fifth, and they are g. c. f. thus  
These in the conjoined System are thus put, and are distant from one another by a Diapente.  
In a simple System they are variously placed by reason of the Profundity and Altitude of a Song; As,  
But Keys not signed are known by the signed.  
4. Out of these seven Keys there is a double b. viz. flat and sharp. These two Letters in the signing are distant by the lesser half Note. So that the regular or dural Scale beginneth in C. and the irregular or flat Scale in F. b dural is thus marked ♯ and is called b. quadrate.  
5. Besides b. molle, as they call it, there is need of Cancels ♯. and cis, dis, fis, gis: which are called fict Letters by instrumental Musicians. But David Mostar● so accommodateth the Musical Keys to ●even n●w Voices. Four Keys in the whole are here to be held. The first is C. in which he will always have bo sung. The second is G. five Tones below and four above G, he always singeth bo. The third is F. and four above, and five Tones below F. bo. is always sung. Also five Notes above B. molle, and four under B. molle, bo. is always to be sung. 6. Musical Voices are one way rehearsed by the Ancients, and another way by later Musicians. The ancient Musicians did constitute these six ut, re, mi, fa, sol, la. To these six Voices some do add the seventh Simo, lest there should be need of some Mutation. Concerning this thing Erycius Puteanus in his Musathena doth so for the most part play the Philosopher. Guido Aretine (lived under Henry the third Emperor) for his Skill in Music among the prime of his Age, and delighted with the perfection of the Senary Number, introduced these six Syllabic Notes, ut, re, mi, fa, sol, la. which he borrowed and translated out of the Hymn. 
Ut queant laxis Resonare fibris,  
MIra gestorum FAmuli tuorum,  
SOLve pollutum LAbij reatum.  Sancte Johannes.  
These six Notes so invented, do show their use every where among Musicians, but very slow and difficult. For what impediment is there of Mutations, confusion of Keys, substitution of Voices? You may see most (whether with Indignation or no) to have spent a good part of their Age upon this Art, and yet to have profited very little, though perfect many years before in the Lection thereof. But the Difficulty doth hinder, and make it a remora to most. Which some do thus take away by joining si. to the●e six received Not●s. For which Note you may put Bi. out of the ●aid Hymn. Solve polluti la BY. i. reatum.  
This therefore shall be the order of Notes, ut, re, mi, fa, sol, lafoy▪ by, for th●s Heptade these following Reason's are brought. 1. Whereas Notes are the Index's of Voices, and as certain Signs, it is of necessity that there should be as many Notes as Voices. But there are seven distinct voices established in that half verse septem discrimina vocum. Therefore there are seven Notes. For by voices are understood those sev●n Sounds, which are distinguished by certain intervals. Those intervals or Diastems are called Tones. Therefore a Sound, and Tone or Interval do differ. A Sound is the Voice itself, which being form by the Mouth, is brought by the Air to the Ears. A Tone is a Space circumscribed by two Sounds: or, the distance of a grave and acute Sound: So that Tones are tho●e Intervals, which are placed between the first and secon●●ound, the second and third, the third and fourth, the fourth and fifth, the fifth and sixth, the sixth and seventh. But this Heptade of Voices, Ptolemy in his eleventh Book concerning Music doth confirm; saying, that by nature Voices can be made neither more nor fewer than seven. 2. The Egyptians and Grecians have approved the seven Voices by the number of seven vowels. For the Egyptians as Demetrius Phalereus doth testify, did commend their Gods by the modulated enunciation of seven vowels. And Plutarch doth accommodate the Greeks seven Vowels to so many Voices of Music. 3. The Lyre, Cithrens, and certain other musical Instruments which are strung with strings, were anciently of seven strings, without doubt, by reason of the seven Voices. The Chords of the Lyre were of old in this order, and by these Names, Hypate, Parhypate, Hypermese, Mese, Paramese, Paranete, Ne●e. The first is called Hypate, not only for the acuteness of the Voice, but for a certain excellency and virtue. For Hypatos as it were Hypertatoes, doth signify a degree of Eminency and Dignity. Neat, as Neat, that is, the last or ultimate. Neither have the Chords been only by these Names, but also the Sounds themselves, nigh this manner. Hypate hath to himself Bi. and soundeth acutely: Parhypate, lafoy, and doth lullaby: Hypermese, sol, and doth sound sweetly: Mese, fa, and doth sound temperately: Paramese, mi, and doth delight pleasantly: Paranete, re, and doth grate tremulously: Nete, ut, and doth, as it were low hoarfly. Furthermore the Ancients did attribute the seven Planets to so many Chords of the Lyre, in this Order. To Saturn, Hypate: to Jupiter, Parhypate: to Mars, Hypermese: to Sol, Mese: to Venus, Paramese: to Mercury, Paranete: and to Luna, Nete. In which Comparation the acuteness and gravity of the Chords and Planets do respond exactly. Although others invert the order, and attribute to Saturn Nete, and to Luna Hypate. Which Comparation although it may consist: Yet notwithstanding the first is more allowed: because Saturn doth proceed in a mundane motion most quickly, Luna most slowly. Look Cicero in his Dream. From the Chords to the Notes we transfer this Comparation, and ascribe to Luna, ut; to Mercury, re; to Venus, mi; to sol, fa; to Jupiter, lafoy; to Saturn, by. For surely as the Planet's do run round the Week, or the Septenary Circle of days in their Term or gliding Course, and each of them by a certain diurnal vicissitude of Government does obtain the primacy: So these seven Notes do complete the universal harmonical Lection, divided by Musicians into seven Types. These Types are certain and appointed Progressions of Notes, distinguished by judicial Letters. 4. These seven Voices do render all Music very facile, aswell in the Theory as in the Practice, thus. All Music is accomplished by Voices. The Voices being known, Notes are adhibited: To the Notes Characters of Letters; as appeareth by this Diagram.  

In a Flat Song.  Between A and B also mi and fa Hemiton● B C fa sol Tone C D sol la Tone D E la by Tone E F by ut Hemitone F G ut re Tone  

In a sharp Song.  Between A and B also la and by Tone B C by ut Hemitone C D ut re Tone D E re mi Tone E F mi fa Hemitone F G fa sol Tone Therefore in a Flat Song, A hath mi conjoined with it, B fa, C sol, D lafoy, E by, F ut, G re. In a sharp Song, A hath lafoy ascribed to it, B by, C ut, D re, E mi, F fa, G sol. Which difference the variated Disposition of the Hemitones hath begotten. Moreover of these Letters only four are expressed, B, C, F, G. Nor yet those together or conjoinedly, but one or two in the beginning of Lines. The other Letters not noted, you may know by these four. If you ascend from the Index Letter, number the first seven according to the Order of the Alphabet, but if you go further, then iterate the same: but if you descend, proceed by a retrograde Order, from the Line to the Interval, and from the Interval to the Line. Then you may rightly find out the Letters; by the Letters, the Notes; by the Notes, the Voices; which is the Sum of Music. Therefore see that you be most exactly skilled in the ascending and descending Order of the Notes: and that the Tones and Semitones being observed, you may rise and fall with your Voice. After that, a Song being proposed, you may pass from the Sign and Letter noted, to the Note answering it: from hence, omitting the ●etters, to the other Notes. And this tr●el● is easy in a flat Song, when B. is marked in the beginning of the Lines, there it showeth that ●a is ●o be sung. But in a sharp Song the difference is of these three Letters, C. F. G. of which by that you may know Sol, by that fa, lastly b● this Sol Therefore every where consult the Signed Letter, find out the Note, and call it by its proper Vo●ce, and so proceed from thence by ascending and descending: but if in Singing a Note do occur, which hath a peculiar Letter prefixed, the Tone is to be changed, and the Note of the Letter sung. Therefore if you have rightly accommodated the seven Notes, you may mix any Consent, or read any Melody that you would, whether it be the simple Aeolian, or the various Asian, or the querulous Lydian, or the religious Phrygian, or Warlike Dorian. But you will say that Songs are not concluded in those Seven Voices, but rise higher. The Answer is ready; As in numbers when we rise from the Monade to the Denary, the first is the chief of numbers, and by iterating and compounding them we proceed in infinitum. So in these Voices after every seventh Sound, it returneth to the first, but more subtle; and after every seventh Note the first: and so also afterward the second of Notes doth agree with the ninth; the third, with the tenth; the fourth, with the eleventh; the fifth, with the twelfth; the sixth, with the thirteenth; the seventh▪ with the fourteenth, etc. Of Sounds there is the same Judgement. From a Musical Instrument, which by way of Eminency is so called, you may take the Experience of your Ears. But in these Notes observe a double order of Intention and Remission. Intention (by the Greeks Epitasis) is the commotion of the Voice, from the graver place to an acute: Remission (by the Greeks Anesis) from an acuter to a grave. But it is worth the pains, that here some Director or Ruler of the Voice (as Tertullian speaks) go before and lead. Hitherto Puteanus, with whom worketh David Mostart in his Introduction of Music, as indeed he proveth the Septenary of Voices. But he doth substitute other Voices in this manner, bo, ce, di, ga, lo, ma, ni. But so that in C of a sharp Song bo is sung. Also in F. of a flat, bo. e. gr.  
But let Mostart himself be heard. Who saith thus, It is worth our labour seriously to invent such Musical Voices as exhibit unto us a perfect Octave, so that it be the Consequence of eight Tones or Notes: by which Connexion and Series the perfection of any Melody may be performed, without any Mutation: which indeed is the torture of tender wits. And the Series is this, bo, ce, di, ga, lo, ma, ni. bo Which Abridgement if it should be admitted, those old vulgar Keys should be abolished, the Letters of those seven Syllables being only retained in every Song, viz. b. c. d. g. l. m. n.  
For Example sake.  
Therefore Mostart rejecteth the six Voices of the Ancients; because they complete not an Octave, and for that Cause require Mutation, which is the torture of the Ingenious: and also the seven Voices of latter Musicians, because they do not respond to the seven Letters or Keys. But because those Voices of the Ancients be much used in Schools, therefore let us see their use. For 1. Some of those Voices are superior, by which a Song descendeth, viz. lafoy, sol, fa, and others are inferior, by which it ascendeth, as ut, re, mi. 2. All those Voices are equally distant one from another by a Tone, besides mi and fa which are distant by a Semitone. 3. Of these Voices, ut and fa sound flatly; mi and la sharply; the rest, meanly. But concerning this thing others speaks thus, ut and sol denote Sweetness, re and la gravity, mi Lamentation, fa threatenings. Lastly, others consider these Voices thus. Vt and fa are flat Voices by b moll, because they emit a flat and effeminate Sound: re and la natural, because they afford a natural and middle Sound: mi and la b durales, because they make a sharp and manlike Sound. According to these Verses; 
Vt cum fa mollis vox est; quia Cantica mollit:  
Mi cum la dura est, Nam duras efficit odas.  
Sol naturalis (quoniam neutras facit) & re.   
4. Certain Voices do answer all Keys. Thus A la mi re B fa mi  C sol fa ut D la sol re E la mi  F fa ut  G sol re ut  
5. These Voices are circumscribed in certain parallel Lines, so that in a Song we may ascend and descend; and that in a progression either continued, or discontinued. Continued Progression is that which observeth the natural Order of Voices, and is called a natural Song; As,  
Discontinued Progression is the Mutation of a Voice, which is considered either in the minor or greater System. Mutation in the lesser System, is made for the Paucity of Voices: and it is either Vocal or mental. That is called explicit, this implicit. And both is divers in a flat Song, and in a sharp. In a flat Song Mutation is made in d. a. g. whose memorial Note is dag. In a sha●p Song Mutation is made in d. a. e. Whose Voice of remembrance is dea. In the greater System Mutation is made according to the triple Scale. The first is b dural Scale; which is the Progression of Musical Voices, rising from a. into b. sharply, that is, by the Voice mi. The second is b moll; which is the progression of Musical Voices, rising from a. into b moll, that is the Voice fa. The third is the fict Scale, which in every Key admitteth a strange Voice. And hence it is called fict Music: because modulated by feigned Voices. i e. by such as are sung in any Key, in which essentially they are not contained. As ut in e. re. in f. and so on.  
This is the Type of the Triple Scale. 5. Tetrachord ee b       la dd       la sol cc       sol fa bb       fa mi 4. Tetrachord of excellents. aa b     la mi re g      sol re ut f      fa ut  e b    la mi   3. Tetrachord of Superiors. d    la sol re   c    sol fa ut   b b   fa mi    a   la mi re    2. Tetrachord of Finals. G   sol re ut    F   fa ut     E b la mi      D  sol re      1. Tetrachord of grave Sounds. C  fa ut      B b mi       A b re       Γ  ut        
In this Table musical Sounds are so contained, that first there is the Simple Unison. 2. The Tonus minor. 3. The Tonus major. 4. The greater Semitone. 5. The Semiditone. 6. The Ditone. 7. The Fourth. 8. The Fifth. 9 The lesser Sixth. 10. The greater Sixth. 11. The lesser Seventh. 12. The greater Seventh. 13. The Octave. And this is the Cyclus or Compass of the Diapason. Concerning the Proportions of all these Sounds, look into the former Chap. thus v. gr. To the Octave ascribe 1.2. to the Septima 8.15. and so of others: So that the lesser number be applied to the upper Note in the Scale. The significates of the Letters. B. L. b.l.bb. are a little before called bo. ce.di.ga.lo.ma.ni.     

CHAP. VI Of the Musical DYAS.  

PRECEPTS.  
HItherto of the simple part of an harmonical Song: the compounded part thereof followeth; whose tractation is called practical or Melopoetical Music, if the form of the Song be added.  
The compounded part of an harmonical Song, is that which ariseth from musical sounds or Monads conjoined according to three Dimensions.  
And it is either primary or secondary.  
The primary is called harmony and consonancy, which doth arise from grave and acute sounds united by such a proportion, that it may delight the hearing.  
The secondary is dissonancy or Anarmosty, which ariseth from such a proportion of grave and acute Sounds, that it offendeth the hearing.  
And this double part is either a musical Dyas, or Tryas, of which the one is perfect, and the other imperfect.  
A musical Dyas, is that which ariseth from two sounds: consonant and harmonical from Consonants, and dissonant from Dissonants.  
And it is more simple, or more compounded. That is called radical, this radicated.  
The simple Consonant Dyads, are seven, viz. An Octave, Fifth, Fourth, Ditone, Semiditone, greater Sixth, and lesser Sixth: the dissonant Dyads are the other simple intervals, as the Tone major and minor, the Semitone greater and lesser, the Seventh greater and lesser; and lastly, all sim●le intervals not Just, as the Semioctave, Semififth, etc.  
The Dyas more compounded is that which ariseth from the simple Dyas: and that again is either consonant or dissonant: and both compounded either once, twice, thrice, or so forward. In Dyads once compounded the double Octave, also the Octave with a Fifth, the Octave with a Fourth, and Octave with a Ditone do consonate: but the Octave with both tones, with a Semitone, and with an Interval not just doth dissonate. In Dyads twice compounded the triple Octave, and double Octave, with a Fifth do consonate: but the double Octave with both tones, with the Semitone, and so forwards; doth dissonate.   

RULES.  

1. There are two Arbiters of congruous and incongruous Proportions.  
The first is superior, which doth judge of Proportions à priori, to wit, Logos: the other is inferior, which doth exactly judge of Sounds à posteriori, to wit, the Hearing. And there is a necessity that both these Judges should concur, as Ptolemy doth rightly teach: but falsely Pythagoras, who doth think that nothing here is to be attributed to the hearing; and falsely Aristoxenus, that supposeth nothing here is to be attributed to Ration. But the nature of Proportions is demonstrated by the Monochord: for that in it all Musical Diastems are contained.   

2. The Simple Unison is the Radix of all Consonancy and Dissonancy.  
Vulgarly they imagine that the Unison doth both consonate and dissonate. But they err; for the Unison doth equisonate only, because it hath the proportion of Equality, and is the principal of every Interval. e. gr.  
Rightly therefore the simple Unison is made the Radix of Consonancy and Dissonancy.   

3. The Simple Consonant Dyads are in number Seven, and may be called Simple Concordancies.  
Vulgarly they thus rehearse the Simple Concordancies. There are twelve Concordancies, the 1.3.5.6.8.10.12.13.15.17.19.20. And these are divided two waves. First, there are Simple, replicated or triplicated. The Simple Concordances are the 1.3.5.6. which are also called primary. The Replicated are such as are equisonant to the former, conceived by a double Dimension, as the 8.10.12.13. Otherwise called Secondary. For in Sound the Octave doth associate with the Unison, the tenth with the third, the twelfth with the fifth, and the thirteenth with the sixth. The triplicated Consonants are the 15.17.19.20. otherwise called tertiaries. Of these the 15. is coequated in Sound with the Octave and the first: the seventeenth with the tenth and third, and the nineteenth with the twelfth and fifth, and the twentieth doth equisonate with the thirteenth and sixth, According to this Type.  
1. 3. 5. 6. 8. 10. 12. 13. 15. 17. 19 20.  
Lastly, There are Concordances perfect, or imperfect. The Perfect are those which can stand by themselves, that is, begin and terminate a Song: as the 1.5.8. The imperfect are those which may concur in Counterpoint, as the 3.6.10. The Discordances are nine, viz. the 2.4.7.9.11.14.16.18.21. Others also do number the perfect Concordances thus, the 1.3.5.8. because they respond to the Pythogorical Quaternary. But it behoveth them to play the Philosophers of Concordances more acurately. There are seven Concordances or simple Consonances. Of which the Octave is the first, which is of a dupla proportion between 2. and 1. In his Terms the most simple Conveniency is divers, as is between the whole and the half. The Fifth doth obtain the second place; then followeth the fourth; then the Ditone or third in a sharp Song; then the Semiditonus, which is the third in a flat Song; in the last place save one is the Sexta major in a sharp Song; and in the last place, the Sexta minor in a flat Song. And this is the Order of Perfection. For although every Simple Consonancy is perfect in his degree; yet notwithstanding in respect of another, it is either more perfect or imperfect; yet so as the first and most perfect is the Octave, that compounded Unison; the most imperfect and last, is the lesser Sixth; the intermediate are measurably as the most perfect or most imperfect are nearer. Here Musicians do wonder, why the Septinary begetteth no Consonancy, when as it numbereth all simple Consonances. And this is the Scheme of those seven simple Consonances.  
Of these the first three are perfect, the four latter are imperfect. And indeed principally the Octave, in respect of his excellent perfection doth equisonate and unisonate after the Unison an●●imple Equison. After it the Fifth for its perfection doth consonate by his most grateful, firm, and masculine Sound. After it the Ditone or greater Third by his sweet Imperfection doth consent but more cheerfully, strongly, and lively. Then the Semiditone or lesser Third also by his sweet Imperfection doth consent more softly, remissly, and heavily. Then the greater Sixth by his Imperfection doth circumsonate as it were more high and pleasantly. Last of all the lesser Sixth doth also so circumsonate but more slowly, flatly, and weakly. These four latter Consonances were not used by the Ancients in their Diatone Scale: but now they are used most chiefly, naturally, and artificially in the Syntonian Scale. And this is the Order of Perfection in the seven simple Consonances. The Order of the Crassitude of Sound, or of Intention and Remission is this, which is firmly contrary to the first. After the simple Unison is the Semiditone, than the Ditone, than the Fourth, Fifth, six minor, Sixth major, and Octave. From these it is an easy thing to Judge of Simple Dissonances, to wit, because they are all Tones placed without the Septinary of Consonances; as the greater and lesser Tone; the greater and lesser Semitone; the greater and lesser Seventh, and lastly Intervalls not just deficient. For in these are disagreeing Proportions, whose extreme Sounds do but ill agree, and therefore if they be put together, they offend the Ears.   

4. Compounded Dyads do imitate the nature of Simple.  
This is true both of compounded Concordances and Discordances, according to that elegant Axiom of Musicians. Of Octaves there is the same and like Judgement. And that for the essential Similitude of dupla, quadrupla, octupla, and sedecupla Proportion, as 16.8.4.2.1. Also of compounded Dyads the Order of perfection and Crassitude, is like unto the Order of their simple Dyads. Otherwise although the Composition of perfect Concordances might proceed in infinitum: yet notwithstanding because they are not the same Terms of Sound and Hearing (which thing therefore obtaineth in the rest of the Senses) it is necessary that we be mindful of Mediocrity, lest we create trouble to the Ear, by any Sound too great or too acute.   

5. It behoveth us always to have in our Eye the Radixes of Simple Dyads.  
As it is very compendious, to observe simple only and radical Dyads both consonant and dissonant, and then by those to judge of compounded Dyads: so also it is very compendious to consider the Roots of those simple Dyads, according to this Type.  
Bo. ni. ma. lo. ga. di. ce. 90. 96. 108. 120. 135. 144. 160. 1.2.4.8.   3.6.  5.   
See before in the Syntonic Table. Here, between the Consonances of the Octave and fourth, the Radix is the Fifth: of both Six, both Thirds. Therefore the Octave and fourth may be reduced to the Fifth; and the sixth to the third. The Root of simple Dissonant Dyads is the second, to which both Sevenths may be reduced.     

CHAP. VII. Of the Musical TRIAS.  

PRECEPTS.  
THE Musical Trias is that which doth arise from three sounds and as many Dyads: otherwise called the unitrisonous Radix.  
And it is either consonant or dissonant.  
The consonant Trias is that in which a third and a fifth doth concur, yet so as that it ariseth from two thirds.  
The dissonant Tryas is that which ariseth from seconds.   

RULES.  

1. The Harmonical Tryas is the Root of all the Harmony that can be invented,  
And may be called the unitrisonous Radix: because it doth consist of three Monads or Sounds, and as many Dyads: all of them in that whole Tryas, and every one most sweetly consenting one with another, because they are joined together in a certain Order by just Proportions. Those Sounds or Monads being three in number, and as many Dyads, making this Trias, are these. First, the two Extremes are distant one from another by a Diapente, which is of a Sesquialtera Proportion. Then there is one middle, which by his softer sweetness doth join those two Extremes, consenting together by a perfect and masculine Sound, and is distant from one of them by a Ditone, and from the other by a Semiditone. There is the Proportion of a Sesquiquarta, here of a Sesquiquinta. e. gr.  
Here 4. and 5. then 4. and 6. then last 5. and 6. do conspire. This unitrisonous Radix is the Rule and Measure of all Consonances, and is always in one manner. Yet this only is the difference, that in a flat Song it is more imperfect and soft, but in a sharp Song, more natural, perfect, nobler, and sweet. The first hath the Ditone above the Semiditone, the latter hath the Ditone beneath the Semiditone. Moreover this Radix is either increased or diffused. The increased, is that which hath the Octave for his Companion, to excite the more various and fuller Harmony. The diffused is that, who●e radical parts or voices are not so near unto one another, because dispersed into various Octaves. For the nearer the Voices are one to another, the more excellent is the Symphony. The best Disposition of all look above Chap. 5. Rule 6. where I do write of signed Keys.   

2. The Musical Trias doth arise both from Arithmetical and Geometrical Proportion.  
Proportion is threefold: First arithmetical, which is, when the numbers are distant one from another by an equal Difference, and that either continued; as 1.2.3.4. or disjoined, as 3.6.8.11. The●e the Difference is an unity, here a ternary. Secondly, Geometrical; which is, when there is the same Ration of more Terms compared with one another: and it is either continued, as 4.8.16. or disjoined, as 2.4.8.16. Thirdly, musical or harmonical Proportion, ariseth from arithmetical and geometrical: and it is no other, than a Symmetry of Concents, which is discerned in the most perfect musical Triade; which Lippius therefore calleth the chiefest, sweetest, and plainest Compendium of Melopoetical Music. But let us pursue these things further. Musical or Harmonical Proportion is the Symmetry or Equality of Concents which doth arise from Proportion arithmetical and geometrical; so that three Terms being put, even as the greatest is to the least, so is the Difference of the middle, and the greatest to the Difference of the middle and least. As 3.4.6. Here, as Six are the Duplum to three: so two (which is the Difference between 4. and 6.) are the Duplum to the Unity, which is the Difference between 3. and 4. Such is the proportion in the unitrisonus Radix. 1.3.5. Also between 6.8.12. For three Terms musically proportional are found from three arithmetically proportional, if the first arithmetically proportional be multiplied into the second and third, and the second into the third. So from these three arithmetically proportional 2.4.6. are found these three musically proportional. 8.12.24. But that numbers are musically proportional, is hence manifest, if in them those three Proportions are found, on which all Music doth depend: to wit, Dupla, or Diapason, which doth constitute an Octave: Sesquialtera, or Diapente, which doth constitute a Fifth: and Sesquitertia, or Diatessaron, which doth constitute a Fourth. So in these Numbers 6.4.3. between 6. and 3. is dupla: between 6. and 4. sesquialtera: between 4. and 3. sesquitertia. I say, three to four, are in the sesquitertian Ration, as the Diatessaron System: four to six are in the Sesquialtera Ration, as the Diapente: three to six are in the dupla Ration, as the Diapason System. And of these the rest a●e compounded, viz. the Disdiapason, etc. This also is of force in Organical Music. For if two Strings equally thick and stretched differ in Longitude by a Sesquialtera Ration, benig struck, they will equally Sound the Harmony of a Diapente: if they differ in Longitude by a Sesquitertiae Ration, a Diatessaron: if by a dupla, a Diapason, which vulgarly they call an Octave, as a Diapente a fifth, and a Diatessaron a Fourth. The same is in Hollowness, or in Whistles. From this Operation always except the unitrisonous Radix, because it is the foundation of other musical proportions.     

CHAP. VIII. Of the Form of an Harmonical Song.  

PRECEPTS.  
THus much concerning the matter of an harmonical Song: now of the Form thereof, which is the artificial disposition of Musical Monads, Dyads, and Tryads, according to the Text, and this is called Melody.  
Melody is simple, or compounded. That is called monody, this Symphony.  
Simple Melody is that which is content with one only Series of musical voices: as is discerned in Choral Music, called Unicinium.  
Compounded Melody is that which doth conjoin more simple Melodies between themselves: and is usually called Counterpoint; as is discerned in figural Music. To which appertain Songs of two, three, and four voices, etc.  
Counterpoint is either simple or coloured.  
Simple Counterpoint is that which hath least of Artifice: and may be called pure Composition, whose Rules or Ornaments are the Sounds of Longitude, Latitude, or Crassitude.  
Counterpoint coloured is that which hath more of Art: and may be called adorned Composition, whose Rules or Ornaments do respect the Longitude, Latitude, and Crassitude of a Sound.   

RULES.  

1. A Musical Text doth give as it were a Soul to an Harmonical Song, as to the Image thereof.  
Wherefore seeing the Image is such as is the Archetype, the practical Musician or Composer as they call him, is to take care that he understand aright the nature of his Text, in respect of things and words. For an Harmonical Song ought to be accommodated both to things and words. The things may be all divine and humane matters, but chiefly practical, which concern the active felicity of man; the mean to acquire which, is virtue moderating the Affections, which do depend upon things or objects either great, or low, or mean: and those again either pleasant or delightful, or unpleasant and sorrowful, or moderate. Words may be either of prose or verse, yet so as that they be like unto things practical, even, and congruous. So that he ought to know the nature of all Letters, (of which in my Rhetorics.) Moreover, an harmonical Song will rightly express the Text, if the Musician give heed to the trine Dimension of Sound, viz. Longitude, Latitude, and Crassitude. For things grave are rightly expressed by long and profound Sounds: light things by short and acute Sounds: Masculine things by sharp Sounds: soft things by flat ●ounds: pleasant things by lively and quick Sounds: Sad things by languid and slow Sounds: and mean things by mean Sounds; as we see it falleth out in Poesy.   

2. More Simple Melody, which is called Monadie, is first to be composed.  
A young Composer should first compose the most simple Melodies, which arise not from Musical Dyads and Tryads, but from Monads, or a simple Disposition of musical Voices. e. gr. Let this be the Subject, Laudate Dominum, which may be sung with this Melody.  
Or after the new manner, which Lippius hath, which dependeth upon the Syntonick Table, in the 5 Chapter before mentioned.  
288. 320. 288. 270. 270. 288. Lau damn ●e do mi num. 2. 1 1/2 ½ ½ ½ 2.  
Here the Numbers placed above the Text do show the Notes of the Syntonic Table: and the numbers underneath do express the measure of the Touch. Therefore such will be the Series according to this new Mode.   

3. Compounded Melody doth respect either two, three, or four Simple Melodies, cardinal and radical.  
Of these the Composition and Connexion of four Melodies is most perfect. For as a body mixed of four Elements, is a temperament of four humours: So every harmonical Polyphony doth arise from four simple Melodies. Of these two are extreme, the Bass which is the gravest; and the Discantus which is the acutest: and two are intermediate; the one is nearer to the Bass, which is the Tenor; and the other is nearer to the Discantus, which is the Altus, according to the Disposition of the four Elements, Earth, Water, Air, and Fire. Of which, two are extreme, and as many Median, as is noted in our Physics. And this is the Musical Tetras, in which the Melody of the Bass is fundamental▪ whence its name is from Basis a foundation: or Bassus profound: the Melody of the Tenor and Discantus (whose vicissitude is very elegant) is principal or regal. Lastly the Melody of the Altus is explemental. This Tetras, or Song of four voices, doth comprehend both musical Monads, Dyads, and Tryads, aswell Simple as Compounded, and is the Radix of all perfect Musical Composition. This therefore is the Order in Musics. The Musical Monade is the Radix of one Melody, or Song of one Voice: the Dya● of two: the Trias of three: and the Tetras of four: Moreover this Composition is called Counterpoint, because point is put against point.   

4. Pure Composition, or Simple Counterpoint; hath this Artifice.  
1. Pure Composition doth make the four Melodies, more simple, plain, and easy: yet so that it keepeth the trine Dimension of Sound. 2. This is the Rule of the Longitude of a Sound. Every one of the four radical Melodies doth so proceed by his Monads, that Notes of more simple value may be added, the Touch being every where equal. 3. The Rules of Latitude is this. 1. All the members of all the Melodies do make a Consonancy; which doth depend upon that unitrosonous harmonical Radix, of which mention is made in the foregoing Chapter. And because the parts and productions of that Triade are various, the Consonancies may be mingled among themselves, yet so as that the peculiar Ration of the perfecter of them be kept: for in every Genus that which is most perfect is the measure of the rest. 2. All melodies should be compared with themselves most diligently. viz. The Bass with the Tenor, the Tenor with the Altus, the Altus with the Discantus, the Bass with the Altus, the Tenor with the Discantus, lastly, the Bass with the Discantus. Or more briefly, the Tenor with the Bass, the A●tus with the Tenor and Bass, the Discantus with the Altus, Tenor, and Bass. For so every one compared with another will make six times an excellent Song of two Parts: So that every part of the Melody will be adorned with some harmonical Dyade. And also in those Dyades, variety is to be used, yet so that the perfecter do rule. 3. Consonant Dyades by ascending and descending together may all mutually antecede and follow one another, if they be of divers species: but if of the same, as the three perfect Consonancies with the simple unison, they may not, but the other imperfect Dyads may. But more briefly, two simple Unisons may not be put together ascending or descending: nor two Octaves, nor two Fifths, nor two Fourths. 4. Those Dyads which are nearer in Crassitude, will better precede and succeed, than those which are more remote. To which purpose is that saying of Musicians, By how much nearer Voices are to one another, by so much they make the better Symphony. 5. Monads should be applied so in all Melodies, that every one should elegantly walk in his own Region, and commonly of one Octave, or Diapason. 6. Let the Bass always take the lower part or foundation of the harmonical Triade in the place of the gravest: but the Tenor in the place of the graver, the Altus of the acuter, and the Discantus of acutest Monads: So let them take all three parts of the harmonical Triade, viz. The lowest or first, the middle and last. But in augmentation and multiplication the first of the Triade is chiefly to be repeated, the last more rarely, the middle seldomest. 7. ●et Melodies associate by gradual, not by skipping motion. For if every Melody do proceed rather by degrees, then fly violently by greater intervals and Leaps, it will be more grateful to the Ears; yet the Bass is allowed to move by Leaps. 8. Let the Bass be first composed. Because it is the foundation of the Triads. Hereto belongeth th●s Rule. Better is that harmonical Triade who●e Basis is lowest, than those whose Basis is in an hi●her place. But now let us see an Example. Let the Text be Laudate Dominum. And this you may thus express in a pure Song. Go to the Syntonian Table, and from thence pick out Consonancies after this manner.  
 2. 1 1/2 ½ ½ ½ 2. Discantus. 180 192 180 180 180 180.  Altus. 240 240 240 216 216 240.  Tenor. 288 320 288 270 270 288.  Bassus. 360 480 360 540 540 720.  Lau da te do mi num.  
These Consonancies you may thus transfer into the great System. Lau╌da╌te— do╌mi╌num.  
Or if you had rather you may thus write the several * Touches in several Cells.  
* Touch is that which Musicians call Tactus, or the stroke of the hand by which Time is measured. Or it is the successive Motion of the hand, directing by equal measure the Quantity of all Notes and Pauses in a Song, according to the variety of Signs and Proportions. The parts thereof are Elevation and Depression; or the Fall and Rise of the hand. Be╌ne dic╌a╌ni╌ma╌me╌a— Je╌ho╌vae.  
In the latter Example you may observe the Tenor to have the same Voice with the Bass in the first Cell: and in the Sixth and Seventh, two Minums put for one Semibreve.   

V. Adorned Composition, or Coloured Counterpoint, is contained in these Rules.  
1. Adorned Composition doth constitute a Song harmonical more broken, florid, and coloured, therefore more difficult and effectual. Therefore this doth as it were garnish these three Dimensions of a Song with various Gems and flowers: so that pure Composition may rightly be compared to Grammar, which teach●th to ●peak purely: and adorned Composition to Rhetoric, which teacheth to speak Elegantly. 2. Artificial Licenses are used in adorned Composition. For as there are allowed Poetical Licenses, which do beautify Art, and not destroy it: so also there are Melopoetical Licenses, by which the pure and simple Dimensions of a Song are beautified. 3. These are the Ornaments of Longitude. 1. An harmonical Song is adorned with the variety of a Spondaic, and trochaic Touch: and of unequal Notes, especially Syncopated. So the Bass doth move more slowly, and the other Melodies with coloured celerity; which is that in Music, as flourishing is in Writing. 2. An harmonical Song according to the Nature of the Text, is distinguished by Rests and Closes. For even as Speech is distinguished by Commas, Colons, and due Periods; so ought an harmonical Song, according to the nature of the Text, to be distinguished by greater and lesser Rests; also by Closes native, primary, secondary, tertiarie, peregrine, more perfect, or more imperfect. A perfect Close doth consist of three Voices; the antepenult, penult, and last: by which the Close is chiefly known, and which is to arise out of an harmonical Triade. e. g.  
The Primarie Close is that whose last is the first; the secondary, the supreme; the tertiarie the middle of the Triade; but of these in the following Chapter. 4. The Ornaments of Latitude are these. An harmonical Song should be so expressed by Voice or Instrument, or both together; that according to the Condition of the Text, an asperous, sharp, swift, full, gentle, flat, submiss, or small Spirit, etc. should be heard. 5. The Ornaments of Crassitude have these Axioms. 1. Variety should chiefly rule in an harmonical Song; I say variety of Dyad's and Triads, more grave, more mean, more acute, simple and compounded, diffused and augmented, more perfect, and more imperfect, natural and fict. Hence is a various Licence: for in the Bass it is lawful to use the last and middle Monade of an Unitrisonous Radix: and Dyads prohibited, may antecede and follow one another; and a Dias and a Trias also anarmonical may be used. All which things are done either covertly or openly. Covertly, either by greater Rests, or by Sounds not offending by reason of their swiftness, or by contrary made Sounds; or by an excuseing Polyphonie, or by Syncope. Openly for the texts sake, and singular Artifice. v. gr. If the Text command, and as it were compel to manifest some Discord. According to that of the Logicians; Contraries placed nigh themselves are the more clearly illustrated. When therefore in Singing some harsh sound is heard, which presently passeth into a sweet harmony, the hearing is therewith more affected, than if there were a current of perpetual Harmony. 2. When the whole harmonical Song is rendered more beautiful by the ornament of Celerity and Syncope; then chiefly the Close should be artificial. 3. Polyphony or multiplication of cardinal melodies do very much adorn Singing. e. gr. As if there be two, three, or more Bases, Tenor's, Altus', Discant's, and those placed in certain Quires, according to the Text and Circumstances. 4. The various manner and motion of ascending and descending, is granted to principle Melodies and sometimes out of their Proper Regions; as for the Bass to invade the Confines of the Tenor, or the Tenor of the Altus. 5. The ornament of musical ornaments is that which they call a Fuge. This Ornament at this day is most excellent, difficult, ingenuous, efficacious, and full of Liberty. And this Fuge is nothing else then a more artificial repetition and imitation of certain Parts: to which a more Simple Repetition and Imitation is opposed, which also hath his Commendations amongst Musicians. And this is the Example of a Fuge in the Unison after two Times. Unum est necessarium.  
* I suppose that this Example was mistaken or rather misplaced by the Printer or some other, for I cannot imagine that the Learned Author would give the Reader Four parts of Simple Counterpoint, for an Example of a Fuge in the Unison after two Minims. Of which let this be an Example.  
And thus the Composer may continue his Fuge as long as he pleaseth.  
6. The Exercise of a Fuge is to begin in an Harmonical Tryade only. For so other forms and species of Fuges may more easily be apprehended. And for Examples you may look amongst those Principal and Heroic practical Musicians, as Orlandus and Marentius. Of which two, the one in his Mottets, and the other in his Madrigals, hath brought Melopoesie to his highest pitch. There are latter Imitators of these principal Melopoets, who notwithstanding aught to have their due praise.     

CHAP. IX. Of the Affections of an Harmonical Song.  

PRECEPTS.  
IN the last place the Affections of a musical Song do follow, wherewith it is affected and perfected.  
And they are either material or formal.  
The material Affection of a Song, is that which floweth from the matter thereof. And it is a certain Genus of Modulation.  
The formal Affection of a Song, is that which floweth from the Form thereof: and is called a musical Trope or Mood; which is a Rule, according to which we direct the course of a Song. Otherwise called Nomus and Tonus. And it is the same in Music, as a certain kind of verse is in Poetry.  
A musical Mood is either simple or compounded.  
The simple is primary or secondary. That is called Authentic, and this Plagal.  
The primary mood is either legitimate or spurious.  
The legitimate is either more natural in a sharp Scale, or more soft in a flat Scale. And both is threefold; the jonick, Lydian, Mixolydian, Dorian, Phrygian, and Aeolian.  
The spurious, bastard, ●or illegitimate Mood is the Hyper-Aeolian, and Hyperphrygian.  
The secondary or Plagal Mood is also called remiss and submiss: and it is Hypoionic, Hypo-Doric, Hypo-Phrygian, Hypo Lydian, Hypomixolydian, and Hypo-Aeolic.  
The compounded or connex Mood, is that which doth arise from simple Moods: when the Authent is joined with the Plagal Mood: whence it is called the Plagiosyntactical-Trope.   

RULES.  

1. The mixed Genus of Modulation is now for the most part in use.  
The Genus of Modulation is certain, according unto which the Song doth proceed in his Melodies in a certain Musical Scale. Therefore as the Scale of Music is simple, or mixed, and that old or new: (also the old Scale is either Enharmonic, or chromatic, or diatonic: the new, Syntonic) So also the Genus of Modulation is simple, or mixed, or compounded: the simple is old or new: Again the old is enharmonic, chromatic, or diatonic. And is also called Enharmonisme, Chromatisme, and Diatonisme. The new is Syntonic or Syntonisme. The mixed Genus of Modulation is that which is variously compounded of the Simple. Of the Simple, at this Day, Enharmonisme and Chromatisme (to wit alone:) partly for their Imperfection, partly for their Difficulty are not in use; but the Syntonian-Diatonisme, or Diaton-Syntonisme, yet so, that chromatisme be often mixed, and sometimes also Enharmonisme, if there be need, according to the force and acuracy of the Text.   

2. A Musical Mood is the most certain Rule of a Song.  
A musical Mood is that, according to which a musical Song is limited, and without it would be too ample and wand'ring. The Mood therefore doth contain Melody with certain Limits, and as it were Bounds of an harmonical Trias, in the Compass of an Octave or Diapason; so that wholly it doth continually proceed in a due order, from the beginning, by the middle, to the end, for the artificial expressing unto, and imprinting upon the hearers the virtue of the Text.   

3. The Doctrine of Moods is contained in these Rules.  
1. We cannot moderate or modulate any Song, unless we first know the Tone thereof. The Tone is known by the end, according to Rule: in the end it is seen of what Tone it is. The end also of a Song is judged by the musical Mood, which therefore by some is called a Tone, according to this Diversity of Tones, there are also divers Melodies. For as one Tone is in ut, and another in re: So also are the Melodies. Yet here you must remember, that every Tone or ●ood may not only be known by the end, but also by the beginning, and middle or Division thereof: al●o by his skipping. 2. A musical Mood, is an Octave mediated by his neighbouring voice. Otherwise it is defined to be the Species of a Diapason, which is made up of a Diatesseron and Diapente. 3. The Simple Mood is that in which one harmonical Triade only doth rule with his Octave, in respect of the Text and more simple Affection. 4. All the Moods are six, even as there are six voices. ut. re. mi. fa. sol. la. The Ancients had only four Moods, the first, second, third, and fourth: to which now the four final Voices do respond. re. mi. fa. sol. These four Moods the Grecians call Authentic, and the Latins herile or Clamous. For they have, as I may so speak, a greater Authority of ascending then the rest. But the Latines more narrowly considering the ascension and descension of every Tone, have constituted to every Mood a subjugal Mood; and those four they call Plagal; also subjugal, servile, and the like. And these descend more than the first. And hence arise the eight Moods, by which every Song is governed per Arsin & Thesin, by rising or falling. But our Latter Musicians more diligently considering the variety of Tones, have constituted twelve legitimate Tones. viz. six Authent, and as many Plagal. For as there are six Voices. ut. re. mi. fa. sol. la. so also there are six Authent, and as many Plagal, which are vulgarly named by strange Names of Nations: I say, of those Nations who commonly were delighted with them. And to these twelve legimate Tones, two illegitimate were added. Unto all which, various mixed Moods may be added. 5. An Authent Mood is primary, the Plagal secondary, and this doth not differ from that, but in respect of subjection, when it is called Hypotropus, remiss and submiss, because the harmonical Mediation of the Octave, which doth agree with the primary, is changed into the arithmetical, by the inversion of the fourth beneath the fifth with the Triade. 6. Concerning the Excellency and Efficacy of the musical Moods, there are divers opinions. Casus in politicis lib. 8. chap. 5. saith thus, Music is various and manifold. One kind is humble and remiss, as the Lydian; another is vehement and more moved, as the Phrygian; another is more moderate and mean which is called the Doric; and a little after, that grave, divine, and oraculous Music, called the Doric, allureth the mind to the study of Wisdom and true Piety. This, both the heathen of old used in their Synagogues, and Christians now use in their Churches. For in it there is a certain imitation of Celestial Harmony, by which as by a sweet and wholesome Medicine, the Diseases of the mind are cured, Vices are dissipated, Cares are lessened: and th● Dew of Divine Grace is leisurely, and by little and little distilled. And in the end of the Chapter, he saith, that the Doric Music hath respect unto Virtues, and divine Inspiration; and that it forceth men into Ecstasy of mind, and oblivion of the world; so that it driveth away evil Spirits, which he proveth by the Example of Saul. Lippius in his musical Synopsis, saith thus: the most natural and chief of all the Moods in these times, is the jonic, with his secundary the Hypo jonic. (against which many ancient and modern Musicians do speak.) But let us look upon the nature of the Moods in Specie. 7. The nature of the Authent Moods is this. The Authent Mood hath his final Key in the Diapente below, and is divided harmonically. And that is called harmonical Division, where the Octave hath the Fifth beneath the Fourth, thus; First the jonic doth occur, which is by Lucian called Glaphyrus. i e. pleasant: and by Apuleius wanton. And now it is much used. It runneth between C. and c. is divided in G. and endeth in c. In a flat Song it runneth between F. and f. and is divided in C. and endeth in f. It is most agreeable to Iambic's and Trochaic's. Then the Dorian Mood runneth between D. and d. and is divided in a. ending in d. but raised, or in a flat Song, hath his course between g. and gg. and is divided in d. and endeth in gg. By Lucian it is called grave, and by Apuleius warlike. It is most fit to sing to heroic Verse: for it hath wonderful Gravity with Alacrity. The Phrygian Mood hath his course between E. and e. and is divided in mi which is in b. ending in e. In a flat Song it runneth between a. and aa. and is divided in e. and endeth in a a. Lucian calleth it Entheus, Apuleius religious. For it hath the severe Insultation of an angry man, whence it is called Scolius. It is impetuous, accommodated to warlike Affairs. It is also jambic and tragic; distracting and ravishing the mind, putting it as it were out of itself, as Aristotle saith, 8. pol. c. 5. and Plato 3. de Instit. The Lydian Mood doth take his course between F. and f. is divided in c. and endeth in f. in a flat Song it runneth between b. and bb. and is divided in f. and endeth in bb. It is harsh, threatening, and merry. As Plato 3. dial. de rep. who condemneth the Lydian and jonic Harmony as sottish. This Mood is sharp, and according to Apuleius, threatening: and to Lucian Bacchicus. q. raging. The Mixolydian Mood runneth between g. and gg. and is divided in d. and endeth in gg. In a flat Song it runneth between c. and cc. and is divided in gg. And endeth in cc. It moveth the Affections, and rendereth them sorrowful and contracted; because it is mingled with the Doric gravity. Lastly, the Aeolian Mood runneth between a. and aa. and is divided in e. and endeth in aa. being raised up, it runneth between d. and dd. and is divided in aa. and endeth in dd. It is mild and very sweet, being sung to Lyric Verses. 8. The nature of the Plagal Moods is this. This Mood is called Plagal, as if we should say oblique or inver●ed; which hath its final Key in the lowest part of the fifth, but above the fourth: and is divided arithmetically. That Division is by Musicians called arithmetical, Where the Octave hath the fourth beneath the fifth; which is the more unpleasant. This Mood borroweth his name from the Authent, Hypo being prefixed thereunto. First the Hypoionic Mood runneth between Γ. and g. and divideth and endeth in C. being raised up, it runneth between C. and c. it is divided in F. In this Mood, the Molity of the jonic Mood is rectified. The Hypodorian Mood runneth between A. and a. is divided and endeth in D. being raised up between D. and d. is divided and endeth in g. It hath a harsh kind of Gravity, and flattereth not. The Hypophrigian Mood runneth between B sharp, and b sharp, is divided and ended in E. being raised up, it runneth between E. and e. is divided and ended in a. This Mood is humble, and inclineth to weeping, as making a sorrowful Complaining and pitiful Lamentation. The Hypolydian Mood runneth between C. and c. is divided and ended in F. being raised up it runneth between F. and f. is divided and ended in b flat. It expresseth a kind of sorrowful Continency, and is called the pious, and as it were puling Mood; and stirreth up tears. The Hypomixolydian Mood runneth between D. and d. is divided and ended in g. being raised, it runneth between G. and g. is divided and ended in c. In it there is a certain natural jollity. The Hypo Aeolian Mood runneth between E. and e. is divided and ended in a. being raised up, it runneth between a. and aa. and is divided in d. 9 This is the nature of the illegitimate Moods. An illegitimate or bastard Mood, is that, which cannot aptly be divided into the fifth and fourth: but into the Tritone and Semidiapente. And it is either the Hyper Aeolian Mood, or the Hyperphrygian. The Hyper Aeolian Mood is the illegitimate of the Authent; which runneth between b. and bb. having below a Semidiapente, and above a Tritone. The Hyperphrygian is the Bastard of the Plagal Mood, which runneth between F. and f. having a Tritone below, and a Semidiapente above. 10. Every simple Mood, out of his own proper harmonical Triade, doth give to every harmonical Song, peculiar Ornaments. To wit, Fuges and Closes proper, primary, secundary, and tertiary. Unto which, strange Closes from a strange Triad may be added; if they be well taken. The primary Fuge, and also the Close is from the first of his proper ●riaede: the Secondary from the highest: and the ●ertiat from the middle. 11. Every Mood in respect of his Effect and Affection, doth follow his Radix. i e. his Monads, Dyads, and Trias of which he doth consist. Hence it is (saith Lippius) that one Mo●d is very cheerful and lively; as the jonic very much, the Lydian devoutly; the M●xolydian moderately; another flat, soft, sorrowful, and grave, as the Doric meanly; the Aeolian less; and the Phrygian exceedingl●. 12. A compounded Mood doth proceed from simple Moods, and from it a Song is called mixed. A Mood is compounded of Moods near unto him, as the jonic and Hyper-Ionic which is often seen: or of Moods wholly divers, as the jonic and Doric; which is less used. This mixture dependeth more or less upon the affected Text. 13. The Mood in instrumental Music, by the Mediation of Chromatisme, is transposed either to the fourth above; or, which is the same, to the fifth beneath. Hence, from a regular or sharp Mood, an irregular Mood is made, which is called mollis. It is transposed also to the second, third, or other Interval: So that one Mood is changed into the nature of another; as the Lydian, into the jonic: the Hypolydian into the Hypoionic. 14. Always the two proximate Moods (the Authent with his Plagal) have the same fifth, and the same fourth. Thus, 1 & 2. Quartam. re sol. Quintam. re la. 3 & 4. Quartam. mi la. Quintam. mi mi. 5 & 6. Quartam. ut fa. Quintam. fa fa. 7 & 8. Quartam. re sol. Quintam. ut sol. 9 & 10. Quartam. re sol. Quintam. re la. 11 & 12. Quartam. ut fa. Quintam. ut sol. But here let us place Schemes to illustrate this thing.  
Authent Moods in a sharp Song.  
Authent Moods in a Flat Song.  
Plagal Moods in a Sharp Song.  
Of the Plagal Mood in a Flat Song.  
By these Tables it doth appear that the Plagal Mood differeth not from the Anthent but by remission into the fourth: when in the Authent here is an Elevation into the fi●th v. g. if in the jonic Mood it be ut, sol, in the Hypolonic, it will be ut. fa. hence also the Compass of all Moods may easily be found. v. gr. the Compass of the jonic Mood in a sharp Song, is sol. ut. in a flat Song fa. ut. the Compass of the Dorian Mood in a sharp Song is re. la. in a flat Song re. sol. and so of the rest.     

CHAP. X. Of Special Music.  

PRECEPTS.  
THus far of the general part of Music: the special remaineth, concerning the various kinds of Music, which are taken either from the matter: or the Character of the matter: or the Organical Cause: or Artifice of Music.  
First, From the Matter, Music is either sacred or civil.  
Secondly, From the Character, Music is either great, or mean, or humble.  
Thirdly, From the Organical Cause, Music is vocal, instrumental, or mixed. That is made by the voice of man, the next by divers Instruments, and this by the Uoice and Instrument together.  
Fourthly, From Artifice, Music is either Choral or Figural. That doth in his Notes observe an equal measure, and from the Author is called Gregorian: and this is either old or plain.  
This is such whose unequal Notes do vary their measure, and from the Author is called Ambrosian.  
Also mensural, and new Music.   

RULES.  

1. The asper Artery [or Windpipe] of a man, Vocal by the Tongue, is the Law of all Musical Instruments.  
Lively or Vocal Music as they call it, seeing it is the Cause of Instrumental Music, without Controversy is the noblest of all. And if it be joined with instrumental Music, it is an incredible Means of moving the Affections and Senses. Also Vocal Music is called the Exemplary or paradigmatical Cause of Instrumental Music: whatsoever they talk of Pythagoras, that he found out Music by the striking of divers Hammers upon an Anvil.   

2. A Song which may be sung both by Voice and Instrument, is various.  
To this belongeth a Mottet, Madrigal, Intrade, and bound Fuge: and this of one harmonical Triade only, or of more. Also the unisonous Simply, or multisonous, and that through the eight, fifth, third, etc. Also to these may be referred Songs of one, two, three, four, or five Voices, and likewise Songs of many Voices, or Polyphoniacs: which for their perfection may swell to forty or more Melodies. Of these the Song for one Voice is an harmonical Song potentially: the Song for two Voices, is the first harmonical Song, in Act; but more imperfect: but the Song for three Voices is perfecter: and the Song of four voices most perfect.   

3. Musical Instruments may conveniently be reduced to these two kinds.  
For some are called Pshelaphetus: and others are called Pneumatic: and these are called Crosta's, which only by striking do make a Consent, and by others are called Entata. These are also called Empneusta, and they are moved with the Fingers and Wind. Various kinds of Instruments are comprehended under these. As the Whistle, Pipe, Cornet, Sackbut, Trumpet, Bagpipe, and the like, which are blown. Also the Clavichord, Psaltery, Pandore, Cithrens, and the like, which are struck with strings: So also the Lute, Harp, Lyre, Tabor, and other Instruments struck with strings. The Cymbal, great Bell, and others struck with Brass. Also the musical Triangle struck with Iron or Steel. Or the Wooden Craticle (by the Germans called einstrofiedel' item ein holtzerngelachter) struck with Wood And lastly the great Wind Instrument or Organ which is both blown and struck together. And here it will be necessary to lay down certain Aphorisms concerning musical Instruments. 1. The Canon, Mother, and Radix of all Instruments, is the Monochord: which is an Instrument most simple, and entire, made of one or more unisonous Chords; and may be divided into how many, or how great parts you please, according to radical numbers by the bipartition, tripartition, quadripartition, etc. thereof. And we may observe fully in this Instrument, all the proportions of all musical numbers. And this will be the most simple Example of a Monochord, if you shall put one Chord upon a fit pe●ce of Wood; into so many parts as you shall divide the Wood, certain Notes being added, so many distinct Sounds there will be, if you apply your finger to the Chord. 2. The Wooden Craticle is next in plainness unto the Monochord. This is made ready without any trouble, if a Wooden stick being very dry, be proportionably divided into many parts; which according to the Order of Proportions, being bound together by links made of a string, do afford harmonical Sounds, if they be struck with a stick, and put to straw bound together. 3. The Lute is the chiefest of all Instruments of Music. For no Invention of ancient or modern Musicians did ever make a more grateful consent. 4. In Clavichords and the like Instruments there is the most evident Reason of the Scale of Music. Those Instruments do consist of certain Tetrachords, which are double, ordinary, and extraordinary. The ordinary Tetrachords are four. The first is called Hypaton i. e. of greater and gravest Chords: from B. to E. and this is the Bass. The Second is Meson, i. e. of Means: from E. to a. and this is the Tenor. It is called Meson, because in old time when there were only three Tetrachords, (the Tetrachord Hyperboloeon not being added) it was in the midst. The third is Diezeugmenon of distinct Chords, which is disjoined from a. by a Tone, which is from b. to e. and this is the Altus. The fourth is Hyperboloeon i. e. of excellent or most acute Chords: from e. to aa. and this is the Discantus. The extraordinary Tetrachord is Synemmenon. i e. of connexed Chords; so called because it is joined with a. and it extendeth from a. to d. There is also a threefold progression of these Tetrachords, viz. diatonic, enharmonic, and chromatic. The diatonic progression is by a Ditonus and lesser Semitone. The enharmonic by a Ditonus and two Dieses, viz, the greater and lesser Diesis. i.e. the half of the lesser Semitone. And the chromatic progression is made by the Semiditone, and greater and lesser Semitones. (vide triple Scale chap. 5.) This Doctrine will be clearer, if the Doctrine of Sounds, or musical intervals, or Moods (as they vulgarly call them) be rightly propounded. For there are in all Ten Moods according to a known Song. The Moods are three times three, and one, by which every Song is made. sc. The Unison, Semitone, Tone, Semiditone, Ditone, Diatessaron, Diapente, Semitone with a Diapente, Tone with a Diapente, Diapason. And whosoever shall diligently consider these Moods, shall easily know the Ration of musical intervals, and so of all Harmony. And the Artificial Division of these Moods is this. A Mood, or rather a Sound, is an Interval or Distance from another, and that is either equal or unlike. An equal Mood is that which is in the same Degree, and is called the unison or Basis. Also an Unison is the conjunction of two or more Notes in the same place. c. gr. if sol be repeated in the same Key, or lafoy, the Mood is unlike, in which there is both Arsis and Thesis'. i e. Elevation and Demission of the Sound. And this is either continued or interrupted. A continued Sound is a Tone or Semitone. A Tone is the skipping of a Voice from a Voice by a perfect Second sounding strongly. Hence it is called a Second. In the progression of six musical Voices, every next is distant from his next by a Tone. e. gr. ut re. except mi fa joined together; which Connexion is called a Semitone, which is the skipping of the Voice into a Voice by an imperfect Second, sounding flatly: as is the Leaping from mi into fa, and again from fa into mi. scil. the next. By the Greeks it is called Hemitone: and by Musicians the lesser Semitone. The interrupted Mood is discrete by certain intervals. The first is Diaphonus, as the Ditonus and Semiditonus. The Ditonus is a sharp and perfect third: and doth consist of two Tones, as is between ut mi. fa la. otherwise called the Third. The Semiditonus is the Interval of the Voice from a Voice by a flat and imperfect Third As between re fa. mi sol. The Second is Paraphonus. As a Diatessaron and a Diapente. A Diatessaron is the leaping from a Voice into a Voice by a fourth. As is between ut fa. re sol. and mi la. otherwise called a fourth. The Diapente is the skipping of a Voice from a Voice by a Fifth: called vulgarly Quadrimode and Quinta. As between ut sol. re la. mi mi. fa fa. And again a Fifth is either compounded with a Tone or a Semitone. Hence a Tone with a Diapente is a perfect Sixth, as is between ut from c to lafoy in a. The Semitone with a Diapente is the imperfect Sixth. As between mi from e to fa in c. and contrarily. The Third is Antiphonus. as the Diapason: which is the Distance of a Voice from a Voice by an Eighth; whence it is called an Octave. And it is made seven ways i e. from every Letter to his like; as from A to a. from a to aa. etc. To these Moods or intervals there are four prohibited intervals opposed by vulgar Musicians. 1. A Tritone which containeth three Tones, and is made from fa to mi. 2. A Semidiapente which passeth from mi to fa. containing two Tones and as many Semitones. 3. A Semidiapason, which is an Octave containing three Semitones and four Tones, reaching from mi to fa. 4. A Disdiapason, which is an Interval by a Fifteenth; within which there is a Limit appointed to the Voice: beyond which it may not wander; and if it wander it is but feigned; For if more Distances than a Diapason occur, they will equisonate with the former Distances in the Octave.     

Conclusion.  
AND this is the MUSICAL TEMPLE, whose Foundation is Harmony, or Concord: whose Covering is honest Pleasure: whose Wood and Stones are the Harmonical Monads, Dyads, and Tryads. That thou mayest not only enter this Temple, but build thyself; after the diligent reading of this Synopsis which we here present thee with: Consider those melopoetic Classic's and prime Musicians, Orlandus and Marentius. But chiefly exercise thyself in the Analysis of many examples; and then from that betake thyself to the musical Synthesis.  
FINIS.