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HEORY OF MUSIC
AND
HARMONY
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James M. Tracp.
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1817
7
MOTORITATILE
SCIENTIA
ARTES
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MYYNTIHIUTATIVIITTYWATUNUTTUM
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THE GIFT OF
LIMITIL
PUBLIULUNUL
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Music
МТ
Бо
Trt,
THEORY
AND
RUDIMENTAL HARMONY.
BY
JAMES M. TRACY, A. M.
TEACHER AT TUB Bostox CONSERVATORY OY MUHIC.
WHITE, SMITH & CO
Copyrighted, 1878
MOST RESPECTFULLY DEDICATED
TO THE
2
President and faculty of Penteronth lattge,
LY
BY THE AUTHOR,
This work is designed for all students and others who wish to beu
some thoroughly acquainted with the numerous signs and characters
used in Wi'iting music. It also gives the various forms and sizes of in-
tortals, together with their appropriato names; the movement of the
Tort voices or paits, the different divisions of time, the farions
kinds of chords with their inversionis and relation to each otlier, and
arrangement into fundamental harmonies. It also contains a large
nurrber of practical exampfes in writing harmony correctly, intro-
ducing all the intervals and chords as used by the best composers of
modern tiines.
It is confidently believed this little work will prove a most valuable
aid to all who are in pursuit of accurate musical knowledge, emiliracing
as it does, ererything necessary to be understood by first-class teachers
and amateurs. The author's practical experience in this branch of
1:usical education is sufficient evidence of liis ability to issue a work
which will be found useful, practical, and reliable. Hoping that all
those who study these pages will not be disappointed in good results
is the earnest trish of the author.
Boston: Gould, dusic Pr., 18 r. 0. Squaro.
supt
HEODORE LOUIS TROST
7.17.30
CHAPTER 1
MUSICAL SOUND AND MUSICAL ART.
IN order to understand this subject thoroughly we must begin by stat.
ing the difference between general and musical sound, for they must be
separated.
Sound comprises everything which is perceptible to our sense of hearing
or everything hearable. Sound is produced on our ear by oscillation, or
vibrating motion of air, or any other intermediate body which is perceiver
by our auditory nerves.
MUSICAL SOUNDS are produced by a regular number of vibrations, fast
or slow: if slow, the tone is low; if quick, the tone is high. The ear
nught to be able to distinguish between slow and quick vibrations, (high or
dow tones,) otherwise there can be but little use for a person to study mua
sic. A musical sound of some definite pitch is called a tone.
Sound is a hearable action of a vibrating body. A musical sound is a
sound of perceptible determinable pitch. A tone is a sound of known
pitch, either high or low. Unmusioal sounds are those which do not have
Bregular well defined number of vibrations. They are mixed or confused,
of unknown pitch, and toneless - such sounds are termed noises. The
string of a violin, piano, or guitar can be seen when vibrating, but the
stroke of a bell or common drum-head is produced in a different manner,
and cannot be so readily seen.
Elastic bodies are employed for musical instruments, as bell metal, steel
ror tuning-forks and piano wire, cat-gut for violins and guitars, glass for
bells, &c.
;. . .
.
On wind instruments it is the column of air within that vibrates and not
the instrument itself; the length and breadth regulates the pitch, high or
low
THEORY AND RUDIMENTAL HARMONY.
CHAPTER II.
ON TONES
THERE are two ways of producing musical tones: one by the human
voice, and the other by inanimate musical instruments. Music produced
by an inanimate instrument is called instrumental music. Vocal music, or
music produced by voices, is called human music. The inventive musical
art is the talent of being able to combine musical ideas and put them in
form so as to produce a perfect musical composition. The executive mu-
sical art consists in the power and ability of rendering a piece of music
properly after it has been composed, whether yocal or instrumental. The
theory of musical composition teaches us how to put tones grammatically
together in order to form a piece of music according to the laws of beauty,
it also treats of signs and characters used in writing music.
. CHAPTER III.
MUSICAL TONES AND PITCH.
MUSICAL ART embraces the entire compass of all perceptible tones, and
the realm of these tones is unlimited in number and variety. In musical
composition we can only make use of such tones as our ear is capable of
distinguishing as being high or low. The human ear can only recognize
those vibrations as sound which are neither too slow nor too quick. That
is to say, beyond a given heighth or depth the ear cannot comprehend dis-
tances. It requires about thirty-two vibrations a second to make a musical
highest tone is nine octaves above this, and consists of several thousand
vibrations in a second. The pitch of tones is the distance between any one
tone and another, whether high or low. The easiest way of furnishing a
clear illustration is by the keys of a pianoforte. It will be perceived that
the keys are divided by white and black, the object of which will be ex-
plained hereafter. "
CHAPTER IV.
NAMES OF TONES.
As a means of naming the different tones it is usual to employ seven let-
ters of the alphabct, C. D. E. F. G. A. B. These seven letters taken tow
gether constitute what is called an octave, and, as before stated, there can
·
THEORY AND RUDIMENTAL HARMONY.
2
be only nine octaves recognizable in music. Now, from C. to C. again is
an octave; or, from D. to D., E, to E., F. to F., is the same. The black
keys, situated between the white ones, are secondary, and will be treated
of in their proper place.
The distance between one white key and another, above or below, is
calld a tone, or step. It will be seen that every white key has a letter of
Its own, but the black keys have none; they borrow their names from the
white keys, either above or below, as the case may be. We will designate
all white keys as natural, or independent, in contradistinction to the black,
which are chromatic. Chromatic means colored, and in this work has ref-
erence to the black keys. The Greeks used to write their chromatic signs
with different colored ink (hence color to represent different keys, &c.)
To simply write the seven letters of the musical alphabet without ary
other symbol or sign to designate their location, position, or pitch wouin
leave us entirely in the dark regarding distance or pitch, and as a ineans to
obviate this difficulty a linear system or staff has been furnished upon
which to place the notes, and thus the exact pitch of any note can be reacl-
ily ascertained or deterinined. For this purpose five lines are written, thus:
Fig. 1.
STAFF.
Every position between a line or space is called a degree. A note placeil
in a higher or lower position is said to be higher or lower in pitch; but to
understand exactly where the true pitch is, it is necessary to have a fixed
location or position for each letter, and usage has introduced other signs
for this purpose called clefs. This character or sign is called a G clef,
and it is placed on the second la líne, thus: " Fig. 2. With this line
fixed as the clef line it is easy to ascertain y
where the oth-
er letters must be placed.
- -
Fig. 3.
Fig. 4.
DF
B-
* 1 2 3 4 5
1 2 3 4
The first line is named E, second G, third B, fourth D, fifth T. The dis-
tance between the lines are called spaces, and are named F, A, C, E; or,
taking all the lines and spaces together they form all the letters of the mu-
THEORY AND RUDIMENTAL HARMONY.
Fig. 5.
_
EDO BIGE E-
related
. Ema A-BODEF
in the example given above, other lines and spaces are used called added
lines or added spaces. They are written both above and below the regular
staff, thus:-
17 mp
B
.
Fig. 7.
A
-
-
-
12
23-56-
The above series of letters must be thoroughly learned and committed to
memory, otherwise it will be useless to proceed further. No one can learn
to read vocal or instrumental music with facility without first thoroughly
committing to memory all the rudimental signs, and especially the letters.
Having learned all the letters and tones of the : G clef, which represents
the higher tones of music, we now come to the Bass cleff, which rep-
resents the lower tones. thus:- Fig. 8.
Ā
:-F-
This cleff is called the F. or bass cleff, and is used for the lowest notes
or tones, bass voices or instruments. The fourth line is the cleff line: -
· Fig. 9.
Fig. 10.
A-
Ge-
THEORY AND RUDIMENTAL HARMOŅY.
To more clearly indicate the clef line a dot is placed on each side of the
fourth line. Added lines and spaces to any number can be placed above
and below the bass staff, thus:-
-B-
Fiy, 11.
.
Ġ-
Fig. 12.
..
-
-
-
-E-
-o-
2A-T =
To facilitate reading music when it runs very high it is usual to place
8va --- above the notes, meaning an octave higher than written, instead
of having too many added lines, as the lines confuse the eye. When mu-
sic runs very low, we write 8 va --- below the notes, which means an or
tave lower than written. Examples will be given further on.
There is another clef which is used quite frequently, it is called the
Tenor, or C clef; and is made thus: Het or, sometimes thus: tatt This
clef is a very useful one, because it Het is movable, and for RIF this
reason is particularly well adapied in writing music for the various instru-
ments of the orchestra.
fourth line is the chef
line.
A-
The
__
2
3
4
5
Fig. 14.
Fig. 15,
IANO DE
T
1
2
3
4
5
6
:
1
2
3
4
5
6
7
8
1
2
3
To understand thoroughly this clef we will place it in the various posi-
tions where it is most frequently found:-
8
THEORY AND RUDIMENTAL HARMONY.
.
Fig. 17.
Fig. 16.

Hallo-I AGF-ID-CB-ad
tista
.
BOD GA Ban
1 2 3 4
5 6 7
8
I
8
7 6
5 4
3 2
1 7 6 5
Fig. 18.
Fig. 19.
--I IGMA
DIGA Bm
Fig. 20.
IMI
wa
-
T
-F-
=
=
i
In example 16 the fifth line is the clef line. Ex. 18, with the clef on the
third line. Ex. 19, with the clef on the second. Ex. 20, with the clef
placed on the lowest line. From the foregoing examples it will be seen
that the c clef is very useful, and students should study all the positions
thoroughly.
If, as is frequently the case, a piece of music runs very high or very low,
it may with propriety be changed, as in the following example:--
Fig. 21.
The two C's, one on the added line above with the bass clef, and the
other on the added line below with the G clef, represent one and the same
tone. This C is called middle C, because it is situated midway between the
higher and lower parts of the musical scale. The three clefs showing the
true position of all the letters on them when embraced together:-
THEORY AND RIDIMENTAL HARMONY.
C.
DVIG-BODHG AB-C-

-
GA
BINDEFG A B Co.
G
I
C D-
E
TG IBCDEFGAB -C-
CHAPTER V.
DURATION OF VOTES AND RESTS.
How long or short is to be the duration of a tone is shown in part by the
characters called notes. There are two ways of showing the duration of
tones, one, by the particular form called notes, and the other, by figures
placed at the beginning of every piece of music. Here follows the present
note form; it will be seen that we have discarded the ancient names of
notes, because we like the modern plain English best:-
(1) O A whole note.
(2) P
A half note.
(6)
A thirty-second note.
(3) A quarter no
(7) A sixty-fourth note.
(4) An eighth note.
It will be seen there are seven different notes.
o The whole note is a round, open note.
p The half note is the same, with a sten.
The quarter note is a black dot with stem.
The eighth note is a black dot with stem and one hook.
0
TIT
THEORY AND RUDIMENTAL HARMONY.
The sixteenth note is a black dot with stem and two nooks,
The thirty-second is a black dot with stem and three hooks
The sixty-fourth is a black dot with stem and four books.
A whole note
equals two half notes,
or four quarters,
or eight eighths,
or sixteen sixteenths,
or thirty-two thirty-seconds.
.
A
Q
g
AS
BBBBBBBBBBBBBBBBB382333333333333
A note may be increased (lengthened) one half by the use of a dot place
after it, thus:-
D equals
equals
d. equals dd
A
di
equals d
. equals
· equals
- THEORY AND RUDIMENTAL HARMONY.
A second dot after the first adds one-half the value of the first dot:--
7.. equals del ] equals l
.. equals
d.. equals don
'
I
equals
FORMS OF NOTES AND RESTS.
Toe different forms of notes, or signs of tones, have different forms cor-
responding to them, called rcsts, pauses, or marks of silence.
A whole note rest, or mark of silence, is indicated-thus:
a bar placed under the fourth line. .

A half note rest is placed above the third line, and is made
tlus:
A quarter note rest is made with a hook turning to the right,
thius: .
An eighth, the hook turns to the left, thus:
A sixteenth has two hooks turning to the left:
A thirty-second has three hooks:
A sixty-fourth has four hooks:
Another kind of quarter note rest now in frequent use
is made like an inverted seven, thus: "
THEORY AND RUDIMENTAL HARMONY.
A rest can be prolonged by a dot in the same manner as
notes, and the result is the same:
Or, a bar is placed thus in the music staff to show or indi-
cate a measure, as music must be regularly divided into
measures for the purpose of indicating time.
The distance between the bars is called a measure:
Double bars indicate the end of a phrase or of the piece:
THEORY AND RUDIMENTAL HARMONY.
CHAPTER VI. .
DISTANCE OF TONES, INTERVALS, &c.
Thus far we have acquired a knowledge of notes or tones, their names,
and the manner in which they are written, that is, every tone has appearel
by itself; we will now examine them in their natural relation to each other,
when situated one above another. Two tones of liké elevation is called a
unison. Ai
Two tones not exactly alike in point of pitch, but
situat-
ed at the distance of a tone higher, or tone low-
er, is u On called an interval. The name of every interval,
higher or lower, depends on the distance between the tones. A note which
stands one place higher on the staff, one line or one space higher, is one
degree distant from its thus: A
The first or lowest note is
called a prime, and the sec-
ond a tone or second. The
Interval between the two is the
called a degree, step; 0. sec-
ond. For perfect uniform-
ity we will hereafter use the
terms whole tone and semitone to represent distances between any two
notes of a higher or lower degree.
III
Hof
th
ot
LA
(A.) Interval of a third, or two tones; (B.) interval of a fourth; (C.)
interval of a fifth; (D., interval of a sixth; (E.) interval of a seventh;
(F) interval of an eighth, or octave. We can go still further, by using
ninths, tenths, elevenths, and thirteenths, but beyond this it is unnecessary
to go, and rarely beyond the ninth (G). After the eighth, or octave, has
been completed, it is usual to call the ninth a second, and the tenth a third,
and so on. As previously stated the musical alphabet is composed of secen
letters, but to complete the octave the first letter has to be repeated, thus:
Intervals are always reck-
oned from below, upwards.
It will be remembered in our
treatment of intervals, thus
far, we have only spoken of
Fig. 22.
DEIGIDO
THEORY AND RUDIMENTAL HARMONY.
the white keys of a piano, or the so called natural tones of a scale. The
black keys of a piano represent no distinct letters or tones of their own,
but an accessory to the white keyg' (principal tones), showing whether a
tone is large or small, whole' tone or semitone By these accessory tones
(black keys) we are enabled to measure the exact magnitude of every intéra:
val, small or great. We find by this arrangement that there are two differa
ent species of seconds, large and small, or major and minor.
Beforeo proceeding further with intervals we must first learn that are
termed chromatic signs: they are a sharp is a flat , and a natural bl. The
sharpis a sign of elevation, showing that the ngte is made a semitone higher
when the sharp is placed before it, thus fa T II: The sharp
before the F raises the pitch a semitone to
cet higher,
which is represented by the black key
I I between F
and G, and the sharp before the C raises the pitch a semitone higlier',
represented by black icey between C and D. The seven notes (letters) of
the scale can all be sharpened, raised, or elevated by this sign :
Fig. 23.

نتعلتتتتتننننسس
-
the

Lalike manner all the keys (letters) can be flatted. This sign (k) shows the
note is lowered or depressed a semitone when placed be. A m i
fore it. The flat before A shows that the black key be- th-by-
tween A and G is to be used, and the flat before E, that I
the black key between E and D is used.
Fig. 24.
to bo bobo
سنسنلبمسلسعععسعسمسمنلححسسه
The natural is used to cancel the effect of a sharp or flat. A double sharp
X, a double flat b2; cancelling sign for a double sharp bi#, and cancelling
sign for a double flat 62. The same black key may represent at one
time asharp, and at another, a flat.
:
THEORY AND RUDIMENTAL HARMONI.
15
Fig. 25
VIEW OF THE KEY-BUARD OF A SEVEN-OCTAVE PLANOFORTE.
itses
V
ABCDEFGA LCD TGA Bodega b c d e f g a b c d e f za b'c d e f g a b c dc
ollll
Smallll.
11110
BABS PART.
.
TREBLE PART.
It will be seen or remembered that the key board of a piano is divided
into groups of eight white and five black keys, thus:--


odepg
MIRI
4BCDEFGA BODEGAB
This key.board embracce sever, octaras, viz: from. A. to a
THEORY AND RUDIMENTAL ÉARMONY.
.
This key-board einbraces seven octaves, viz: from A to a. Between
B and C, and E and F, there is no intermediate or blaclä key, and there-
fore the difference between these letters is only a semitone, according to
the following chart
Fig. 27.
- - - G -
whole tone large, scmitone, large, large,
or whole step. whole, half step, wole, whole,
znajor, major, minor, major, major,
B
- C-
large, small.
whole, semitone.
major, minor:
1
1
Fig. 26.
**
A
halfi
half.
Con
beya
8
The lines under the A means the large A twice marked; and the lines
(marks. will enable us to definitely fix any letter found in the musical al-
phabet. By referring to the key-board the exact location of the different
octaves (each octave) will readily be found.
CHAPTER VII.
THE SCALE.
THE seven tones (letters), c, d, e, f, g; a, bc, form what is called a scale,
and are reckoned from the lowest (tonic) upwards, by counting the lowest
tone as one, second two, third three, and so on to the end of the octave.
Each individual tone has a distinct name of its own. Thus: the first tone
THEORY AND RUDIMENTAL HARMONY.
is called the tonic; the next above, second, or super tonic; third degree, the
mediant; fourth degree, the sub-dominant; fifth degree, dominant; sixth
degree, the sub-mediant; 'seventh degree, sub-semitone or leading note;
cightli degree, the octáve: All tones which do not belong to this key (scale)
are said to be foreigii'to the scale, and therefore we call these the natural
or appropriate' tones of the scăle;' tonés belonging to this scale."
There are two keys (scales) connected with each letter: major and minor.
Every major scale contains five whole tones and two semitones, according to
the following forin :-
whole, whole, half, whole, whole, whole, half.
d
e f
g
a
b c
major, major; minor, major, major, major, minor.
semitova.
Fig. 28.
semnitoue.
do rae me fa sol la see do see : la sol fa nie rae do
1 2 3 4 5 6 7 8 7 6 5 4 3 2 1
ē Īē 7.5ā ūc ū ã ã 7ē di
The degree from one to two is a step; from two to three, a step; from.
three to four, a half step; from four to five, a step; from five to six, a step;
from six to seven, a step; from seven to éight, a half step, It will be seen
that there are five, whole.steps. (tones) and two half steps (şemitones) in the .
completion of this scale. The half steps occur between e and f, b and c,
all.the others being whole steps. This is called the major diatonic scale of
C', all other major scales must be constructed after the plan of this scale,
and for this reason is often called the model scale, because the others are
inodelled after it, but only in respect to the intervals are the scales alike.
It will be seen that we have given peculiar (fixed) names to those letters
which make up the major kej (scale) of C, and so long as they remain un-
changed by toñes forcijn to this scale, so long it must, continue in this key
or scale. The letters c, d, e, f, g, a b, constitute what is termed a natural
series of tones (white keys), and is therefore called a natural scale. If we
introduce ariy tone which is foreign to this pecüliar key, the scale or key is
said to be transposed; because the introduction of this foreign tone dis-
places the natural series of degrees" (tones) 'already established. Other
18
THEORY AND RUDIMENTAL HARMONY. .
major scales can be constructed with our system of notation, but they are :
copies of the C scale placed on other degrees of the staff. As this system
is particularly adjusted to the major scale of C, we cannot make any
change without introducing some additional element not as yet brought in-
to practical use. If music were all written in one key, there would soon
cease to be any charm in it; and for this reason, to give a greater variety,
characters called chromatic signs (sharps, flats, and naturals) have been
introduced (employed).
CHAPTÉR VİII.
-
TRANSPOSED SCALES.
We will take G as the first or tonic of a new key, but on an examinatioti
of the tone series we find they do not correspond with our model scale C:-
g
a
b
d
e f
lu
major, major, minor, major, major, miuor, major.
It will be scen that the interval between E and F is minor (semitone), and
that according to our model scale C, the interval should be major, and that
the interval between F and G is major when it should be minor la semin
tone). This difficulty can be easily overcome (obviated) by introducing a
sharp before the F; for, as the sharp elevates or raises the pitch a half step
or semitone, the F is sung or played on the black key at the right of it,
making it a semitone higher in pitch, and therefore adjusts the intervals
80 they correspond to those in the scale of C:
Fig. 29.
HI
Nilo
alf
half-
a . b c
2
3 4
dorae me fa sol la see do
This scale is an exact copy of the C scale in respect to intervals, but it
differs in position (pitch), being a fifth higher than C. The changing of."
THEORY AND RUDIMENTAL HARMONY.
19
the scale from C to G is called transposition. We will give examples of
all the transpositions by sharps, or transposition by fifths. G is a fifth
higher in pitch than C. A fifth from G would be D, and D will be the
next transposition:-
Fig. 30.
soeo de
. half
half
e . fig
c d
. 2 i 3 4
7 8
do rae me fa sol
a
see do
Note. When a letter has been once sbarped like F, in transposing the
scale, it is usual and more convenient to place the sharp on the fi, lh line, at
the beginning instead of before the note, in the course of the music.
Hereafter we will follow this rule. A is a fifth higher than D, and in order
to have the intervals come in their proper places three sharps are required:
A
#
at
Fig. 31,

1
os
-halt-
half.
2
6
7 8
do
rae me fa sol la see do
These sharps are placed on f, c, and g. In the above, the first two sharps
are placed on the fifth line and third space of the cleff. E is a fifth higher
than A, and is the fourth transposition from C:-
# # Fig. 32.
ta
---

lialf-
2
3 4
6 7 8
doraeme fa sol
sol l a see do
B is a fifth higher than E, and requires five sharps, namely: fi, ,

Fig. 33.
ho

t
or
do they
do
1
rae me
2 3
fa
4
sol
5
la
6
see do
✓ 8
20
THEORY AND RUDIMENTAL HARMONY.
F sharp is a fifth higher than B. It will be remembered that the inter-
val between E and F is only a semitone, and consequently. E sharp becomes :
the same as F natural, or, the white key of F represents E sharp in its.elem.
vated position, thus:-
Fig. 34.
hall.


ho 12160p
Do not leto
-half-
2 3 4 5 6 7 8
do rae me fal sol la see do
C sharp is a fifth higher than F sharp, and requires all the letters to be
sharped:-
Fig. 35.
half.
half.


tro
22
Dci'
de fi
1" 2 3 41 5" 6" 7" 8"
do rae me fa sol la - see: do..
The scale can be further transposed by sharps, þut as there is an easier
way, less chromatic, we will carry it no further. i
. The rule for finding the key note by sharps, is the next letter above the
lust letter sharped, or a fifth higher than the last key note.
We will now proceed to transpose the scale by fourths. . The reason for
this will be obvious enough as we progress with our subject. The fourth :-
from C is F:-
..
Fig. 36.
.. . . ..
***** half. .. ... ... ; .
half.
-
hoo-
obo eo
• f g
bb c . d e f
1 Ž 3 4 5 6 , 8
doraeme fasolla see do
The reason for placing the flat before B is to make the interval from
three to four a half step (semitone), without this flat, the interval would be
a whole step. It will be remembered that a flat placed before a note lowers
or depresses it a semitone (half step), that B is no longer represented by the
white key, but by the black key immediately at the left of it. In like man-
THEORY AND RUDIMENTAL HARMONY.
ner we transpose all the keys by fourths, &c. From F to B flat is a fourth :
Fig. 37.“
.."; half.
- --
..
half.
-a-
प
. Co
7
8
: 3 b c d ek. f . 8. a. bk
1 2 3 4 5
do: rae , me fa sol la. see do
A flat once introduced continues in force through all the subsequent keys.
From B flat to E flat is a fourth...E is the third letter flatted:-
Fig. 38.
**: half. ----
... half.

Ꭰ
abea
1. gak bb
3 4
5
do rae; ' me fa sol
Fourth transposition by flats. A flat:..
Fig. 9. . . " balf.:
d eh
7 8
see do
.
Lalf.

o
ovo
el
a
ak .bb ..C.dk
1
2
3 4
dow'räeme fa
Fifth transposition by flats. D flat:-
Fig. 40.
half.
5
sol
ỹ
sce
8
do
half.

a 2
"..e
. f gk
ab
ak
bb
6
la
- rae
sol
"me få
Sixth transposition by filats. G flat: -
. fig. 41. .'
half.
half.
70%-25-
O o
Scale in G fiat.
22
THEORY AND RUDIMENTAL HARMONY.
If there are any more transpositions to take place it is better to return to
some of the sharp keys, as it is less work and facilitates reading. In
finding the key note in transpositions by flats, look a fourth below the last
flat; or, it may be found on the last flat but one.
C major.
-half-
- half-
G major.
-
Ni boco
half-
lialf-
Jo
h
4
U

D major.
half-
alf-
ashto
ES)
er as

major.
-
W
alf-
#
DQ |
os
Ft
model
E major,

1
half
HA
. 900

B major.
NILA
-half-
half---
ort
LOCO
#
#
THEORY AND RUDIMENTAL HARMONY,
.
23
F sharp major.

half
alf
#
#

C sharp major. I
tha_to_12
Il
-alf
iala
Stand
| QQ
F major.
10
o
obom
half
notre
a
3
half
bé
.4

B flat major.
2.Po o oberoe
half-
half-
0.00
à b2
7 8
3
4
E fat major.

-ola
halt
half
de
7 8
A fat major.
half-
e
5
OWN
o
THEORY AND KUDIMENTAL CARMONI.
D fiat major.
طواب

-all-
21:11
빨
​얌
​뺨
​먕 ​양 ​일 ​양
​G flat major.

-
-
M
-
-
i à ß
in 2
be
3
bile ole
idle 2
ole
ole
. 2000
1
4
5
CHAPTER X.
MINOR SCALES.
If we examine the major scales it will be ascertained there are twelve in
all. Now there is another scale closely connected with every major scale,
but having an entirely different order of intervals; it possesses the saine
signature, but begins with a different letter. This scale is called minor.
The ininor scale belonging to the C maj r scale is placed on A, or a minor
third below the C. It' is known ör indicated by having a sharp placed
before the G. The following is the ordę of the letters, a, b, c, d, e, f,
a; or,

Fig. 42.
- 0
lialf-
--aug-
half-----
-ialr a un-
b c . , . e. f
2 3
sec do rae me fa
see lit ,
An exainination of the intervals will disclose three whole tones, three
half tones, and what we shall term an augmented tone. An augmented
· tone consists of a whole tone and a semitone, and is represented by the ill-
'terval between f and g sharp. The following is the order of intervals :
from one to two, is a whole tone; two to three, a seritone; three to four,
2 whole tone; four to five, a whole toue; five to six, a semitone, six ta
THEORY ACID RUDIICNTAL UANZIONY.
seven, an angmented tone; and seven to 'cight, a semitone. Like the
muajor. scale of this a minor is the model for all the other minor scales.
Perlaps the following diagrain will make this minor scale more intelligi-
1;lo:-
A : B
ef
whole tonc. scmitonic. whole. whole. ' semitona. ungmented. semitone.
We will now give the transposition of the twelve minor scales:
. Il. 43.
-To-
e
half.
ft
,
a
uum.
alhalf.
c
lialf.
b. C
5 6
' ine fa
.
2".
11
7
17:
8
lal
see: do
.
r:le
see
la
The interval from e.to f sharp, whɔle tone; f sha:p to , semitone; g to
a, whole toue; a to b, whole toue; b toc, semicone; c to d shari, augmented
tone; d sharp to e, semitoue.
Şecond transposition of the ininor scale by shards, B:-
Tix. 4t.
-
half.
auguzicuted.
Da!r.
li.
: Cd.
a # b
8
see
do
le
me fa
sce
sce
Third transposition, F sharp:--
Tig. 43.

a
'.1:21f.
.
half.
.
aug.
!!:ur
c
Nog
26 THEORY AND RUDIMENTAL HARMONY.

Fourth transposition, C sharp.
Fig. 46.
hall.
11:1!f.
hair.
ão
a
---
f
croa
an

*Fifth transposition, G sharp-
too
Wau
ialf-
-half
lill---
a
b
fx gt
5"
6
2 3 . .
Sixth transposition, D sharp.
,,Fig. 48.

-
--
casoo
lialr.
luur.
#
Xt
liall.
cxa
8"
x
ܕܬܩܝ
5*
6
MINOR SCALES ON RASS CLEF BY SHARPS.
This scale consists of three major seconds, three minor seconds, and .
an augmented second.
A minor,

half
aug.*
half-
--
b C
2 3
se do
rae
* From f to g sharp is an augmented second.
E minor.
alf-
e f
5 6
, me fa
a
see
aug.
key-uote.
ma
half.
ъс
Ellos
be to ous
lia!l.
die
7 S
THEORY AND RUDIMENTAL HARMONY.
B minor.
-half-
lail-
aug-
half-
بعد
artta
asio
I sharp minor.
ooo
half
lialfang.
lall
1
.
нь
B1 3
a
H
-
4
5"
6

C sharp rinor.
halls
- lialf
i ng
half-
Ich
G sharp minor.
half
halfang.
de
5 6
Bull
fx g#
7 . 8"
· P
is twice slurped, or double sharped.
D sbarp minor.
A
ooo
lialr
aug.
half
F
cus
28
THEORY AND RUDIMENTAL HARMONY.
That the minor scales may be thoroughly understood, we present some
examples in the Melodic form.
A minor. . . . .

@
la
-half-
b
C
see do
rae
A miuor.
D

lalt
lalt-
ono
see
la
E minor.
^

half.
.
Wer 2009
D minor.

half.
e: f
- 1-...----2- 3-
i.d.,
8
.
ico
1
2011111
lala
alt...
Co my
THEORY AND RUDIMENTAL HARMONY.
The scale illustrated on page 28 (melodic form) consists of five major
seconds and two minor seconds, the minor seconds occurrir.g between
two and three, and seven and eight. "
This-scale is changed in the descending form, inasmuch as the seventh
and sixth are flatted, or made natural.
A minor.

d
etali-
d . c b . a
Ś 4 : 8 2 1
see fa me rae : do. see la
We shall not transpose this form of the minor scale any further, but
the intelligent teacher will assist his pupils in doing 80, should it be
thought advisable. We will now take up the Harmonic form of the mi-
nor scale by flats. This scale is sung and played the same in ascending
and descending. .
Dininor.
---
M
liall.
half.
half.
2
3
6
G minor.

LD
ANO
alfa
half
a b2
2 3
half
el.
snoo
nor.
baf
balfot...
f
.
"C
...d
eb
C
.
37.
.. : . 1.7 8
From c to d, whole tone; d to eb, semitone; e), to f, whole; f to 8,
whole; g to ab, semitone; ak to bf, augmented; bly to c, sémitone.
THEORY AND RUDIMENTAL HARMONY.
F minor.
No
alf-
half-
gak
2 3
c de
5 6
1.
4
Bk minor.
ão
half.
cdk.
ek
half. augwented.
f gk a
half.
b
E minor.
Aaee
half-
a
OS
Wos
MINOR SCALES OX BASS CLEF BY FLATS.
D minor.
-
all-
-hali-
a b 2
.
half-
Chod.
From b flat to
sharp is an augmented sccond.
G minor.
1
half, aug.
half
laulf
a be
2 .3
. del
TIEORY AND RUDIMENTAL HARMONY.
C minor.

.. INI
liali
-half--aug-
gal
half-
by C.
7? 8
F minor.
)
-
-
half
half
half, ang
Cd 2
5 6
B flat minor.
lialf-
lialf
-Hug
h alf-
2
3
E flat minor.
دوس
half.
aug.
halt.
One more scale, the Chromatic Scale, (colored) completes the series of
scales. This scale is constructed by a series of semitones, thus ;

oooooooooo
Beth d d e f f g. &#a
- In the descending Chromatic Scale, flats are used.
a
b
c
ale apo o bombo
c
b
bh
a ak g
g2
f
.ek
d dh c
THEORY AND RUDIMENTAL HARMONY.
A musical circle representing all the major diatonic keys: - .,..
Fig. 576
B sharp is the same as C.
e . This same circle can repre.
sent the transpositions by .
O flats as well as. -by-sharps,
and also the minor transpo 51
F#sitions. :
As we stated in a previ ç!
nous chapter the excessive
transposed keys can bebel... ! "avoided l;y the usc of others
in simpler form. Tor in
stance, seven sharps can be
written with five flats, the ema
individual tones being repre-
sented by exactly the same keys. Six Nats and six,shazps also representi
the same series of individual tones... We will now give a table showing the
dear relationship of some of the keys to one another:
c d e f g a b c
F .
g a b flat c d e f
c d e f g a b c
G a b c d e fsharp ģ
Between C sharp and C there is no characteristic connection, they being
diumetrically opposed to each other
C .
d e . f g
b . C .
C sharp d sharp e sharp . f shaip g sharp a sharp · b sharpc sharp.
An examination will show there is an entire different order of tones.
There is also a close relationship between some of the major and minot
keys as the following table will show:---

& b c d e f g sharp. ..
C d : e f g a b c .
c d e flat f. & a flat b.flat c.
.
O d e f g a b c
e fsharp ģ b b c d sharp e
- If we wish to write a piece of music in a transposed key, we are accos-
tomed to write the requisite number of transposition signs at the begin-
ning, to save trouble in prefixing, a sharp. or flat to each individual note:
w which is to be effected by such a sign as it accurs along the piece. One or .
more such. signs thus placed at the beginning. is called a signature, . Here
follow the different signatures in
THEORY AND RUDIMENTAL HARMONY.

WE
Bass signatu ires.
)
11
E
TF1
C#
F
Bb
Ер
Ар
Db
Gb
雪莲臻霆骚辈遊路
​Đább
chnikbh
PV-
bo
- We have treated this subject - transposition of scales ---thus elaborate-
ly because it is one of the great stumbling-blocks of nearly all our students
in inusic; without a full understanding of this part of our subject we
might as well stop study and close our book in despair.
We advise all students to make it a point to write out all the scales in
standing of the subject.
CHAPTER XI.
DESIGNATION OF TIME.
sesses in a relative point of view, but not in a positive or absolute sense;
they nerely tell how many times longer or shorter one tone is than an-
other, but not how long a tone is in itself -- this is indicated by other signs
which we will now proceed to explain. The term teinpo relates to the
mythmical movement, and was formerly adjusted by technical terms: alle-
Gró, iindante, adario, and inany othare, but these terms are very uncertain
and variable, causing the necessity of a more sure scale for ineasurement
THEORY AND RUDIMENTAL HARMONY.
of time. A machine called Maelzels Metronome has been invented, which
indicates the time exactly, whether slow or fast. By means of an adjusti-
ble slide on a penduliun, the time can be regulated faster or slower as the
tempo may require. As a substitute for the Metronome a threaci pendu-
lum can be used, which any one can inake by attaching a common leack
for the weight. If a piece of inusic is añarked 50 quarters, the pondulur
must be 56 inches long. If 60 quarters is indicated the penduluin must be
39 inches. If 72 quarters is indicated, 27 inches, if 80 quarters, 22 inches,
84 quar., 19 34 inches, 108 quar., 12 inches, 152 quar., 6 inches
88 - 18 " 112 " 11 14" 160 66 51-2"
92 0 16 1-2 16 120 66 91-2 « 168 66 434 66
98 66 15 14.66 132 " 8 66 176 " 41-2 "
100 16 14 16 138 66 71-3“ 184. - 4 66
104 " 13 " 144 .66 6 1-2 66 192 66 33-4 66
Pendulums of equal length vibrate in equal time, even if their weights
are unlike. A pendulum to vibrate twice as slow as another must be four
times as long. Although this scale or table is not exactly perfect, it is suf-
ficiently so for all practical purposes.
CHAPTER XII.
DIVISION OF MEASURES.
Rythim consists in a symmetrical combination of different groups of
time, which may be larger or shorter. There are two different species :
one consists of time which are equal or even among themselves, and the
other of unequal numbers. These groupes are divided into what is termed
measures, and are bounded by bars. Bars are of two kinds: single and
double, the single is used for dividing the measures, while the other is
used at the end of a passage or the end of the music. A measure contains
two or three parts: if two parts, it is called even measure; if three parts,
uneven measure. The parts of incasure can be represented by either long
or short notes, at the pleasure of the composer. To show what species of
notes are to be used, a sign, calcd the rythmical signature, is placed at the
beginning of the music, and is written in the lollowing manner:-
THEORY AND RUDIMENTAL TARMONY.
85
2 2 3 3 3 4 4 4 0 0 0 9 12
2 4 2 4 8 2 4 8 2 4 8 8 8
and so on to the end. The signature is to show, in the first place, whether
the measure is divided into two, three, or more parts; and secondly, what
kind of notes are required. The upper figure shows the number of parts
the measure is divided into, and the lower figure the kind or denomination
2
-
2
of notes required to fill the measure. Thus: 2, two, two, the upper figure
shows that the measure is divided into two parts, and that two half notes
fill the measure; 2 shows the measure is divided into three parts, and that
it requires three half notes to fill the measure; 4 requires three quarter
notes to fill a measure; 8, three eighth notes fill a measure; 4, four quarter
notes fill a measure; 8, six eighth notes are required to fill a measure.
The simplest species of even measure is called two half measure, and is
represenied thus: 2 r . The whole note represents a full weas-
ure, as du also the two halves. We also have another specie of two part
ineasure, thus:
This is called two quarter measure. We
also have mae more form of this measure, called two eighth, thus: A
though it is seldom found.
CHAPTER XIII.
DIFFERENT SPECIES OF UNEVEN MEASURE.
UNEVEN measure consists of three parts:
Three hall
three
measure, or, three half notes fill the measure.
quarter notes fill the measure. . . .
Dieasure.
Three eighth notes fit a
THEORY AND RUDIMENTAL HARMONY.
SUBDIVISION OF THE PARTS OF MEASURE
Even subdivisions of even ineasure: -
oleo
Even subdivision of uneven
even teagures
dalah
Uneven subdivision is found written in the following form:
alat
Three quarters are here played in the time of one
half note. They are called triplets,
2ddd
Three eighths are here played in the time of one
quarter note.
aludto
Three sixteenths are here played in the time of
one eighth note,
2
Uneven subdivision of uneven measure, thus:-
dd
oggen
We might go on with numerous other divisions, but it is better for the
THEORY AND RUDIMENTAL HARMONY,
student to scek them out for himself. In rendering a piece of music, it
becomes often uncertain how a certain number of notes shall be grouped
together, and, for a better understanding of them, it is usual to designate
by the use of figures, thus:-
Fig. 58.
Fig. 59. a

A
or
tbus:
2
2
It will be observed that the first group is accented by sixes, while in the
second figure they are accented by threes. In 2 measure the delivery is
somewhat more heavy than in 4, though the degree of quickness is the
same; for this reason composers emplcy the longer notes to represent
heavy, and the shorter ones to represent the light or weaker character of
music
CHAPTER XIV.
MUSICAL ACCENT.
sic; but there is another property requisite, which enhances the effect and
gives more definite meaning to a whole performance. Musical accent is
This accent comes from an instinctive impulse within us to sing or play
some parts of a measure with greater force than another. In our method
of writing music, it is divided into ineasures by bars, and it is usual to acu
cent the first note after every bar, or, we begin the first part of every meas-
ure with a heavy accent. In two part time the first is the accented, and
the second the unaccented. We say down beat, up beat: the down beat is
2
on beat is
the accented, and the up beat the unaccented, thus:
A heavy
light
heavy
light
THEORY AND RUDIMENTAL HARMONY.
In three part measure the first beat requires the accent, and the two fol
lowing are light:
heavy light fight
It must be borne in mind that by accent we do not mean a force suffi-
cient to stun or shock us, but only a slightly increascd force, to distinguislı
it from the others; like soldiers marching, the left foot is the accented or
heaviest.
HIGHER RHYTHIM.
Thus far we have only had groups of two and three parts in a meas-
ure, but there is a still higher symmetry than this. As parts of time taken
together form small groups, so also can several groups taken together
form a larger group, or 2. rythm of a higher order. We mean by this,
several measures forming a sentence or musical phrase, like so many words
in language forming a grammatical sentence; like this melody from Mo-
zart:-
. MINUET.
Even compounds of even measure, consists in doubling the simple form of
two, two ineasure:-
ddd
This time is often designated by this sign: C
12
12
* Double whole note.
THEORY AND RUDIMENTAL HARMONY.
Three fold ineasures brought into one produce nine fold measure:
g. 10.10
9 1 9d. . .
2 z. z. o.
40d 18. d. d.
Vecdddddd! didid. 1°•...
Loddooddod
With one more example we will close the subject of compound measure:
So far as quickness or slowness of movement is concerned it does not
matter whether a piece is written in simple or compound measure, but
custom hias established a different kind of delivery of compound mcasure
from that usually given to simple, and, therefore, composers sometimes
use the one and sometimes the other, as thcir ideas or taste may dictate.
There is another species cf measure soinetimes used, composed of an
5 7
uneven number of parts, like 8 °F 8, but it is only used for its quaintness
by composcrs who wish to produce some peculiar musical effect, or to show
their eccentricity; we opine the latter,
THEORY AND RUDIMENTAL HARMONY.
CHAPTER XV.
As we have already stated, music is divided into figures called phrases,
or sets, and consists of two, three, or more measures; but this rythmical
arrangement does not imply that the notes must all be of equal length,
like sixteenths, eighths, and quarters, for they may consist of a variety of
unequal notes, only the notes must correspond to the time stated in the
signature. It often happens that a phrase begins in the middle of a meas-
ure, or even on the last part of it, for sometimes it begins with a heavy ac-
cent, and at others with unaccented or light part of the measure. Musical
passages are usually composed of rythmically round numbers or parts, and
are, or should be, reducible to the primary numbers 2 and 3, but these
parts are often extended so as to produce greater variety and to prevent
inonotony in phrasing. It frequently happens that the heavy part of the
measure occurs on the last, or unaccented part, and this is called inversion,
or changing position:-
Fig. 61.
.
Fig. 62.
A
b--
-
.
Inversions of this kind can only take place in uneven divisions of time, .
though examples of this kind are of frequent occurrence.
4 1 1 2
Music written in this way is called syncopation.
Syncopation, then, is where a measure begins with an unaccented note,
followed by an accented one; or, it is where a long note occurs between
two shorter ones. There are many ways of expressing these syncopes or
interruptions, but we need not dwell on them, and will only give a few ex-
amples: -
THEORY AND RUDIMENTAL HARMONY.
Fig. 63.
TII
Fig. 64.

Syncope produces a shock or revulsion of our feelings, because the stress
of voice falls on the light portion of the measure instead of the heavy,
which accords with our feelings best. Syncope differs from the rythmical
inversion mentioned, inasmuch as the syncopated note begins on an unac-
cented note, and holds over to the accented one, whereas the inverted ac-
cent does not continue so. Rythmical inversion:-
...dord door ddddordd dd
hdd ddod 2 doada
Syncopated notes occur in the following: -
As we have already recommended, we advise the student to seek out oth-
er forms of inversion and syncopation, to such an end; the orchestral
scores of overtures and symphonies will furnish a great variety.
INTERRUPTION OF RYTHMICAL UNIFORMITY,
There are some pieces which liave no time at all, and there are others
with a well defined rythm, which, in order to give it the proper expres-
sion, it becomes desirablc in particular places to disturb the regular course
“ of rythin. This interruzdion is termed accelerated, or retarded (faster or
slower), piu accelerando, a little faster, piu adagio, a little slower. There
are many other terms in use, like ad libitum, but the one most frequently
literally; at the will or caprice of the performer.
42
THEORY AND RUDIMENTAL HARMONY.
The recitative, used so much in oratorio and opera, is a form of vocal
declension, having no marked time; it is true there are long and short
notes, to represent certain words intended to be longer or shorter than oth-
crs, but it is left to the will or choice of the singer to accelerate or retard,
as his feelings may dictate, a liberty which is almost uniformly misused
and abused. There are other terms employed in music which indicate a
change in the style of rendering other than that indicated by the written
botes. We shall treat of some of the most common under the head of
expression and style.
CHAPTER XVI.
The movement of a piece of music is generally indicated by the ryth-
mical sign, placed at the beginning, with the addition or prcfix of certain
Italian words, indicating how fast or slow the movement is to be played.
we give a few of these terms, though they come more properly in the mu-
sical dictionary which will appear at the end of this work:-. .
Grave, very slow,
Affectuoso, gently,
Adagio, a degree faster,
Agitato, with emotion,
Largo, slow, and in a large style, Amoroso, tenderly,
Larghetto, a degree faster than largo, Cantabile, in a singing style,
Andantino, somewhat slow and flowing, Con brio, with spirit,
Andante, a degree faster than andant- Con fuoco, with fire,
ino,
Brillante, brilliantly,
Moderato, moderate time,
Pastorale, in a simple, unaffected
Allegretto, lively and tripping,
manner,
Allegro, fast,
Sostenuto, sustained,
Vivace, quick,
Scherzando, playfully,
Presto, very quick,
Vigoroso, with vigor.
Prestissimo, as quick as possible,
GRACES AND EMBELLISHMENTS.
The principal embellishments used in music are the trill, turn, fore and
afternotes, and the appoggiatura. Long fore notes are written thus, and
borrow half of the time of the principal note.
THEORY AND RUDIMENTAL HARMONY.
Fig. 65.
Written,
Il
1
Fig. 66.
ya
Played.
How
ITTI
-E-F-theme
Long after notes are not of very frequent occurrence; they borrow their
time from the principal note like the fore note, thus:-
Fig. 67.
Written.
Fig. 68.
Played.
TITI
-0-
AL
The appoggiatura is played very short, and is made thus:

A
.
|
-
-
· The turn consists of three or four notes, and is performed in a variety of
ways:
Fig. 69.
Fig. 70.
Written. Played.
Written. Played.
_KL-
It is sometimes made from below, thus:-
Fig. 71. 2 Played.
Played.
.
THEORY AND RUDIMENTAL HARMONY.
44
The trill can be made with or without a finishing note or turn, but it
sounds inuch better with the turn.
Whicn a sharp is placed above the sign it shows the next degree above
the principal note is to be sharped; when plaeed below the sign, that the
degree below the principal note is to be sharped. A flat placed above the
turn indicates that the next degree above the principal note is to be flatted,
and when below the sign that the degree below is to be flatted. A trill.is
the quick alternation of two notes on different degrees, but generally at
the distance of a semitone or whole tone from the principal; it can be made
a degree above or a degree below the principal note
From above the principal note: -
tr
1
. From below the principal note: -^
Without the turn.
There are so many ways of making this embellishment, and authors dif-
fer so much in regard to it, that we deem it inexpedient to lay down any
set rules. It is known by this sign: tr w
Expression of music means the coloring of it: loud, soft, fast, slow, and
attention to the accents, phrasing, and other marks used in writing music,
Signs of emphases:-
> > sf sfz do: . . ..!!
These signs can only be fully explained by practical examples, such as the
student will find in almost every well written piece, and which the com-
petent teacher should be particular to explain to his pupils in a clear, in-
telligent manner. Legato means in a smooth, connected, or sustained man.
ner; it is is known by the term legato, or these marks, called slurs or binds:
THEORY AND RUDIMENTAL HARMONY.
45
Fig. 72.
Wor
Staccato means in a short, detatched style, it is known by the following
signs: lll....
The pointed dot means very short, one-fourth the length of the note; the
round dot, short or one-half the length of the note: ---
Fig. 73.
Played.

Search
لمحتتتتتتتتسلسجسته
ستلمتتشمتحمست
Played.
fibi
Arpeggio, or broken chords (harp style), is known by the following ex-
ample. It must be played rapidly from the lowest note upward: --
Fig. 75.

R
.
سسسسسسسسسسسسسسسسسسسسسسس
A tie is used to connect two or more
notes on the same degree, and shows
that only the first note is struck, the I
others are held till the time has expired.
A hold or pause is indicated thus a, or thus U; it signifies that the
note or rest, over or under which it is placed, is to be prolonged double its
given length.
Dots placed before or after a fe
double bar indicate the music is A
to be repeated. The words dal
segno, D.C., or this sign , in-
40
THEORY AND RUDIMENTAL HARMONY.
dicates a repeat from it to the double bar. Notes are often abbreviated to
avoid labor and space:
tritten.
Played.

--+*+TTIISIH-+4+,
UT
-
--
-
-
Written.
Played.
The sign M.D. means right hand, and M. S., left hand.
PHRASING,
A musical phrase may be complete, as when it embraces any regular
symmetrical course of notes which begin and complete the intended ex-
pression; or, so to speak, when a full question is asked, or when fully ail-
swered. Dfusic, like language, is divided into sentences of longer or short.
er duration, according to the marks, signs, and slurs of the composer.
A musical phrase is incomplete when it does not include a full question,
or a full answer, or a full symmetrical course of notes. This subjcct rc-
quires personal instruction to be fully compreliended, though much can be
learned from examples, which, in a book of this size, we have not the
space to devote to it. A few hints will sufñce our purpose, and give the
student points by which he can explore the field wider, and make discova
eries for himself. A full musical phrase equals in language what is em-
braced within a period: it is generally known by the double bar, or the
end of a slur or bind. The beginning of a phrase should always be stronga
ly accented, and unaccented at the end: the more complete the sentence
or phrase the stronger should be the accent at the beginning. The begin-
ning of all phrases should be accented, but the shortér or incomplete ones
THEORY AND RUDIMENTAL HARMONY.
do not require, and must not receive, so strong an accent as the complete,
or full periods. Phrasings included within the semicolon or comma do not
require so much of 'an accent as those embraced or concluded within the
sface of a period. In playing the piano always take the hand or finger up
from the keys at the end of every well defined phrase, so as to begin the
next phrase with an accent and with precision. The singer should always
take breath at the end of every phrase, no matter how short! There is
phrasing; it gives color and expression to it, the same as good reading does
to language. A reader who uses the saine stress of voice throughout, and
*vho passes all the punctuation marks without stopping to take breath,
will never make any sense out of his subject, and will never become pop-
ular as a reader. So with the singer and player, for what is true of one is
also true of the other. We advise all students to make it a special point
to hear and watch artists of mcrit, as through this mcans much can be
2carncd which cannot be obtained through any other sourcc.
We have endeavored to give a full, clear, and concise stateinent of all
the signs and characters employed in writing music, and we feel assured
that if the student has followed the examples closely, as laid down in this
work, he will experience no difficulty in reading or writing any music he
inay desire, so far as the signs and characters are concerned.
We again urge the necessity of a thorough commital of all the signs and
characters used in this book, as it will greatly facilitate the student in
gaining a complete mastery of this difficult subject. Remember "that
what is worth doing at all is worth doing well.”
(End of Part First.
THEORY AND RUDIMENTAL HARMONY
PART SEOOND.
HARMONY.
CHAPTER 1.
DIFFERENT INTERVALS WITH THE SAM2 NAME.
In the first part of this work, the intervals were named from the number of
their degrees from each other, we will now treat them according to their actual
dimensions. For instance, we called the interval from e to f, a degree, and from
c to d, a degree; but it must be observed that from c'to d is a whole tone, while
from e to f is a semitone.
EXAMPLE 1. Major and minor seconds belonging to the major scale of C.
major second. major second. minor second. major second.
II
Et
Whole tone.
whole tone.
half tone.
.
whole tono.
major second.
major second.
---G -
A
mini r second.
-B
A-
-B
wholc tone.
whole tone.
half tonc.
There are still ther sizes of intervals for which we must have specific names,
We will therefore icsignate all intervals by the name of major, mặinor, dinin-
ished and augmented, or four sizes of every kind of interval. Some authors give
only three sizes of intervals. We shall rigidly adhere to this order, because we
desire to make this part of our work plain and intelligible, avoiding the error of
proſuse names, which must result in confusion, especially to the young student;
mye, and to the old as well,
THEORY AND RUDIMENTAL HARMONY.
49
In the regular order of the scale, we find two sides of tones; namely, whole
Fone, and semitone.
c d e f f g a... b to
whole whole. hall.' whole.' whole. whole.half.
In addition to the semitones between e and f, b and c, many others may be
formed by means of tlre chromatic signs of elevation and depression. We will
how write aninor tone, instead of semitone, or, the name minor will be substituted
for semitore, and major will be used hereafter in place of whole tone.
Ex. 2. Minor Seconds.

LI
xo
habet
Watchizosovo
aproapaathaalbobototho I
wers
few
Et
tandent
tool
toe pola bobono
Ex. 2. Minor Seconds are found from c# to.d, d# to e, e to f, f
to g, g# to a, a # to b, b# to c#, cx to d#, fx to g# c to by bh to a,
a to g, g2 to f, f2 to eh, ek to d, d2 to c, bk to ch, or a to b2, g to a2,
d to eh, e to d2, f to g2, bl2 to ok, ez to fk, az to b2.
Ex. 3. Major Seconds.

LAT
bertat
TH-
Late
1:50
THEORY AND RUDIMENTAL HARMONY.
to bola bobo trobot
bba
&c.
E
Ib090-100
Major Seconds. Ex. 3. c to d, c to dif, d to e, df to eft, e to f#,
f# to g#, G# to all, af to bit, ef to fx, bff to cx, b5 to c, as to b5, g5 to
ag, f5 to g5, d5 to es, e5 to f, bab to ch. .
Ex. 4. Thirds.
major: major. inajor. minot. minor. rinor. minor.
LI
Thirds. Ex. 4. A third consists of two degrees; namely, froni c to e,
f to a, g to b, a to c. There are two different kinds of thirds found in
the series of natural tones, major and minor,
b
major.
minor.
major.
minor.
or, c to e, major, d to f, minor, c to g, minor, f to a, major, g to b, ma-
jor, a to c, minor, b to d, minor. Beside these two sizes, many others
can be formed by means of the chromatic signs .
Ex. 5. Minor Thirds by Chromatic Signs.

1
1
th
711
Ex. 5. Minor Thirds. c# to e, df to f#, ef to g#, f# to a, gint to be
a to ce b# to det, fx to at, ab. to ch, bato 057 g to b5, c to e, f to a
e to gz, db to f5, g5 to bbb."
THEORY AND RUDIMENTAL IARMONY.
51
Ex. 6. Major Thirds by Chromatic Signs.

A
V
Ex. 6. Major Thirds. c# to e#, dit to fx, d to f#, e to go f# to all
8 to bit, a to cx, a to Ch, b to a4, b5 te d, e5 to g, ap to c, dā to f, g'
to b), cā to e), f5to ab, bəs to ube
There are two species of fourths, major, (the same as perfect,) and
minor: c to f, d to g,. e to a, g to c, a to d, h to e, are minor: f to b, is
major.
Some of the minor fourths which can be formed by the chromatic signs.
Ex. 7. Major and minor Fourths.

tatott
th
taa
th
Lot-pitba
A- -
Ex. 7. f# to b, c to f#, gh to che ał to s ay to dłt, e# to all, bt
to eh, fX to f' to b, bj to ek, ek to a2, as to db, dj to g5, g5 to 5,
e to f'b, f5 to b55.
Some of the manjor (perfeet).four!ls.
Ex. 8. Major Fourths,
-
52
THEORY AND RUDIMENTAL HARMONY.
52

Ex. 8. c to f#, d to g#, e to at, g to c#, a to df, b to e#, f# to bu,
4 to fx, b k to fk, e5 to a, .a5 to d, dā to g, g5 to c, 5 to f, f5 to 55,
155 to e5. According to the old method, fourths are called pure or
perfect instead of minor, and false instead of major. Other names are
also given, varying as the whim or caprice of the author dictates; but
uniformity is necessary to a thorough understanding of the subject,
and therefore we shall, as previously stated, adhere to one system of
names, so there will be no possibility of the student getting confused,
or lost in the mazes of a promiscuity of terms. The same name will
mean the same thing throughout. We give these examples in two
ways, that the eye may readily take in the contents, whichever way is.
stated.
Fifths are also of two sizes, major and minor. The only minor fifth
in the natural series of tones is from b to f; all the others are major.
Ex. 9. Minor Fifths, (sometimes called diminished.).

Tutt-
ti
el.
Ex. 9. ff to e, c# to g, # to d, df to a,' ał to e, e# to b, b# to f#, .
fX to c#, e to bta, a to 85, d to abs & to db, c to gb, f to c5, b5 to'for
es to be there
THEORY AND RUDIMENTAL HARMONY.
53
Ex. 10. Major Fifths, (sometimes called perfect.)

TA OTT thoa Thatbottt..
-t-na tába
50
Ex. 10. b) to f#, f# to C#, c# to go to dł, a# to allt, ał to e, con
to b#, by to fx, b5 to f, es to b5, ag to es, d5 to a5, 85 to d5, c5 to g5,
f5 to ch, b 55 to fb.
The term diminished or false fifth is frequently used for minor, and
pure or perfect for major. We discard these names. The minor sixth
consists of three major degrees and two minor, E-C, A-, B-g.
Ex. 11. Minor Sixths.

toetat
t
-
-
Ihot.
bombo
bo
-bo
toth
Xesonde
Ex. 11. Minor Sixths by chromatic signs. ff to d, c# to a, o to e,
af to b, a to f#, e# to c#, b# to G#, fx to d#, d to b5, g to es, c to' a,
f to d5, b to g5, e5 to c, aš to f5, dɛ to b5.
Ex. 12: Major Sixths.

I
THEORY AND RUDIMENTAL HARMONY.
.
Ex. 12. Major Sixths by chromatic signs. a to f#, e to c#, b to H,
f# to df, c# to a#, g# to e#, d# to b#, ał to fx, b5 to g, ek to c, az to f,
d5 to bk, gk to er, c2 to ak, fk to dk, bkk to ge.
Major and Minor Sevenths. There are only two major sevenths in.
the natural series of tones, C—b, and F-e.
y Ex. 13. Minor Sevenths.

AETH
7558
Foto
debo
Ex. 13 Minor Sevenths by chromatic signs. f# to e, c# to b, g#to
f#, df to c#, a togh, e to a bto af, fx to e#, c to bb, f to .ek,
hk to ak, ek to d2, ak to gb, d5 to c5, gb to f5, cś to b5b.
Ex. 14. Major Sevenths.

NIN.
ME
*
tho
F
bo
*Ex. 14. Major Sevenths by chromatic signs. ig to f#, d to ch, a to
#, e to dł, b to at, f# to e#, Cht to bł, g#to fx, b2 to a, e to d, ap to
g, d5 to c, go to f, ck to b5, f5 to ek, bz2 to a2.
THEORY AND RUDIMENTAL HARMONY.
55
· The octave is always the same, it being neither great or small; it is
called pure.
Octaves.

f
--- -
____-att8T+-
to be the bo
+ Polo 20 botot
i
it to be bo be
obo bobo
b
=
t
Major and minor ninths, tenths and elevenths are only repetitions of
the second, third and fourth. We have seen that intervals so far in
our study have been only major and minor, and that the difference be-
tween them is just one key, or a minor second. There are other inter-
vals produced by means of the chromatic signs, which we will proceed
to explain in our next chapter.
CHAPTER II.
DIMINISHED AND AUGMENTED INTERVALS.
Intervals which are a minor second larger than major, are called
rrugmented; and when a minor second smaller than minor, they are
called diminished. It must be stated and horne in mind, that two notes
occurring on the same degree is called a prime, and that when one of
these notesgis raised or depressed by a chromatic sign, it is called an
augmented prime. There is no such thing as a diminish.cd prime, The
augmcnted prime and the minor second represent one and the same key
on the piano, though harmonically speaking, they are treated differ-
(nily. Sorne theorists treat of the diminished and augmented tone, or
second; for instance, c to cand o to dk is a diminished second; and
though c# and dk represent the same key on the piano, they have
56 THEORY AND RUDIMENTAL HARMONY.
entirely different names. On the violin or violoncello, ch is not quite
80 high in pitch as d5, and d5 is not quite so low as C#. ..
Ex. 15. Diminished Seconds. (Not used by many theorists.)

I-
-
y hot
elo belsboliserate
Ex, 15. Diminished Seconds. "c# to d5, dito eh, e# to f, f# to g5,
to as, ał to b5, b#to.ch, cx to d, ax to e, fx to g, b55.to a, 855 to
f, d 5b to c, &c.
Ex. 16. Augmented Seconds.
2
I totobetonoptit
Thea
75502
boa-
Augmented Seconds (tones) are a minor second larger than major
seconds. c to d#, d to e, f to get it go to att, a to h#, eb to f#, aby to l,
dy to e, g5 to a, c5 to d, 15 to g, h 55 to é, ekz to f, &c.
Ex. 17. Diminished Thirds.

X
ft
Diminished Thirds are as follows: 4 to e5, a# to f, f# to ab, b to da,
e to gb, a to c2, d to fk, g to b bb, # to bh, ał to c, ef to g, bi to d,
fx to a, cx to e, gx to b. In respect to keys, the diminished third is
the same as a major second.
THEORY AND RUDIMENTAL HARMONY.
57
Ex. 18. Augmented Thirds.
Augmented Thirds are as follows: eb to gł, bb to df, f to at, c to
g to b, d to fx, a to cX, e to gX; a5 to c#, d5 to f# go to b, ch to c,
f5 to a, b 55 to d, e55 to g.
Ex. 19. Diminished Fourths.

12nt
ta
Diminished I'ourths are as follows: a to g, e to ak, b# tó e, c to fli,
fX to b, f to b 55, &c.
Ex. 20. Augmented Fourths. Ex. 21. Diminished Fifths.
beba
astrot
tetibo
Soort
to the
-trei-ari
.
Augmented Fourths. f to hi, fk to b, c to fx, b 55 to e, ek to all..
Diminished Fifths. c to g5; b to f5, fx to c, e to b 55, &c.
Ex. 22. Augmented Fifths.
Augmented Fifths. c tog# g to di#, ak to e, e to b#, fb to c, b to fx,
b hk to f, &c.
58
THEORY AND RUDIMENTAL HARMONY.
Ex. 23. Diminished Sixths.

hot-rot-too-
Diminished Sixths. b to gz, ał to f, e# to C, e to c5, fx to d, d to kh2,
f# to d5, &c.
Ex. 24. Augmented Sixths.

H
t
ET
Thotho
bo
- Augmented Sixths. ep to c#, g5 to e, f to d# g to e, c5 to a, b bez
to g, e to cX, as to f# &c.
Ex. 25. Diminished Sevenths.
Cibo e berbeza
foon
cotxoFat !
Diminished Sevenths. b to ak, # to f, to b5, b# to a, g to fb,
fX to e, f to ekk, f# to eh.
· Ex. 26. Augmented Sevenths.
OF
- - --
19bet
= -bbo
Augmented Sevenths. fb to e, c to b# g to fx, ehk to d, as to go, &c.


1
· As we before stated, octaves are pure intervals, but by some harmo-
nists are treated as augmented and diminished, though this work will
not include any such elaborate treatment, or dispute points of different
theorists.
THEORY AND RUDIMENTAL HARMONY.
si
SIGNS FOR DIFFERENT INTERVALS.
To represent different distances of tones by short signs, we employ
our ordinary figures : 2 stands for the second ; 3 for third ; 4, fourth;
55, fifth; 6, sixth ; 7, seventh. To still further represent the size, (spe-
cific) we will employ dots before and after the figures. A dut before
the figure, thus, .2 represents a minor second ; after the figure, thus,
2. major. Tro dots before the figure, thus, ..3 a diminisheil third;
two dots after the figure, thus, 5 .. an augmented ſiſth. Minor intervals
coincide with augmenteil, ando augmentect with minor. It will be ob-
served that each interval contains a specific number of minor seconda,
and when once learned can always be readily recognized.
CHAPTER III.
INVERSION OF INTERVALS.
By inversion we mean, changing places. If the lowest note of an
interval is carried up an octave, the interval is said tô be inverted. In- ·
version means then, that the lowest uote must be carried up an octave.
Ex. 27. Inversions.
In. In. In. In. In.
In.
tostogtooe
Inverted.
Invertei.
o
g-d
C-d
d-g
It is easy to see that in cvery inversion the interval is changed, and
that the distance of tones does not remain the same.
THEORY AND RUDIMENTAL ILARMONY.
TABLE SHOWING THE CHANGE OF INTERVALS.
The 2d becomes a 7th,
3d 6th
4th 66 " 5th.
or 2 3
or, v 6
The 5th becomes a 4th,
6th 16 1631.'
7th. 66 662d.
5 6 7
4 3
4
5
The octave when inverted gives no other interval, and consequently
the same interval is represented over again. By inversion, intervals
which are major become minor, and minor become rajor ; augmented
become diminished, and diminished become augmented.
ts - :ܚܞ 3
iy
TABLE SIOWING AUGMENTED AND DIMINISHED INTERVALS
.2 minor seconds become major sevenths...
.3 6. .3 minor thirds become major sixths.
. 5 4minor fourths become major fifths.
.5 4. 5 minor fifth's become major fourths.
nós i aj
2.
7. minor sevenths become major seconds.
We would advise the student to go through all the inversions of the
different intervals, for they will prove an invaluable exercise.
INTERVALS OF THE SCALE ACCORDING TO RICHTER.
Major Seconds.

os
132 baboliszthez

Minor Seconds.
1 sec. Minor,
Minor.
Minor.
tynyt
THEORY AND RUDIMENTAL HARMONY.
61
Augmented Seconds.
9 scc.
mil

i
taire de
-
of-
O
منلنلععععه
Major Thirds..
4 sec.

11
mit
hvad
44a abutalent than sual
mshots
ttt
Minor Thirds.
3 sec.
2226|52 .
2g
cenfeta 212121
Diminished Thirds.
2 sec.
9
fecum
U11
Major or Perfect Fourths.
5 800.

O
rientation de
la fin
Augmented Fourths.
6 sec.
ORIOLISI
iztrtez.
THEORY AND RUDIMENTAL HARMONY.
Diminished Fourths.
4 sec.

IN
LIT?
}
to
dal
belanden die
Velo
Perfect Fifths.
7 sec.

FALFITRI IZTI,
1922 32
222II-
-
-
Augmented Fifths.
8 SCC.
t
Rollather-of-of ott
31 VOIRZIbetooth
trottotapety
Hea
السسسیمهبللسمينعله لمنه
o olhat
.
Diminished Fifths.
7 scc.

AFIFe 216 beibetb
RA
Major Sixths.
9 SCC.

Augmented Sixths.

10 sec.
wise
کتا
بوسهسيعلن
Sobe obore
THEORY AND RUDIMENTAL HARMONY.
:
63
Minor Sixths.
8 SCC.

2
obo e
100
Major Sevenths.
Il sec

Led
ed
Minor Sevenths.

10 sec.
toto frotatatate Restata
t
he amint
Diminished Sevenths.
9 sec.
=
befalte the patarole e
tattoo oftelele otteet

Octaves.
12 sec.
hetonte

tobate papo
-
A
l
Gore
Augmented Octaves.
-]3 SEC.
st

-tittit
thothethe
2
THEORY AND RUDIMENTAL HARMONY.
Diminished Octaves.
11 sec.

Lagoge be borbehe
thatto the stototas
Ninths.
14 sec.

Otame27
ولد
L
ist
Minor Ninths.
13 sec.
be obefore

ta
med
CHAPTER IV.
THE MOVEMENT OF VOICES OR PARTS.
Musical art connects the various tones into a musical composition in
two different ways: first, in such a manner as to let us hear them fola
lowing one another successively; and second, in such a way as to let
is hear two or more of them sounding at the same time. A successivo
series of tones following one another according to the principles of mua
sical art or grainiar, in a musical sense, is called a melody or theme.
Several tones sounding at the same time, is called a chord. Several
„successive chords following one another in accordance with the gram-
matical rules of the art, is called Harmony. A person singing a suca
cession of musical tones, (melody,) is called a voice. When an instru-
ment plays a succession of musical toner, it is called a part. The
movement or carriage of voices or parts, is called Theory, or Musical
Composition.
THEORY AND RUDIMENTAL HARMONY. 65
Every passage of music consists of one or several voices or parts.
In the former case it is called one-voiced ; in the latter, several-voiced.
Harmony is usually written with four parts, but it may have more.
Rousseau states that it is impossible for the ear to distinguish more
than two voices at once, while Marpurg contends that it is possible to
hear a hundred and thirty-three. The margin between these two cele-
brated writers is so great, that we conclude both are wide of the mark.
Our object is not to ascertain how many voices can be heard at once,
but to make ourselves acqnainted with the best method of moving the
four parts, which is adopted as our standard. In four-voiced compo-
sition, the highest voice is called soprano ; the lowest, bass; the two
iniddle voices are called tenor and alto. How these several voices are
to move according to the grammatical rules of music, is called musical
progression ; but as writers and composers differ so materially on this
point, our treatment will necessarily be somewhat limited; that is to
say; we shall not prescribe how or in what way a voice shall move,
except in a general way. The two outer voices usually make a stronger
impression upon the ear than the middle voices, and the highest voice
is strongest of all. The outer voices are therefore called the principal,
and the middle, secondary voices. As the principal voices particularly
impress the ear, they require the most careful construction in accord-
ance with the laws pertaining to the carriage of voices, as a slight de-
viation from the regular purity is quickly observed, making it offensive
to the ear.
It has already been observed that there are two ways of producing
musical sounds : one by the human throat, the other by musical instru-
ments. In respect to singing voices, they are of far greater importance
than instrumental voices, and when used together, the former take the
higher rank, while the latter appear only as secondary, or forming an
accompaniment to the vocal parts. In respect to the nature of voices,
male and female, male voices are an octave lower than female voices.
Male voices are divided into three classes : Tenor, the highest male
voice; Barytone, the low tenor; and Bass, the lowest male voice.
There are also three classes of the female voice : Soprano, the highest;
86
THEORY AND RUDIMENTAL HARMONY.
Contralto, the middle; and Alto, the lowest. Boys' voices are gener-
ally alto, though there are instances where they possess an excellent
quality of soprano voice, singing as high as 7 three times marked.
A single voice is called a melody; two voices is called a duet; three
voices a trio; four voices a quartet; five voices a quintet; six voices at
sextet, &c. The difference between a few and many-voiced composi-
tion consists in the following things. The many-voiced composition is
in general more full, ample, and richer in sound than the few-voiced.
Another difference consists in the fact that the larger the number of
voices, the more difficult it is for the ear to distinguish or follow out
the different parts or threads; and the less the number of voices, the
easier it is for the ear to distinguish them. In many-voiced composi-
tions, a slight deviation in the strict rule of the movement of the parts
may easily be made unperceived, while in a fer-voiced composition,
more care must be exercised, &c., dii A four-voiced composition
has the advantage over either the many or few-voiced, because it seems
to be the happy medium between them, neither sounding too full por
too thin.
Several voices sounding together in a musical com-
position are commonly written on several staffs, con-
nected by a character called a Brace. The whole is
called a Score.
The movement of a voice is either quiek or slow,
According to the number of tones passed over in a given time. In
general, a quick movement is better adapted to nigh voices, while a
blow movement is better for low voices. The sounds of low voices and
bass instruments vibrate slowly, and therefore cannot express a quick
movement with any good degree of satisfaction, from their very nature
and construction. On the other hand, high voices and high instruments
represent a greater number of vibrations, and are consequently better
adapted to all quick movements.
The direction of voices may be either upwards or downwards. They
may move a single step, two, three or even more steps at once. Like

BRACE.
THEORY AND RUDIMENTAL HARMONY.
67'
movement is whare several voices move in the sam.. time and direction.
Unlike movement is wbere one voice proceeds faster or slower than anoth-
er. Like movement produces more sameness than unlike movement, and
therefore, for variety, unlike movement is the best. Two voiccs moving
in the same direction is called parallel motion. Two voices moving in
contrary direction is called contrary motion. Two voices, one moving.
either up or down from the other is called oblique motion. There are
then, three movements : parallel, contrary, and oblique. Converginy:
movement is when the parts come toward each other. -
Diverging movement is where the parts move opposite from each
other.
This subject will be further illustrated in the treat-
ment of Harmony, which comes in our next chapter.
CHAPTER V.
FUNDAMENTAL HARMONIES.
The lowest tone of any group of notes is called the bass or funda-
mental tone.
Dominant.
Mediant.
3 Fundamental.
The variety of chords occurring in music is almost infinite, though they
are all reducible to a few species in name, and are called fundamental
chords. There are two species of fundamental harmonies, called three
and four-fold chords; the latter are sometimes called chords of the
seventh. The three-fold harmonies consist of three tones: a bass tone,
(lowest), the third, and fifth, viz: ceg, fac, gbd. These three-
fold chords are sometimes called Triads, because they consist of three.
tones.
Ex. 1.
ob
- -
123-
oboch
THEORY AND RUDIMENTAL HARMONY.
Triads may be formed on every degree of the scale, and are either
major, minor, or diminished, according as the intervals are major or
minor. We present the major scale of C, with all its triads. The first
chord, ceg, the fourth chord, f a'c, and the fifth chord, gb d, contain
major thirds from one to three, and minor thirds from three to five; we
shall call them major three-fold chords or major triads. The chords
il f a, e gb, and a ce, contain minor thirds from one to three, and ma-
por thirds from three to fire. We denominate these, minor three-fold
chords or minor triads. The chord b d f, on the seventh degree, con-
tains two minor thirds, and is called a diminished triad.
The natural major scale of C, it will be observed, contains three man
jor, three minor and one diminished three-fold chord. On the first,
fourth and fifth are found major; on the secondi, third and sixth are
found minor; and on the seventh degree, a diminished triad. All the
twelve major scales contain just the same number of major, minor and
vliminished chords, and they are situated in just the same order or po-
sition as in the example given above. The student must transpose
these chords into all the other major keys if he wishes to be benefitted
lor the study of harmony in this or any other good instruction book;
lvut fearing he will fail to do this, we here present them in tabular form.
.
MAJOR SCALE OF C WITH ITS FUNDAMENTAL THREE-FOLD HARMONIES
TRANSPOSED INTO DIFFERENT KEYS.
Ex. 2. In C.

Minor.
ajor.
IN
Minor.
aior.
Mejor. Mojar
· Minor.
Mjuar. Dimimiked.
Diminished.
- IV
.
V
Azbor. Mjpor. Mijo
6113

-
D-
-B-
-G-6
For--
GE
E- --
TC-6
1. Tonic three-fold chord.
4. Subdominant chord.
5. Domiuunt chord.
THEORY AND RUDIMENTAL HARMONY.
69
Major.
major.
major.

II
.
III
VI
WIL
minor. minor.
minor.
diminislicd.
OVII

In G.
IV
II
Major
III
minor
VI
ininor.
wiajor
innjor
VIL
diminished.
minor
In F.

'
T
IV
III
Major.
II
minor.
major,
major.
VI
minor.. diininished.
mninor.

in
D.
Major.
minor.
minor.
major.
major.
minor. diminished.
ASS.
11
III
III
VI
70
THEORY AND RUDIMENTAL HARMONY.
:

Major. · minor.
minor.
major.
nujor.
minor.
dinn
ho
11
III
IV
had .
11
VIVI
VII

wajor.
Major.

julur.
climinished:
Minor.
ninor.

000
1
2
3
4
5
6
7
1
2
3
4
Š
6
ģ

11!
vdim.
2
3
4
5
6
7
The Minor scale already explained, with the augmenteil serenth,
contains its different three-fold chords arranged in the following order.
THEORY YYY
AND RUDIMENTAL HARMONY.
MINOR SCALE OF A, WITH ITS FUNDAMENTAL HARMONIES TRANSPOSED
INTO DIFFERENT KEYS.

-
Minor.
Aug.
major.
dim.
II
minor.
minor.
IV
major.
VI
diin.
VII

too oht to za
lin)
11
V
VI
dadim,
II
VII*
VII
Minor.
dim.
minor.
major.
major.
dim.
minor.

Bass.
Minor.
dim.
inin.
dim.
mini.
D minor. ·
Minor.
dim.
inile.
dim.
miu.

E minor.
.
& bol
muj. maj. dim. min.
Minor.
dini.
miu.
THEORY AND RUDIMENTAL HARMONY.
.

B minor.
-
ME
Miuor.
aug.
unin.
maj.
maj.
min.
min.
_
maj.
_

G minor.
Minor. dim. aug. min. maj. maj. dim. niu.
The first degree of the minor scale contains a minor triad; the scr-
ond degree a diminished triad; the third degree an augmentel triail;
the fourth degree a minor triad; the fifth degree a major triad ; the
sixth degree a major triad ; the seventh degree a diminished triad. This
scale contains two major triads, situated on the fifth and sixth degrees
of the scale ; two minor triads, situated on the first and fourth degrees
of the scale ; two diminished triads, situated on the second and seventh
degrees of the scale, and an augmented triad on the thirit degree. An
augmented triad is composed of two major tliirds. Each of the twelve
minor scales contain the same number of inajor, ininor diminished and
augmented triads, situated in the same order as here given.
It will be found that the three-fold chord as arranged, contains two
intervals, situated at the distance of a third-and a fifth from the fun-
denental tone, and that they are sometimes major, minor, or dimin-
ivel, taking their names according to the size of the intervals. We
a !.30 find in like manner, four different species of four-fold chorils, con-
sisting of a fundamental tone, its third, fifth and seventh, thus: ceyb.
-A--
- This species of seventh is called a major four-fold
2 chord. From the fundamental tone to its third is
- major; to its fifth, major, and to its serenti, major.
If all the intervals are large or major, it is a major three-fold chord
with the seventh added. Here follow the four species of seventh :
TIITORY AND RUDLİEXTIL ILARMONY.
BOLR-FOL)) HARMONIES FOUNDEI) OY TIILNLAJOR SCALE OF C.

Ex. t.
.
Major. Minor. Minor. Major. Dominant. Minor. Dimi :ished.
: Tlujor, ceg.b; minor, g buf; diminishel, b df ah; a ceg is a
śccond species of scvent', with a minor third, major fiſth and a minor
sereillir.
The last chord in the above exainple is a four-fold chord on the
seventh of the scale, with seventh flatted, called diminished...
seventh, and is called a major four-fold chord. A similar chord is found **
on t?e fourt degree of each major scale. Minor four-fold chords are
found on the second, third, and sixth degrees of every major scale:.
They consist of a minor third, major fifth, and minor seventh. The
seventh founded on the fifth degree of every major scale is called a
Dominant Seventh; it consists of a Major third, Major fifth, and a li-
nor seventh. This chord plays a very important role in musical com-
position. The Dirninisned seventh consists of a Minor third, Minor
fifth and Ninor seventh. We shall denominate the four-fold chords on
the first and fourth of the major scale as major; on the fifth as 1100.-
inant; on the second, third and sisth as minor; on the seventh as ci-
minished. Transpose these chords into all the major keys.
FOUR-FOLD CHORDS ON THIE MINOR SCALE.

· Dominant. Major. Diminished.
Minor.
· Major. Minor. Major.
In order to distinguish the different kinds o, sevenths, we shall here.
after use large capital letters, thus : C7, 1%, 0%, with a mark throug!!,
the figure, for major four-fold chords. For minor four-fold chords we
F
THEORY AND RUDIMENTAL HARMONY
:
TI
H
will use sınall letters with the plain figure 7:07, e7, a 7. Dominaril
sevenths will be written with large letters, thus: G7, C7, C7, D7,
A7, Eb7. Diminished four-fold chords will be written with small let-
ters, a figure seven, and a cypher, thus: 07, ob 7, 0d 7, 0e7, og#7,.
&c. As we have before stated, the student must transpose all the above
chords into other keys, for practice, if he would be materially benefitted
It is also an excellent practice to accustom the ear to different harmonies
by getting a second person to strike them on the piano while you stand
with your back to the instrument and name them. Too much attention
to this subject cannot be given, for it quickens the ear, and helps culti-
vate all the musical faculties.
CHANGES OF POSITION.
In all the exhibition of the chords so far, the fundamental tone has
appeared only in its original position, as the lowest tone, with the thiral
next above, fifth above that, and lastly, the seventh. All the above
chords are capable of several transformations without altering the mate-
rial character of the chord; one becomes a variation of the other: for in-
stance, the chord ce g buyhmes e g. c or gce; the letters all remain tho
same, but their position is changed. This changing the position of the
letters, necessitates a change of the intervals, so that different intervals
and harmonics are constantly multiplying; in fact, there is no real enil
to the variety of harmonies which can be constructed. This change is
called inversion.
INVERSION OF THREE-FOLD CHORDS.
We have seen that three-fold chords form in themselves thirds and
fifths ; but by inversion other intervals are produced. Now to produce
an inversion, it is necessary to change the fundamental Note, otherwise
the chord is not inverted. If the third or fifish is changed and the
fundamental note remains in position, there is no inversion, but simply
a displacement of the third and fifth into a closer or dispersed position.
. THEORY AND RUDIMENTAL Ut
TT
HARMONY.. 75
It has already been observed that the letters of a chord cannot be
changer ;' they can only be placed higher or lower on the staff, as cir-
cumstances may require. Thus, c eg
-
.
is a three-fold chord in its fundameniil position, though in the second
example the third is carried up an octave. To produce an in version of
this chorl, the cor fundamentul note must be carried into the position
of the third or fifth. We will now give a few examples of inverted
cords:
INVERSIONS OF ALL THE FUNDAMENTAL THREE-YOLD CHORDS IX THE LAJOK
fund. ist inver. 2inver..
00C
-(1 .-ig
SCALE OF C.

Mlol.
mujor. major.
minor.
ninor. minor. Minor.
11:nor.
11or.
-
people .
---
ma. inal). maj. maj. maj. maj. min. min. min. din din. dim.
INVERSION OF THE THREE-FOLD CHORDS OF THE A MINOR SCALE..
-
DA
7-21-39--B8-FH-
-.9-ergore
.-
Bo-
many. -F7
-G#
IBM
0
Co-
min.
min..
inin..
dim.
dins
..
aug.
aug.

os-
U21-
L
.
-
-
inin. min. inin. maj. maj. maj. maj. maj. maj. dim.
dini. dim.
76
HARMONY.
:
TII
THEORY AND RUDIMENTAL It will be observed that the previous chords are all in the close posi-
tion. We earnestly recommend the student to transpose them into
other keys, and also to write them in both the close and dispersed po. :
sitions.
The fundamental three-fold chord in its first position is called the
third-fifth chord; in its first inversion it is called the chord of the sixth;
in its second inversion it is called the sixth-fourth chord, because it
produces these intervals with the bass note.
INVERSION OF THE FOUR-FOLD HARMONIES OF THE MAJOR

Ex. 6.
- -
major.
maj.
minor.
min.
min.

-
-
)
min.
· unin.
imin,
Waj.
maj.
muj.

NON
dom. don. dom. dom. min. min. min. min. dim. dim. dim. dim. ::
There are three inversions of the four-fold chords, (sevenths.) Each
inversión produces different intervals. The fundamental position is
called a chord of the seventh. 7. The first inversion produces the
chord of the fifth-sixth : 3 The second inversion gives the chord of
the six-four-three, or 4; the third inversion, the chord of the six-four-
two, or .
In the appropriate place we shall give the signs and figures ni ebasary
for a thorough understanding of all the chords of the seventh.
THEORY AND RUDIMENTAL HARMONY,
MINOR FOUR-FOLD CHORDS ON BASS NOTES OF THE SCALE.

66 00
min.
maj.
min.
dom.
dim.
1107
IIIM
IVY
TS
MINOR FOUR-FOLD CHORDS ON TREBLE NOTES or THE SCALE.

-
maj.
min.
dom.
dim.
VITORY
INVERTED CHORDS OF THE SEVENTH IN Å MINOR.
bhag 2 h

i
C
.
*The inversions of the chord on tonic minor are impracticable.
THEORY AND RUDIMENTAL HARMONY.
.
THREE-FOLD CHORDS OF THE MINOR SCALS AND THEIR INVERSIONS.
Practical lessons for writing, embracing examples in all the different barmonies or
combinations used, will be found at the end of this book.
a
@ t-on

A minor.
Is
version.
oot
een
IV
V
P
1
I
IV
V

Second inversion.
IV.
'V
1

=
+
-
-
000! 1
E minor.
lycrsion.
-
-
-
th-
-
--
.
JU
la
0
!
2d inversion.
x
THEORY AND RUDIMENTAL T了
​79
HARMONY.

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D minor.
1st inversion,
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21 layersion.
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TIEORY AXD RODDESTAL ILIRMONT.
į UT i
This is
G minor.
Istinversion.
E
stado
-
de mere
bmw
TAI
MON
-
condole
NOO
Second inversion.
$
---
.
Ht
L
helemaal
vas
EXAMPLES OF INVERTED THREE-FOLD CHORDS CONTINUED, IN CLOSE ANI)
DISPERSED POSITIONS.
Ix. 7.
C major.
A ininor.

hendrerit
Thirl, or
Ist in velsion).
fundamental.
tiitli, or
21 inversion,
-
-
late-fororo
-
-
-
Here we have in Example 7, the funilamental position, nainely, one,
three, and five. In the second measure will be found the first invers
siun, consisting of the third, fifth and octave position of the fundamen-
tal tone, the bass being carried up an octave. In the third measure
occurs the second inversion ; the fifth of the original chord becomes
the fundainental or bass, the original third becomes a sixth, and the
THEORY AND RUDIMENTAL HARMONY.
81
original fundamental or bass becomes a fourth of the new chord. In
this inversion of the three-folil chord we have produced two new inter-
vals without using different letters; they are a fourth in the first in-
version, and four-six in the second inversion. .

NON
E minor.
I!!
INO
11
A

FZ-or
try
D minor.
-6-fm-or-o
-

B minor,
or
THEORY AND RUDIMENTAL -HARMONY.

i
000
no
Bb major.
G minor.
-
-
-

A major.
minor.
two-
.
un
-
a
We will now give a few practical examples of the moveinent of the
three-fold chords and their inversions.
Ex. 8.

IT:
Istinyersion.
:
am-
H-
THO
an
V.
IV
.
V
.
. I
I
IV
THEORY AND RUDIMENTAL HARMONY.
83

TTOO
INOD
20 inversion,
TO>
STIAH
I
IV
V
In the above, the bass moves up to the fourth, the fift), the octare,
and back to the fundamental tone again; this makes what is called a
cadence, or a satisfactory close. The inversions are treated in just the
same manner as the fundamental chord... The minor three-fol. chorit
takes the same course as the major. ..
1
Tony
Q00

'
Vi
-
-
-
-
- ...
-
.
.

A
INOO
Vio
18
THEORY AND RUDIMENTAL HARMONY.

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THEORY AND RUDIMENTAL HARMONY,
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INVERSION OF THE PRINCIPAL FUNDAMENTAL CHORDS REVIEWE]).
The chord stands thus : c, e, g: o is the funda- }
mental note, e is the fundamental third, and g is the
fundamental fifth.
E, is a major third from the root, g, is a major fifth from the root,
and a minor third above the major third. In the first inversion of the
chord, the fundamental third becomes the temporary root, and the fun-
damental fifth becomes the temporary third : the fundamental root be..
comes a sixth to the temporary root.
First inversion.
:
Second inversion.
-ca
-G-
G
-2
ES
In the second inversion the original fifth becomes the temporary
root: the original third becomes the sixth to the temporary root, and
the original root becomes a fourth to the temporary root.
86
THEORY AND RUDIMENTAL ILARMONY.
1st.
30.
1st position.
21 position.
3dl position.
This is stated as plainly as it can very well be, and we will now take
up the other chords of the scale in succession.
All chords of the seventh are dissonant, and require preparation and
resolution, except the dominant, which resolves directly to its tonic.
The three-fold harmonies are consonant, as a general thing, and require
no preparation. Consonant intervals may be doubled, but dissonant
intervals are very rarely doubled, though there are exceptions to all
rules.
Major sevenths are very dissonant, but are often employed to good
- advantage by the ingenious composer.
SEQUENCE OF SEVENTHS.
The bass moves up a fourth or clown a fifth. This exercise can be
carried through the scale, and also inust be transposed into other keys
for practice.

.
C7
F7
ob
ez
THEORY AND RUDIMENTAL HARMONY.

1
Nil

0
ON-

-
--
--
-
Dominant sevenths are the most important, and we give thein with
the rule which governs their inovenient.,
RULE. In dominant sevenths, the root moves up a fourth, or down a
fifth ; but when in one of the upper parts, it remains unchanged. The
third moves up one degree. The fifth generally down one degree, but
88
THEORY AND RUDIMENTAL IIARMONY.
sometimes up one degree. The seventh always down one degree. .
Dominant sevenths on the minor scale observe the same rule. Bei
sure to transpose into other keys for practice.
Dominant serenthis.

TO
---
JAS
..
.
-
Oil
To como
-
و مرمت
Minor to major.
tato
-or-6
-
.
tty
MINOR FOUR-FOLD CHORDS. (SEVENTHS.)
Minor sevenths on the second degree of the scale. RULE.-They
more to dominant sevenths and like them are resolved.

DO
Pigeo
.
THEORY AND RUDIMENTAL HARMONY.
و
.
Minor sevenths on the third degree of the scale.

1
.
اتنا
عد
N
/
09
/
N A W/

2-5-
-----------
:
Minor sevenths on the sixth degree of the scale.

-
-
SNO

--
-----
-
, ان
:
THEORY AND RUDIMENTAL IIARMONY.
90
Diminished sevenths.


-
CHAPTER VI.
TONES FOREIGN TO THE HARMONY,
V
The harmonic combinations which have been thus far explained as:
fundamental harmonies always consist of the same tones, but there
are other tones which frequently occur in music not found or explained
in any of the fundamental harinonies; such tones not belongingstrict-
ly to the fundamental harmonies are called foreign to the harmony.
Tri relation to the above, we will remark“tliat an additional tone may.
he added withont changing any notes of the liarmonies already ex-
plained. This is the case with the dominant sevenths and aninor?
sevenths wheñ å inajor or a minor third is added above the serenthi
This härmony appears as a major or minor ninth, gb difa.
THEORY AND RUDIMENTAL HARMONY:
91
Major ninth.
Minor ninth.

LA
Prova .
These.chords are called chords of the seventh. - ninth, because the
upper note is situated a ninth; from the bass not?), (i ninc degrees from
it. Inversions of this chord with the fundamental note left out.

it
I
+-
-
-+-
-
-RT-
-
-
t-o
domi
nicaine
.
Minor ninths.
Fig. 1.

-
PO
:
*
1
2
:1
When and where the ninth is to be applied, is not in our province
to explain; we only have to do witli tlie naming and progression of it.
( treatment..)
... Fig. 2.

.
•
THEORY AND RUDIMENTAL HARMONY.
Fig. 3.

Fig. 4.
The major ninth sounds more agreeable when it lies higher than the
original third: if it lies below the third, the effect is disagreeable, and
on this account, composers, as far as possible, avoid such positions.
Fig. 6.
Fig. 6.

The major ninth usually sounds still more smoothly when it lies
higher than the fundamental fifth. As there are other chords of the
ninth to be explained hereafter, it becomes necessary to give the
ninths above treated, particular names, and we shall therefore call :
them independent ninths. Major independent ninths iỳ some of the
harsher or more disagreeable positions cited for examples.
1
.
000
THEORY AND RUDIMENTAL HARMONY.
THEORY AND RUDIMENTAI. HARMONY.
93
Fig. 8. Disperscd and close position.

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​THEORY AND RUDIMENTAL HARMONY.
Fig. 11. Prepared screuths.
- I

TO
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TIL
11111
UL
H-
L
ti
MODI'LATION BY THE FOU'R-FOLD DOMINANT HARMONY.
Ex 1.

11111
gol
: Tele
C:I 'V IG VI IC:
Ex. 2. Modulation when the dominant is not the leading chord.

.
-
.
.
.
C
Ilus -
G:V
C: V
I

1
.
Id
El
FT I
.
C: VI I.
1 VT É
THEORY AND. RUDIMENTAI IIARMONY,

Ex. 3.
V
I
VI
VII
LITT
Minol.
Lil
A iv
017 I 17 I
A four-fold chord with the fundamental tone omitted and a ninth
substituted therefor, makes it very diflicult to distinguish. The caser
most easily distinguished are those of the first inversion, or, where the
chords stand in thirds, one above another. Fig. 3.
The appearance of the ninth with the root left oạt, is like the screnth,
and becomes very difficult for the unlearned to distinguish; but we
hope farther on to make it plain, even to the novice. plinor indepen-
dent ninths, are often called chords of the diminished seventh, because
the bass tone, (the root heing left off,) forins a diminished seventh
with the upper tone; as, b, d, f; B, d, f, aly, &c.

- 07
Bb7
D7
Ab7
A7
F
Eb7
E7
THEORY AND RUDIMENTAL HARMONY.
These chords are all arranged at the distance of a minor third from
Cach other: distance between each note is a minor third. C#, e, g, hk,
22; d, f, ak, ck: f#, a, c, e2: c, eh, gk, hbb: ał, C, e, g: g, hk, dk, f5.
It will be seen that this four-fold chord introduces tones foreign to the
harmony, and may with propriety be called a chromatic harmony.
The intervals which the ninth forms with other elements of the har-
mony.
What intervals the ninth forms with other elements of the harmony
where they lie hişlier than the ninth. Major ninth, minor seventh,
major fifth, major third and major second. Minor nint?1, diminished ser-
enth, minor fifth, minor third and minor second. If we go into an exam-
ination of the different positions and inversions of the chords under con-
sideration, we shall find in the first inversion of a four-fold chord with
the ninth, the original major third becomes the bass tone; the major
fiſth becomes a small third: the seventh becomes its minor fifth, and
its major ninth becomes-its diminished seventh, and the fundamental
tone itself becomes a minor sixth, or:
A E BAS
mal eis
To
In the second inversion, the original major fifth becomes the hass
tone: the seventh becomes a minor third : the minor ninth becomes -
either a major or minor fifth: the major third becomes a major sixth,
the fundamental tonc itself becomes a minor fourth.

In the third inversion of the four-fold chord with ninth, the seventh
becomes the hass tone: the third becomes the major fourth: the fourth
becomes the major sixth : the major or minor ninth becomes a major
or minor third: the root appears as a major second..
THEORY AND RUDINENTAL HARMONY.
97
N

Finally in the fourth inversion, or when the ninth becomes the bass
tone, the third becomes a major second: the fifth becomes a minor or
mejor fourth: the seventh becomes a major or minor sixth: and the
fundamental tone becomes a major or minor seventh.
_R_ I
s
.
As a useful exercise, the student had better write out all the inver-
sions of these chords, and gire a definite account to himself of every
diote. The major fjur-fold chord of C with ninth, becomes o, e, g, h2,
d: first inversion, e, f, bb, d, c: second inversion, &, bb, d, c, e: third
inyersion, bb, d, c, e, g: fourth inversion, d, c, e, g, bb, or,
11
VN
In like manner other ninthe can be tåken up and gone through withi.
The reason why we call the above ninths independent, is because
they are not confined to the condition of transient notes or suspension,
but are entirely independent of such notes
TRANSITION
One method of introducing tones into a harmony which are entirely
foreign to it is that which is denominated transition:
Transition depends on circumstances: a voice, before giving a par-
wext higher or lower note, thns passing over to its proper harmonie
THEORY AND RUDIMENTAL ILARMONY.
tone: the previous struck norc is called the transition tone, because it
. is struck in advance of the principal tone, the tone to which it Icads. :
This species of transition produces a rich source of new combinations
of which it is not in the province of this book to treat in a definite
manner. There are mariy ways in which tones foreign to the funda-
mental harmonies may be introduced, and which must be learned
through a course of practical writing under a competent teacher,
CONSONANT AND DISSONANT CHORDS,
Teachers of music visually divide all harinonies into consonant and disa'
sonant, or pleasing and displeasing. Consonant tones are those whicha,
constitute the three-fold harmonies, first, third and fifth : and every
other tone or combination, is called dissonant. Thus: the fundamental
tone, its third and fifth, are consonant; with the seventii, mintáig or any
other combination added, it is called dissonant. .
PREPARATION,
It has been ascertained that there are chords which are more or less
disagreeable, such as the major and miror sevenths, and the ninths:
" this harshiness can be done away with by what is termed preparation ;
by introclucing the discordant note into a previous chord, This prepar-
ing the note beforehand, is called the preparation of dissonance. The
tone itself, as it is heard in the chord of preparation, is called tone of
preparation. Most serent's require preparation. The major seventh is
verý císagreeable to the ear, but the minor sevenths are much less so,
though bcth require to be prepared.
The dominant sevenths do not require any preparation, but may re-
solve directly to a concord. Tones which are forcign to the fundamentul
harmonies must be prepared, like the ninth, when the fundamental tone
is heard with it.
Theorists have laid down the rule that cill dissonances must be pre-
pared, but the rule is often broken, as in the case of dominert seventiis,
and therefore the rule does not hold good in all cases.
THEORY AND RUDIMENTAL HARMONY.
99
W
EXAMPLES OF PREPARING THE SEVENTI.
Essential harmonies of the key are the tonic chord, or major three-
told chord, and the four-fold chord on the major fifth: this last harmony
is next after the tonic barmony, and is called dominant harmony, and
the fifth is the doninant. The next harmony nearly related to this key,
is the three-fold chord on the minor fourth of the tonic,-- a three-loll
chord that is major when the tonic harmony is major, and minor when y
the tonio harmony is minor. It is callcu sub-dominant chord, because it į
is the under fifth of the tonic. The three essential harmonies of C, are
cy.e, g: g, b, d: g, b, d, f, and f, a, c.
The four most essential harmonies of every key are the major and
minor three-fold chord: the three and four-fold harmony on the fifth
or dominant, and the three-fold chord on the sub-dominant. These ar :
the leads of the family; they determine its character, they impress the
key on the ear, and are called the niost essential harmonies of the key.
Whole pieces are often constructed on the above barmonies, and even
on the topic and dominant. There are other harmonies nearly rclatei,
which will appear more plain to the student as he progresses in his st.1::-
ies. The harmonies of each key have already been given, but we will
once more enumerate them.
MAJOR SCALE.
9:333-2185

C C7, d, dt, a ei, F, 17, 4, 6*7, u7, ob, Ol?
:: ixon SCALE.

porno-
0000
- nothing
" 3.1.
-
6
il, 17, Oh; Ob7,
d, d7,
E, E7, F, F7, og#
Define
100
THEORY AND RUDIMENTAL HARMONY.
Mode of representing the different harmonies. For major harmonies
we will use large capital letters thus:-G, B, 1), F: for minor harmonies,
small letters will be used thus: a, d, e, and for diminished harmonies a
small cypher will be placed before the letter thus; Oa, od. For four-
fold chord a figure 7 will be used after the letter, thus: d7, D7, &c.
The following figures will be used underneath the chords; I, IV, V, or
large figures for major chords and small figures (11, III, VIO , V117) for
minor and diminished. Tables showing all the appropriate harmonies of
major and minor keys should be constructed on all the different degrees
of the scale, like the following example. C, CH, C or B, B5, A, A5, GH,
G, G5, F1, F, F5, E, E5, D, D5, C#, &c. Each harmony is capable of
having more than one key, and may be represented by a large letter
at one time, and by a small letter at another. On the first degree, on.
ly a major three-fold and major four-fold chord can occur -- thus : I or
17. The harmony of the second degree is always a minor three-fold
and a minor four-fold chord, thus, II, 117.
The harmony of the third degree is minor, thus: III Or 1117.
The harmony of the fourth degree is major ; IV or 117.
The harmony of the fifth degree is major; V or V7.
The harmony of the sixth degree is minor; VI or V17.
The harmony of the seventh degree is diminished; Ovit or Ov117.
The harmony in minor keys on the first degree of the scale is always i.
On the second degree is Oil'or 0117. On the fourth degree IV or 1v7. ,
On the fifth degree V or 17. On the sixth degree VI or V17.
Ou the seventh degree OvII. It will be seen that major three-fold
chords occur on the first, fourth and fifth of major keys, and third, :
fourth or fifth and sixth of minor keys. Minor three-fold chords occur
won the second, third and sixth of major scales, and on the first and fourth ·
of minor key8. Diminished three-fold chords occur on the seventh in
major, and second and seventh in aninor keys. Dominant sevenths
occur only on the fifth of the scale. Minor sevenths occur on the sec-
ond, third and sixth degrees, and iliminished on the serienth ; major
sevenths are found on the first and fourth of major, and fourth of
minor, &
THEORY AND RUDIMENTAL HARMONY.
101
The major or minor keys which are the nearest related, are those
which are most like each other, and are the dominant and sub-dominant
of each key. The relationship of keys must be left here, as we do not
wish to make this a complete book of harmony, and will close this part
of our subject with a table of near related keys.
TABLE OF THE RELATIONSHIPS. OF KEYS.
C - a - A - F# -- F# -- d# — D# 6# B# - g
Em
G# - e* - E#
:-
-
- C# - a# - A#
- F# -
d# -
D#
nomu o-o-o-
1
- Fd
- 5 -
6 -
B
-
---
c# -
C#
-
El-C-
0
-
a -- A -- F# -
- di
- Ab- f - F
-
d - D
- b -
B
– 5#
-
F1-dź
$ - -*-nom u goro
Bbok -
:-
(
-* - E
Ebbe
-- ab - Az
Abbe- fb
db -- Db
Bb
D2b-322 Bhage.
102
THEORY AND RUDIMENTAL HARMONY.
It might be useful, as an exercise, to go through the preceding table
carefully and propose questions somewhat as follows: What keys are
inost nearly related to C-major? What to c-minor? What to f-minor?.
&C.-What keys are thus related in the second degree?-What in the
third degree?—Which of these relationships are the more or the less
intimate?-In which degree are Fand E related to each other? What
is the relationship between c and a ?-&c.
TEMPERAMENT.
To tune an instrument with entire purity and exactness, with the
tone g as the perfectly pure fifth, that is, so that the velocity of the vi-
brations of the tone g would be to those of the toue c as 3 to 2, g accoin-
plishing three vibrations in the time o accomplishes two—and d as a
pure fifth or under fourth and so on through a, e, b, f#,c#, and g#.
The result of this pure tuning would necessitate a great number of
keys, and for this reason, another and more practical method has been
adopted. The difference between d# and ek must be equally divided,
has been
tuning is called equal temperament. No two instruments can be tuned
absolutely alike, because the timber or quality of tone does not corres- ,
pond. A stringed instrument produces a different quality of tone from
a wind instrument, and so we might go through all the various instru-
CHAPTER VII.
MODULATION.
Modulation is the changing of harmonies in or out of a key. That
modulation in which a piece remains in one key, is called morlulation
in the key. That modulation which, after the ear becomes attuned to
one key is changed into another, is called modulating out of the key,
or digressive modulation. Digressive modulation then, is the changing
of attunement from one key to another.
THEORY AND RUDIMENTAL HARMONY.
103
DONNE
a E a G . C
A modulation which wholly erases the impression of the previous
key is called perfect modulation; but when such impression is not en-
tirely eradicated from the ear, it is called imperfect modulation.

ht
tal
TOTO
TOT
Tulo
HO
- NHI
@
The dominant four-fold harmony of the new key is the usual means
by which a modulation is generally effected, and is therefore called the
leading harmony; but modulation can be effected by other means, as
we shall prove by and by
Modulations may be made from any major. key to the eleven other
major keys; from a major key to any of the twelve minor keys; from
any minor key to the eleven other minor keys, and from any minor key
to any of the twelve major keys, making in all forty-six modulations.
How and by what means are we to determine whether a piece is in
this or that key? The principles relating to this subject are quite
simple, as the ear explains to itself every combination of tones in the
most simple, most natural and most obvious manner. Generally
speaking, the attunement of the ear to any particulat key, arises from
the introduction of harmonies which are peculiar to that key. Thus,
the tonic, dominant and sub-dominant harmonies are peculiar to every
104
THEORY AND RUDIMENTAL HARMONY.
kes, and a piece of music usually begins with the tonic harmony, thought
there are instances where a piece of music begins with other than tonio
chords. The ear once attuned to a particular key does not change its
state of attunement into that of another key without a sufficient cause'.
The means by which modulations are made are so numerous, and so
diversified, that we shall not enter into detailed statements, but shall
leave the subject in the hands of the teacher of practical harmony, to
explain to his pupils, how and in what way modulations are best effected.'
There are many forbidden progressions, many rules laid down for iliis
and that chord to be doubled and not to be doubled, together with a
thousand and one rules given for naming and omitting chords, which
are only given to be broken, that we deem it inexpedient to argue alt
length any of these disputed points. For this reason, we have left the
entire matter of arbitrary rules to the judgment of the teacher, 10
teach according to his educational standpoint, and according to the
necessities of the occasion. Hoping our labors have not been in raill,
we wish our students Godspeed.
PRACTICAL EXAMPLES IN WRITING HARMONY
CORRECTLY.
PROGRESSION.
Two consecutive Fifths or Octaves must not follow each other, als
they sound unpleasantly on the ear, and make what is termed fatse
progression.
A few examples.
Used.

t
.
Bad...
Bad.
THEORY AND RUDIMENTAL HARMONY,
105
Octaves arıl Fifths.

WOW
LY
First position. Good.

O.-
CI G V
Second position.

Third position.
11:10 UN

.
106
V21
THEORY AND RUDIMENTAL 2
ILARMONY.
First.
-
Second.
IV
CI · G V
CI
Third.

HI
doo
NU
ODI
TRIADS IN THREE POSITIONS ON THE PRINCIPAL HARMONIES OF THE SCALE.
These examples show how chords can move without making connec-
utive Fifths and Octaves.

.
.
Tot
-
-
.
CI G V F IVCI G V CI CI F IV G VCI F IV 0 I
THEORY AND RUDIMENTAL IIARMONY.
107

..
一十​……
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The above exercises must be transposed into all the other major keys.
Sequence.
一寸
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THEORY AND RUDIMENTAL HARMONY.

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二十一
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All the exercises given above must be transposed into all major keys
in order to familiarize the student with the triads.
EXERCISES TO BE WRITTEN.
No. 1.
当
​上一十一
​II.
V
III
VI
III
I
如图
​34
-
-
THEORY AND RUDIMENTAL ĦARMONY.
109
No. 4.
to
11.
No.5
A minor. The seventh of the minot scale must be sharped.

wir
000-
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o-2o1o2273-8g
3gp
ota
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la
1
.
1
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A sharp or flat over the bass note indicates that the third in the har-
mony must be sharped or flatted. .
Minor exercises.
No.1.
No. 2.
#
#1
TALA
--
-
سنعه تباينتننتالنتن سنش بنسای
ن.
متناننا تحت سلن
No. 3.

#
5#
fairipofani
tatem
test
.
EI
L
istential
* Indicates the fifth is sharpcd.
No. 5. *
D minor. 5

NH
fo
--
-
S
denne
de
* A the highest note in harinony.
110
THEORY AND RUDIMENTAL HARMONY.
:.
No. 6.
No.7.
E minor

#
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--
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No. 8.
No..
5#6
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No. 10.
C minor.
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EXERCISES INTRODUCING THE CHORD OF THE SIXTH.

M
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6
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THEORY AND RUDIMENTAL HARMONY. .
111
منم بدن هست م
منه
مسامسه ساسی مانسنسنا استسننداس
3
4
6
6
3
4
6
3
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اس
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.
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به دسسسسستیل
.د
ا نششش
انتشتعلتتسلتنانتنت س نتان پساینسميسماس مبانیستنسن
تنیس
3
في
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ننوتنتکس
مستند
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به
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9
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تستنشن لیننننن
14
HARMONY.
112
THEORY AND THEORY RUDIMENTAL HARMON
AND RUDIMENTAL 
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CHORD OF THE. SIXTË AND FOURTH:

sappia,
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THEORY AND RUDIMENTAL HARMONY.
113
113
OHORDS OF THE SEVENTH.
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114
THEORY AND RUDIMENTAL HARMONY.
114
INVERSION OF SEVENTHS WITH FIGURES.
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THEORY AND RUDIMENTAL HARMONY..
115.

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116
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116
THEORY THEORY AND HARMONY
AND RUDIMENTAL: RUDIMENTAL HARMONY8.
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THEORY AND RUDIMENTAL HARMONY.
117
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THEORY AND RUDIMENTAL HARMONY.

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· THEORY AND RUDIMENTAL HARMONY.
119
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120
.THEORY AND RUDIMENTAL HARMONY.
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THEORY AND RUDIMENTAL HARMONY:
121

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122
THEORY AND RUDIMENTAL HARMONY


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· If the student has been diligent and faithful in writing all the exam-
ples given in this book, he will have no trouble in writing from any
figured bass, or understanding any chords used in musical composition.
OVER 500,000 ALREADY SOLD.-
WHITE'S SCHOOL FOR THE REED ORGAN
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18 COMPLETE SETS OF WALTZES.
It is almost incredible that such a GRAND COLLECTION OF BEAUTIFUL WALTŻES
can be given to the public for $1.00. All the Latest and Best. are found in this
book, and the selections are of such a pleasing character that they will entertain the
player and also the dancer. .
PRICE. POST-PAID. - - $1.00.
WHITE, SMITH & CO.'S
** Amateur', Orchestra
A new collection of popular and brilliant dance music for an orchestra of seven
pieces, including piano. Each piece can be played effectively by any combination of the
instruments. For PARLOR, CONCERT or BALL-Room,
IT IS UNRIVALLED.
INSTRUMENTS: 1st and 2d Violins, Clarinet, Cornet, Flute, Bass, Piano. Each
part Bound in Paper Govers.
PRICES BY MAIL, POST-PAID:
COMPLETE
$7.00
SIX PARTS (Orchestral), . $6.00 VIOLIN and PIANO - - 3.00
FIVE PARTS,
5.00 PIANO PART.
- 2.00
VIOLIN, CORNET and PIANO, 4,00 SINGLE PARTS (Orchestral), 1.25
Full list of Orchestra and Brass Band Music sent free on application.
Winner's New American Schools for Different Instruments
Comprise the rudiments of music, scales and exercises for instruction.
They are, in every respect,
SELF-INSTRUCTORS.
CORNET, FLUTE, PICCOLO, CLARINET, FIFE, FLAGEOLET,
CABINET ORGAN, ACCORDION, CONCERTINA, GUITAR, BANJO.
Price, post paid, - - - - 50 cents each.
VIOLIN,
PIANO,
Winner's New American Selections for the Violin.
141 selections, arranged in a simple manner for ordinary players. A mint of melody
PRICE, POST-PAID, - - .50 CENTS.
VIVIMB
INIBIISIIKIDINIONI DILINDILNIKIO
.
Music. TEACHERS-ATTENTION !
STUDENTS' * MODERN * METHOD
FOR THE PIANOFORTE,
Compiled by JAMES M. TRACY, is, the combined result of many years of study
and experience as a teacher and player. This instructor is destined to become a
UNIVERSAL PIANO METHOD
in this country for the following reasons:- It is
THOROUGH,
. INTERESTING,
SIMPLE,
PRACTICAL,
PROGRESSIVE,
INSTRUCTIVE.
Published with both American and Foreign fingering. Price, $2,50.

11
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11
UNIVERSITY OF MICHIGAN
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