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LIBRARY

UNIVERSITY OF CALIFORNIA
RIVERSIDE



(O

Lessons in Harmony



COMPLETE



PARTS I AND II BY

C.



Professor of Theory in Oberlin Conservatory

of Music, Author of "Choral Studies"

and "Ear Training"



PARTS III, IV AND V BY

31. JUljmann



Instructor of Theory in Oberlin Conservatory

of Music, Author of "Exercises in

Harmonization at the Piano"

and "Treatise on Simple

Counterpoint" .

Copyright, 1906, by A. G. COMINGS & SON, Oberlin, O.






<' I



PREFACE.

The object of this book is to furnish a suitable text for
the study of harmony, with illustrative examples, and a
definite assignment of lessons.

It was neither the intention nor desire of the authors
that it should represent a work covering the entire ground
cf harmonic structure. But their aim throughout has been
to use only such material as is necessary to give the student
a clear and intelligent knowledge of modern harmonic prac-
tices, and to enable him to continue the work by original
research in the works of the masters. Emphasis is laid
upon the value of being able to play readily, in any key, a
large number of cadence formulae, and also the different
modulations in parts three and four. For this reason the
work is only partially prepared if the work at the piano is
omitted.

Since parts I and II are also issued separately it has been
necessary to duplicate the page and illustration numbering
in these. A reference to anything in part I will always be
accompanied by the words "Part I", when in any other
part, the page or illustration number, only, will be given.

Parts I and II were prepared by Arthur E. Heacox, and
Parts III, IV and V by Friedrich J. Lehmann.

Oberlin, Ohio, June 15, 1907.



TABLE OF CONTENTS.
Part I.



I. Major Scales.

II. Original form of the Minor scale.
III. Harmonic form of the Minor scale.
TV. Intervals.
V. Intervals.
VI. Intervals.
VII. Triads in Major keys.
VIII. Triads in Minor keys.
IX. Triads in both Major and Minor.
X. Connection of the Primary triads in Major keys

with a given bass.
XI. Connection of the Primary triads in Major keys

with a given soprano.

XII. Connection of the Primary triads in Major keys
(con).

XIII. Primary triads in Exercises in Minor keys.

XIV. Chord of the Sixth.
XV. The Six-Four chord.

XVI. Secondary triads in Major in fundamental

position.
XVII. Secondary triads in Minor in fundamental

position.

XVIII. Inversions of the Secondary triads.
XIX. Special progressions.
XX. The Sequence and Review exercises.



TABLE OF CONTENTS.
Part II.



IV.
V.

VI.
VII.



IX.

X.
XI.



XII.



XIII.

XIV.

XV.

XVI.

XVII.

XVIII.

XIX.

XX.

XXI.



The Chord of the Dominant Seventh.
Inversions of the Dominant Seventh.
Fundamental Position of the Dominant

Seventh in Exercises.

Inversions of the Dominant Seventh in Ex-
ercises.

Inversions of the Dominant Seventh in Ex-
ercises in Minor

The Triad on the Leading Tone.

Modulation to the nearly-related Keys.

Continuation of VII.

Modulation through the Use of the Dominant
Seventh Chord.

Continuation of IX, Scale Harmonized.

The Secondary Seventh Chords in the Major
Key. The Chord of the Seventh on the
Super tonic.

Continuation of XI. Preparation of the
Seventh. Introduction of the Dominant
Seventh.

The Chord of the Seventh on the Supertonic
in the Minor Keys.

Cadences.

The Half Cadence and Deceptive Cadence.

Review Lesson from Bach's Figured Chorals.

Uhe Chord of the Dominant Ninth.

Application of the Dominant Ninth in Ex-
ercises.

The Chord of the Seventh on the Leading
Tone in the Major.

The Chord of the Diminished Seventh.

The Chords of the Seventh on the remaining
degrees of the Scale in both the Major and
Minor Keys. The -Passing Seventh.



TABLE OF CONTENTS.

XXII. Regarding Greater Freedom in the Treatment
of the* Seventh. Original Work.

XXIII. Jfeview Exercises. Original Work.

XXIV. figured Choral from J. S. Bach.

Part III.

DIVISION I. MODULATION.
XXV. Modulating to the Dominant Key.
XXVI. Modulating to the Sub-dominant Key.
XXVII. Combining the above Modulations.
XXVIII. Modulating a Major Second upward
XXIX. Modulating a Major Second downward.
XXX. Combining the Modulations in Lessons 28

and 29.

XXXI. Modulating a Minor Third upward.
XXXII. Modulating a Minor Third downward.

XXXIII. Combining the Modulations in Lessons 31

and 32.

XXXIV. Modulating a Major Third upward.
XXXV. Modulating a Major Third downward.

XXXVI. Combining the Modulations in Lessons 34

and 35.
XXXVII. Review or Test.

DIVISION II. SECONDARY SEVENTH CHORDS,
XXXv'III. The Snpertonic Seventh Cord in Fundamen-
tal. Position

XXXIX. Inversions of the Supertonic Seventh Chord.
XL. The remaining Secondary Seventh Chords in

Major.

XLI. The same.
XLII. The same in Minor.
XLIII. The same in Major and Minor.
XLIV. Inversions of the remaining Secondary

Seventh Chords in Major.
XLV. The same in Minor.
XLVI. The same in Major and Minor.



TABLE OF CONTENTS.

Part IV.

DIVISION I. ALTERED CHORDS.
XLVII. Chord of the Augmented Sixth.
XLVII1. Chord of the Augmented Six-four-three.
XLIX. Chords of the Augmented Sixth and Aug-
mented Six-four-three, (con)
L. Chord of the Augmented Six-five.
LI. Chord of the Augmented Sixth, with Doubly

Augmented Fourth.
LII. Chords of the Augmented Sixth in other than

their conventional form.
LIII. Chord of the Neapolitan Sixth.
LIV. Chord of the Neapolitan Sixth, (con.)
LV. Review.
LVI. Test.

DIVISION II. MODULATION. (CON.)
LVII. Modulating a half step upward.
LVIII. Modulating a half step downward.
LIX. Modulating to a Key an Augmented Fourth

or Diminished Fifth distant.

LX. Modulating by enharmonic change of nota-
tion.

LXI. Modulating by the use of the Diminished
Seventh Chord on the raised fourth degree
of the New Key.
LXII. Modulating by the use of the Augmented

Six-five Chord of the New Key.
LXIII. Modulating by the use of the Neapolitan

Chord of the New Key.

LXIV. Modulating by the use of a Deceptive Reso-
lution of the Dominant Seventh of the Old
to the Dominant Seventh of the New Key.
LXV. Modulating by the use of a Deceptive Reso-
lution of Dominat Seventh of the Old, to
the Tonic Triad of the New Key.
LXVI. Test.



Part V.



LXVII. Suspensions in an upper voice.

LXV1H. Suspensions in a lower voice.

LXIX. Retardation.

LXX. Suspensions in more than one voice.

LXXI. Ornamental resolution of the Suspension.

LXXII. The Passing tone and the Embellishment.

LXXIII. The Passing tone and the Embellishment

(con).

LXXIV. The Appoggiatura and the Anticipation.

LXXV. The Appoggiatura and the Anticipation Cconj.

LXXVI. The Pedal Point.

LXX VI I. Figuration.

LXXVIII. Figurated Melodies.

LXXIX. Florid Figuration.

LXXX. Eeduction of Melodies.

LXXXI. The Florid Melody.

LXXXII. Accompaniments

LXXXII1. Additional work.



First Lessons in Harmony.



Lesson I.

DEFINITIONS.

A TONE is sojmd which has cbfmitejjjieli. -

A jiorjE^is a qharacter jised to' indicate a tone7~show
it3 relative length, and rtS~^jieh. by^designafTng a degree
of the staff..

A The STAFF is a collection of five parallel lines with
the spaces belonging to them. /"Each line or space is
called a degree.

A CLEF is a nha.rp.nt.ftr which causes the degree of the
staff with which it is associated to indicate a certain
absolute pitch. The treble, or G clef, causes the second
line of the staff to indicate the first G above Middle C.
The bass, or F clef, causes the fourth line to indicate
the first F below Middle C.

A KEY is a set or family of tones bearing a definite
and close relation to one principal tone called the key-note.

The KEY-NO_TE is that tone from which the other tones
of a key are determined and which makes the best point
of closing.

The SIGNATURE is thasignjpf the key, that is the sharps
or flats or the absence of them at the beginning or divi-
sion of a piece.

A HALF-STEP is the distance from any tone to the next
ajailabj.e_ tone either above or below. Half-steps are of
two kinds, Chromatic and Diatonic.



A CHROMATIC HALE-STEP is one whose pitches are in-
dicated by the same degree of the staff, e. g. c-c$, or c-cb

A DIATONIC HALF-STEP is one whose pitches are in-
dicated by adjacent degrees, e. g. c db, or c-b.

A WHOLE-STEP is the distance from any tone to the
next available tonejaut^ae. either above or below.

A SHARP (#) causes the degree of the staff on which
it is placed to indicate a pitch a half-step higher than
would be indicated by that degree without the sharp.

A FLAT (\>) causes the degree of the staff on which it-
is placed to indicate a pitch a half-step lower than would
be indicated by that degree without the flat.

A DOUBLE-SHARP ($6) indicates elevation one whole-step
reckoning from the unaltered degree, whether that degree
has been previously sharped or not. A DOUBLE-FLAT (bb i
indicates depression a whole step in the same manner.

A Natural (%) used on any degree of the staff destroys
the effect of all previous sharps or flats on that degree.

A Scale is an ascending or descending series of tones
progressing by degrees according to a specified order or
relation.

There are two classes of scales, Diatonic and Chromatic.

A Chromatic Scale is one which progresses always by
half-steps and contains thirteen tones within the octave.

A Diatonic Scale is one comprising eight tones within
the octave and progressing generally by steps and half-
steps, with its degrees named in alphabetical order.

There are two classes of diatonic scales, Major and
Minor.

A Major Scale is one whose third tone is two whole-
steps, a major third, from the first, and whose tones stand
in the following relation : 1 23^4567^8, the

sign v indicating a half-step and a whole-step. The

fifth degree of any diatonic scale is the key-note of the
following scale in sharps, and the fourth degree, the key-
note of the following scale in flats.












,






A^n






WRITTEN WORK.



Write all the major scales to seven sharps and flats in-
clusive. Build each scale without a signature by using
the necessary sharps and flats, and place the signature
after the scale as in the model. Indicate the half-steps
with a slur and use capital letters to indicate major keys.




G



The sharps and flats in the signature must always
appear in the same order, reading from left to right, and
care must be taken to allow plenty of room to make this
order clear.

SIGNATURES FOR C# AND Cb.




ORAI, SCALE

Be prepared to recite all the major scales as follows :
Give the scale of A. Answer: a, b, c#, d, e, f#, g#, a;
signature, three sharps, f, c and g.



Lesson II.

DEFINITIONS.

A Minor Scale is one whose third tone is a step and a
half, a minor third, from the first. There are three common



forms, the Original, Harmonic and *Melodic, the first two
of which are important for present study.

In the Original Form the tones are precisely the same
as in the relative major key and therefore stand in the
following order- 1 2^3 4-5^,6 7 8.

Relative Keys are those having the same signature.
The sixth degree of any major scale is the key-note of its
relative minor and the third degree of any minor scale is
the key-note of its relative major.

WRITTEN WORK.

Write all the minor scales, original form, to seven sharps
and flats inclusive, following the same general directions
as in the first lesson. Indicate minor keys with small
letters




ORAI, SCALE DRILL.

Review the scale drill of Lesson I. and recite the scales
of this lesson in the same manner.



Lesson III.

THE HARMONIC FORM OF THE MINOR SCALE.

The whole-step from seven to eight in the original form

of the minor scale was not found satisfactory for harmonic

writing. A remedy was found in chromatically raising

seven, which reduced the distance from seven to eight to a

* The Melodic Form is left to later study because it has no direct appli-
cation in the present lessons.



5

half-step as in the major scale. This alteration produced
a scale which has become the basis of practically all
modern harmony in the minor mode, and is called the
Harmonic Form. The step and a half from six to seven is
indicated by +. In writing this scale remember that
alphabetical order is necessary, thus g cannot be written
for />*; in the scale of g #. In keys of more than two flats
a natural serves the purpose of a sharp in the other keys.

WRITTEN WORK.

Write all the minor scales, harmonic form, to seven
sharps and flats inclusive. Indicate the position of all half-
steps and use + to locate the step and a half.




ORAL SCALE DRILL.

Recite each major scale and its relative minor scale in
the Original and Harmonic forms.



\t-L



Lesson IV.

RAPID RECITATION OF THE MAJOR SCALES.
Recite the major scales rapidly, giving as many as
possible in one minute. Model: g, a, b, c, d, e, f#, g;
signature one sharp, f . Carry out to seven sharps and seven
flats.

INTERVALS.

An INTERVAL is the relation which one tone sustains to
another with regard to pitch.






6

A PRIME is the relation between two tones whose pitches
are indicated by the same degree of the staff.

A SECOND is the relation between two tones whose
pitches are indicated by adjacent degrees of the staff.

A THIRD comprises two seconds ; a Fourth, three sec-
onds ; a Fifth, four seconds; a Sixth, five seconds: a
Seventh, six seconds ; and an Octave, seven seconds.

In the major scale reckoning from the key-note these
intervals appear as in the following model, P. indicating
perfect and Maj., major.




-&-



P. Prime. Maj.2. Maj.3 P. 4. P. 5. Maj.6. Maj.7. P.Oetaw

Write out in ewry major key, using no signatures but
placing sharps and flats where needed. Write the interval
names with every scale.

This model forms the basis of all rapid interval reading
and should be memorized. Note that the prime, fourth,
fifth and octave are perfect and the others, major. All
perfect and major intervals can be read by this simple
measurement in the major scale. Thus for example, a per-
fect fifth from F is C because C is five in the scale of F;
a major third from E is G# because G# is three in the scale
of E, etc.

INTERVAL READING.

Consider the lower note the keynote in the major scale
and begin : C to G is a perfect fifth, C to A, a major
sixth and so on. Write nothing in as an aid in reciting.

1.



m *-



i



P . ;



2.



&



3.






1



U .Q

t' car-



The intervals exceeding the octave are the Ninth, Tenth,
Eleventh and so on, but the Ninth is usually treated as a
second, a tenth, as a third, etc. Begin the following : C to
E is a major third.

.. 5. _ag_ u.



i



-& - &-



6 }?-<&-



-<s>- -&-



_a sy ^ G*



L



I



Name the upper tone but do not write it in.

. 7.



Maj.3. P. 4. Maj.S.Ma.7. Ma.7. Ma.7. Ma.7. P. 5. Ma. 2.
8.



Maj.3. 26722 636 6



9.



P. 485458445



i



Lesson V.

INTERVALS CONTINUED.

When any perfect or major interval is enlarged a chrom-
atic half-step it becomes augmented, thus the perfect
fourth, C-F becomes an augmented fourth if changed to
C-F# or Cb-F; and the major second, C-D becomes aug-
mented if changed to C-D$ pr Cb-D. In these alterations
no letter may be changed for another, for this would not
be chromatic enlargement.

Augmented Thirds and Sevenths do not occur in harmonic
relations but every other interval has its augmented form.
Read the following:
1.



-es $& f^BflPf'
^T*l*z- & & uT&



2.



>, b^ b-g &s>-

XS ffl J*^, ^r. H -



Aug. 264621 45 6 2

When any major interval is reduced in size a chromatic
half-step it becomes minor, thus the major third C-E
becomes a minor third if changed to C-Eb, or C#-E. Per-
fect intervals never become minor. Read :

3.



Min. 2



4.



11



Min. 62



33



When any perfect or minor interval is reduced in size a
chromatic half-step it becomes diminished.
,;. Diminished Primes, Seconds and Sixths do not occur m
harmonic relations. Read :

5.




Dim. 8,3547 743



WRITTEN WORK.

Write all the intervals that occur in harmonic relations,
using in turn E, F$ and Bb as the lower note in the same
manner that C is used in the following model :



^m






-&- -&- -&- ^

P. P. A. P.



' .&. ^& -&- Qf -&- fc*

Mi. 2. Ma. 2. A. 2.



g



- -&- -&- & O -&- -&- tS -&-

Ma. 3. Mi. 3 D. 3. D. 4. P. 4. A 4. D. 5. P. 5. A. 5.




Mi. 6. Ma. 6. A. 6. Ma.7. Mi.7. D. 7. D. 8. P. 8. A. 8.



10



1.



Lesson VI.

INTERVAL READING.



2.



tr






3.



:f



Aug. 462541 64262
-5



Dim. 3735343357



P. 4 A.6 Di.7Ma.3A.4 Mi. 2 Di.7 P. 5 A.6
7.

^Efty-^r - :-^ - krz E^HaTEE



Ma. 6 A.6 Ma. 7 Ma. 7 Ma. 6 Ma. 3 Di.7 P. 5 Mi. 7



11
Lesson VII.

CHORDS.

A CHORD is a combination of tones sounding together
and bearing a harmonic relation to each other. The
simplest chord is the Triad which consists of a fundamental
tone, called the root, with its third and fifth.

A MAJOR TRIAD has a major third and perfect fifth

A MINOR TRIAD has a minor third and perfect fifth.

A DIMINISHED TRIAD has a minor third and diminished
fifth.

A triad may be formed on each of the seven tones of the
diatonic scale thus :




The triads on one, four and five are major, marked I,
IV, V-; on two, three and six, minor, marked n, in, vi ;
and on seven, diminished, marked vn. These marks
indicate the degree of the scale on which the root of the
chord is found, and by their size denote the kind of triad.
Note the special sign for the diminished triad.

i A

WRITTEN WORK.

Write all the triads in the major keys to seven sharps
and flats, and write the numerals under each. Place the
sharps and flats in each chord where needed. Do not write
the signature.

Model.




IV






~S



12

_ dM**-

To LOCATE CHORDS.
There are three major triads in any major key, namely,
I, IV and V. To locate a major triad in all the major keys
in which it is found, it is necessary to place it in that key
which contains its root as one, then in the key where its
root is four, and last, where its root is five. Thus the triad
c e-g is on one in the key of C, on four in the key of G,
and on five in the key of F. Similarly a minor triad should
be located on two, three and six of three keys, and the
diminished triad on seven. The following table presents
three triads in all the major keys in which they are found.



Maj.



Min.



Dim.



BF




H


1 rr\ ij-^


r/5


~lfrF~~ ;!


1 SSz T?


rjff-.




J ,^

linC
IV in G
Vin F


II in B|j
in in Ab>
vi in Eb


v &>
-$-

vn in Db



Tell what tones make the following chords and give all
the major keys in which each is found.

1.



i



Maj. Min. Dim. Maj. Min. Dim. Maj. Min. Dim.
2.




~f~'



* Z* ^



Maj. Min. Dim. Maj. Maj. Min. Dim. Min. Maj.



Min. Dim. Maj. Dim. Maj. Min. Dim. Dim. Maj.







Maj. Mm. Dim. Dim. Dim. Maj. Min. Maj. Maj.



gy. T1">,~ ff^ P Ti

Dim. Dim. Maj. Min. Maj. Dim. Min. Dim. Maj.






Lesson

THE TRIADS IN THE MINOR KEYS.

The triads in the minor keys are formed of the tones
contained in the harmonic form of the scale. Those on
five and six .are major, on one and four, minor ; on two and
seven, diminished ; and on three, Augmented.

An AUGMENTED TRIAD has a major third and augmented
fifth, and is indicated by an accent added to a large
uumeral thus III',

WRITTEN WORK.

Write all the triads in all the minor keys to seven
sharps and flats as in the following model :




IV



V



VI



To LOCATE CHORDS IN THE MINOR KEYS.

Locate a major triad on V and VI, a minor triad on
i and iv, a diminished triad on 11 and vn, and an aug-
mented triad on IIP, of the harmonic minor scale. This
is done with the four triads on C in the following table.



14

Maj Min. Dim. Aug.

-% - z=^=: =5zfc =$fc



V in f. I in c. 11 in b(?
VI in e. iv in g. vil in dj,, III' in a.

Tell what tones make the following chords and give all
the minor keys in which each chord is found.



1.



Maj. Dim. Aug. Min. Dim. Aug. Maj. Min. Dim. Aug.
2.



=fl

__Jj



= =^=P=^ gi^^^pg=



^J Q.jj^.- [7/^1

Maj. Min. Dim. Aug. Min. Min. Dim. Min. Dim.



3.




Maj. Min. Dim. Min. Min. Min. Dim. Min. Maj. Maj.
4.






Min. Dim. Aug. Aug. Min. Ang. Min. Aug. Aug. Dim.
5.



Min. Min. Dim. Aug. Dim. Min. Min. Aug. Aug. Min.



15

Lesson IX.

TRIADS IN BOTH MAJOR AND MINOR KEYS.

By combining the tables in lessons VII and VIII the
following is obtained :



gBfc


Maj.


Min. Dim. Aug.

k^ ^hi*? i+vi^




^2




II


a


f^ ^^ ^^








II


I V>iy






If





I in C


ii in Bb vn in Dfe






IVinG


in in A|j






Vin F


vi in Eb






Vin f


i in c 11 in ty III 7 in a






VI ine


iv in g vn in db





Be prepared to write such a table on the board using
any letter (sharp, flat or natural) as the root of the four
triads.

Recite the chords in the preceding lesson in both major
and minor keys beginning as follows : a major triad on C
is c-e-g. It is found on I in C, on IV in G and on V in F,
and in the minor keys, on V in f and on VI in e.



Lesson X.

CONNECTION OF THE PRIMARY TRIADS WITH A
GIVEN BASS.

Each tone of a key has a special name as follows :
I Tonic, II Supertonic, III Mediant, IV Subdominant,
V Dominant, VI Submediant, VII Leading Tone ; and
the triads on these degrees are also indicated by the same
names. Thus the chord on one is the Tonic, on V the
Dominant, and on IV the Subdominant, i. e. the Under-
dominant, or five below the Tonic.



16

These three chords (the tonic with its two dominants)
are the Primary Triads. They contain all the tones of the
diatonic scale, and are best adapted to establish the ton-
ality of the key. The connection of these primary triads
in four part harmony is the next step.

SUGGESTIONS FOR WRITING THE EXERCISES.

The bass must be the root of each chord, and one of
the upper voices will also contain the root. (The root is
then said to be doubled).

The four parts are to be considered as the voices of a
part-song for soprano, alto, tenor and bass, and treated as
parts to be sung. The compass of the average voice will
therefore seldom be exceeded, and long or difficult skips
in any part would be in poor taste. Write the tenor on
the bass staff. Turn the stems of notes upward on the
right for tenor and soprano, and down on the left for alto
and bass.

The upper three parts may be written as near together
as the successive chord tones permit (CloseJPosition) or
they may be somewhat removed from each other covering
more than an octave (Open_Position), but the alto should
seldom be more than an octave from soprano or tenor.
The bass is often more than an octave from the tenor but
should seldom be two octaves below it. The parts should
not cross each other.

A figure 8, orjao figure, over or under the first bass note
means that the soprano should begin on the root, a figure 3
so placed requires the third of the chord as the first
soprano note, and a figure 5, the fifth ; but these figures
do not apply beyond the first chord. After the first chord
is written the others are arranged according to special
rules as follows*



17

RULE L

A tone common to two successive chords is generally kept
in the^&iu^^ceij}ossib le, and the other voices progress to
tbe'ltw^^^Mow, tunes. (In this lesson it is always possible
to keop the common tone. Do not give it up.)

RULE II.

If there is no common tone the tipper three voices progress
in contrary motion to the bass to the nearest chord tones, to
avoid consecutive fifths and octaves.

Consecutive Fifths and Octaves occur when two voices
progress in the same direction a fifth or an octave apart.
These progressions are avoided because consecutive fifths
are usually unpleasant and consecutive octaves interfere
with the independence of some voice. In the models at B
consecutive fifths occur in the outer voices, and consecutive
octaves between the bass and tenor. These are avoided at
A by following Rule II.

If the bass note is repeated usually change the position
of the chord, see the measure marked C. While a chord
remains the same as in these cases, the upper three voices
may move from one chord tone to another, even involving
contrary motion among themselves. It is when the chord
changes that Rules I and II must be considered.



Models.



Close position.



B




1 IV V



IV V



18



rr







Open position. Close position.

I J + J^J i J J..



U4

^ -P-


1 3 4 5 6 7 8

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