C I V I IV V I
Harmonize the following basses. Indicate the common
tones with the tie and letter the chords as shown in the
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CONNECTION OF THE PRIMARY TRIADS WITH A GIVEN
The bass will be the root of I, IV or V, but the soprano
may be the root, third or fifth of these chords.
Begin and end with the tonic chord.
Avoid the progression from V to IV if the third of V is
in the soprano.
If the soprano repeats a note usually change the chord.
Generally change the chord when entering a new
mflftHiirfl even if the soprano skip_s_but when the melody
begins on the last part of a measure the tonic harmony is
usually repeated over the first bar. See model.
If the soprano, within the limits of the measure, skips
from one tone to another of the same chord, keep the same
bass and merely change the position of the alto, or tenor,
or both, to suit the movement in the soprano. In following
this rule the voices may be kept in close position through-
out, the inner parts simply following the soprano and thus
keeping on the nearest chord ones (Ex. A), or they may
be more independent, leading to open position with the
high notes in the soprano and again close position when
the soprano lies lower (Ex. B).
Do not let the bass skip a seventh, nor two fifths in
succession in the same direction.
The special rules I and II in lesson X apply here, but
with this important exception to Rule I: With a given
soprano if a common tone between two chords can not be kept,
lead the upper three voices in contrary motion to the bass to
the nearest chord tones as in Ifnfe IT. (Even where the
common tone can be kept it will be seen later that con-
trary motion is sometimes to be preferred.)
A, Close position.
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or B, close.
EXERCISES WITH THE PRIMARY TRIADS CONTINUED.
A CADENCE is the close of a musical phrase, and is
formed by the last two (or more) chords. There are two
general kinds of cadence, Authentic and Plagal.
The AUTHENTIC CADENCE is formed by the progression
V-I, and the PLAGAL CADENCE by IV-I, the Tonic always
falling on the accent. These cadences are perfect when
the soprano ends on the root of the tonic chord and
imperfect when it does not.
In the exercises of this lesson write the name of each
cadence, indicating whether it is Authentic or Plagal, and
also whether perfect or imperfect.
No chords except I, IV and V are to be used until
regularly introduced in later lessons.
4 L 1 1
d. 5 With a low soprano.
e. From a Hymn Tune. Write a good melody.
THE PRIMARY TRIADS IN EXERCISES IN THE MINOR KEY.
In harmonizing a melody in the minor key, remember
that the Leading Tone must always have a # (or b]) every
time it appears. With a figured bass this Leading Tone is
indicated by # (or %) over the dominant.
An accidental affects that degree only upon which it is
placed. If for example, the soprano takes a g$ and later
in the same measure the tenor takes g$ an octave lower,
this degree must also have its own sharp. See A in the
a. 8 8 ft
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THE CHORD OF THE SIXTH.
A triad is said to be inverted when instead of the root,
its third or fifth appears in the bass.
The CHORD OF THE SIXTH is a triad with its third in
the bass. (The first inversion.) In a figured bass this is
indicated by a figure 6 because the root is then a sixth
above the bass note.
In harmonizing a soprano the chord of the sixth will
often precede or follow the root position of the same chord.
This is sometimes effective whe the soprano repeats a
note, e. g. the first measure of the third exercise to be
In the chord of the sixth double either the root or the
fifth. The third is doubled under certain circumstances
but there is no occasion for this at present.
When there are two possible common tones generally
keep the lower if the upper one is the soprano. See A.
In addition to I, IV and V we now have I 6 , IV 6 and
V 6 , affording the bass three new tones. The Roman
numerals always indicate the root of a chord.
6 V 6 I
V6 I IV6 V I
Supply the alto and tenor.
THE SIX-FOUR CHORD.
The Six-FouR CHORD is a triad with its fifth in the
bass. (The second inversion J In a figured bass this is
indicated by because the third and root are respectively
a sixth and a fourth above the bass.
The'six-four chord is employed principally to strengthen
the authentic cadence in the closing formula, I|, V, I ; see
in the models C 1 . It also precedes the dominant where a
partial close is desired, C 2 . In these cases the six-four
chord must appear on a relatively strong beat in the
measure as compared with the dominant which follows it,
i. e. on the first beat in double time, the first or second
beat in triple time and the first or third beat in quadruple
time. This use of the chord is very characteristic and
must be reserved for cadences only. There are three other
uses of the six-four cho!rd, all of which are of secondary
importance, as follows :
The six-four chord may appear,
First, when its bass note is the second of three repeated
notes as at A. (iSfosa strong progression.)
Second, when its, bass note is the second of three notes
progressing degreewise as at B.
Third, when its bass note is taken and left by a skip
and is the second of three notes belonging to- the same
chord as at D.
At E notice a third doubled and at F the third omitted,
both of which progressions are good. Good at E because
the third on the weak beat is not unpleasantly prominent,
and at F because the presence of the third on the accent
In the six-four chord always double the fifth, the bass
Consecutive octaves and fifths as at G from one strong
beat to another should be avoided even if another positron
of the chord seems to have hidden them. These are
avoided at H by changing the succeeding chord, or if the
bass be given, by writing the soprano differently as at I.
The figure 3 over any bass note except the first indicates
a triad in the root position, hence | 3 over the same note
calls first for a | chord and then for a triad whose root is
the bass note.
A. stroke through a figure does not alter its meaning as
a sign of inversion, but indicates that that interval above
the bass is to be chromatically raised, e. g. means a chord
of the sixth with six above the bass raised chromatically.
a. 8 4 6 6
6 6 ' ' 6 6
b. 5446 4 6 64
c. 84 6 tt 4 6
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THE SECONDARY TRIADS IN MAJOR IN THE FUNDAMENTAL
The SECONDARY TRIADS are those formed on the second,
third, sixth and seventh degrees of the scale In modern
harmony they are used mostly as connecting chords.
Unlike the primary triads, these have not the power to
establish tonality of key and if so much used as to largely
exclude the primary triads, the result is likely to be un-
satisfactory unless it is desired to imitate the ancient
church style. The progressions are strong when the bass
descends by skips of a third to successive roots (Ex. A),
while the reverse progression of the bass gives a weak
result (Ex. B). ^y^O V \ n
GI V in I vi IV ii V B V I
. / 1 /
GI n IV vi I m V I
The most important of the secondary triads is that on
the second degree, the Supertonic. It is best used to pre-
cede the dominant, or the tonic six-four chord in the
cadence as follows :
In the progression n-V give up the binding tone and
lead the upper three voices in contrary motion to the. bass
to the nearest chord tones. (C in the following model.)
In this progression the bass should ascend.
In the progression n-I^ the bass ascends and the upper
three voices progress in contrary motion to the nearest
chord tones (D). Here the fifths of the chords must not
be above the roots on account of the resulting consecutive
fifths as at G. Note especially how, in order to avoid these
consecutives, the binding tone is given up in approaching
the supertonic chord at D. This is not simply good
because necessary, but at the same time a better melody is
n I| '
Next in importance is the triad on the sixth degree, the
Submediant. It often follows the dominant with the
following special treatment:
In the progression V-vi the leading tone frequently
ascends to the tonic, especially if in the soprano, thus
doubling the third in vi (E). Elsewhere the use of this
chord involves no special rules.
The triad on the third degree, the Mediant, is of com-
paratively little importance and requires no special rules.
Its best uses are in the progression V-m-I as in Ex. A,
and in I-in-lV with the descending scale, and the leading
tone in the soprano, as at F.
The triad on the seventh degree (diminished) is seldom
used in its root position, except in sequence, and will be
When the soprano is givea use the primary triads as
heretofore, except where otherwise indicated. Any exercise
marked "Unfigured" leaves the choice of all material to
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THE SECONDARY TRIADS IN MINOR IN THE FUNDAMENTAL
In the minor the supertonic triad is diminished. While
not frequently used in fundamental position it may so
appear and in the progressions n-V and n-I|, it is bound
by the same rules as in major, i. e. contrary motion to an
ascending bass. The violation of this rule in minor in
u-V gives rise to the forbiddsn progression of an aug-
mented second, see A. In pure part writing the progression
of an augmented interval in any voice is prohibited.
Aug. 2 Con. 8ths.
The triad on the sixth degree in minor when preceded
or followed by the dominant, requires the following rule :
In the progression V-VI, or VI-V, always double the
third in VI, and do not omit the fifth. In this progression
the leading tone is never taken or left by a skip. See B.
The triad on the third degree, being augmented, is too
harsh to be of any practical value in the present studies
and is not _used here.
The triad on the seventh degree (diminished) is seldom
used in root position and is treated as in major (to be
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INVERSIONS OF THE SECONDARY TRIADS.
The supertonic triad in its first inversion is of special
importance in both major and minor. As a rule its jhird,
the bass note, should be doubled, and in this form it is
generally much better than the fundamental position
before V or I in the cadence, especiallyTn minor. See A.
~~The triall orT the leading tong in its first inversion is
highly useful. For the present double its third, less often
its fifth and never its root, and lead all the voices without
skip to the tonic chord which should follow it. See B.
This important chord is taken up in detail in Part II.
XL & S3
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No special rules are required for the use of the remain-
ing secondary triads in their first inversion. They appear
with doubled root, third or fifth according to the necessities
of the voice leading in general.
The second inversion of the secondary triads is not
available in the present.. lessons. As passing chords they
are weak and on an accent they sound like tonic chords,
thus suggesting a modulation.
From this point onward, practice and observation best
serve the pupil in numberless cases, but the following
general principles are of value :
The Leading Tone is almost never doubled.
Prirnaj^z triads- oftenest double the root or fifth.
Secondary triads in lirst inversion frequently double
In two successive chords of the sixth in close position
> generally double the root or fifth in one and the third in
the other, but this doubled third must not be the leading
j In three successive chords of the sixth with the bass
ascending degr^ewise. double the fifth in the first chord^
fihe third in the next and the root in the last ; and with a
. -descending bass, double in turn the root, third and fifth.
This requires close position. See application of this
principle in examples c and d to be worked out.
At the end of exercise d, however, it is finer to double
the third in the iig, which shows that the third may some-
times be doubled in successive chords of the sixth when
the upper three voices can all be led correctly in contrary
motion to the bass. But this applies in example d to the
last measure only and is not a necessity there.
A FEW SPECIAL PROGRESSIONS.
In ordinary chord progression similar motion of all the
voices at once is generally bad. But in major the pro-
gression from I or I 6 with doubled root, to n 6 with doubled
third permits similar motion of all parts if the root of n 6 is
above the fifth. See A. In minor, equally good down-
ward, but less so with upward progression.
In the. progression from u -to V, in either _ major or
minor, theViownward progressionjof all the voices as at B
cannot be condemned.
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A SEQUENCE is a succession of similar harmonies result-
ing from a symmetrical progression in the bass. In the
present studies the sequence must fill at least three
Harmonize the first measure of a sequence according
to the principles already laid down, and consider this the
sequence unit. Note what voices double root, third, etc.,
and then arrange each measure of the sequence to corre-
spond exactly with this unit or pattern. In attaining thia
symmetry it is permitted to double the Leading Tone.
Similar motion of all the parts at once if not in consecutive
octaves or fifths, is also allowed.
Begin the first exercise as shown below, doubling third
and root in succession. In groups of three successive
chords of the sixth the pupil is reminded of the principle
advanced in Lesson XVIII.
Beginning of a.
Beginning of g.
d. 3 666666666666
g. 3. No inversions
6. 666666 66666
These 6's mean chord of the sixth with root in soprano.
1 a^ \ ' i ~ ^f
Lessons in Harmony.
THE CHORD OF THE DOMINANT SEVENTH,
By adding a seventh to the triad on the fifth degree 01
the scale a chord is formed called the Dominant Seventh.
C V or I or i
This chord is the same in both the major and the minor
keys. It has a major third, perfect fifth, and minor
Write and play this chord in erery major and minor key.
All chords which contain one or more dissonances are
called dissonant or tendency chords, because the ear is not
satisfied to accept such a chord as a point of repose, but
demands that it progress or resolve to a consonance.
The Dominant Seventh chord is the most important of
all the dissonant chords. It contains two dissonances, viz.,
the seventh, from the root to the seventh, and the dimin-
ished fifth, from the third to the seventh. The seventh
being dissonant to both the root and the third of the chord,
has a strong tendency to progress downward one degree to
the third of the tonic triad. The third being the leading
tone, follows its tendency to progress upward to the tonic.
For the purpose of leading these tendency-tones in their
natural manner, the following rules are usually given for the
REGULAR RESOLUTION OF THE DOMINANT SEVENTH CHORD.
1. The seventh descends one degree to the third of the
2. The fifth usually descends one degree to the root of
the tonic triad, but it sometimes ascends one degree if a
smoother voice-leading is gained thereby.
3. The third being the leading tone may always ascend
one degree, or if in a middle voice, it may descend two de-
grees provided the bass moves upward.
4. When the root is in the bass, it skips upward a fourth
or downward a fifth to the root of the tonic triad; if in any
other voice^ it remains stationary as a binding tone.
The application of the rules is the same in either major
or minor keys.
The Dominant Seventh chord with its resolution should
be written and played in every major and minor key, and
in both close and open position.
INVERSIONS OF THE DOMINANT SEVENTH.
The Dominant Seventh has three inversions. In resolv-
ing these inversions the root of the chord should be kept as
a binding tone, while the remaining tones are treated the
same as in the fundamental position, with this exception,
that in V 2 the fifth of the chord, when in the soprano,
frequently skips upward a fourth. See No. 6, 6.
First inversion; Chord of the sixth and fifth.
Second inversion: Chord of the sixth, fourth and third.
Third inversion: Chord of the sixth, fourth and second,
a. . b.
Write and play each of these inversions with its resolu-
tion in every major and minor key, in various positions
and in both close and open harmony.
THE DOMINANT SEVENTH CHORD WITH ITS FIFTH
By omitting the fifth and doubling the root of the dom-
inant seventh (in fundamental position) it resolves to a
complete tonic triad. In this form it is very useful and
often more desirable than when its fifth is present. Notice
that the root only, may be doubled, since to double the
seventh or the third would produce consecutive octaves in
the regular resolution.
The dominant seventh with fifth omitted resolving to the
complete tonic triad.
These resolutions should be prepared in the same man-
ner as those in examples, 4, 5 and 6. In the recitation at
the piano the pupil should play without notes.
The following cadence is to be committed to memory and
played in every major key.
FUNDAMENTAL POSITION OF THE DOMINANT SEVENTH IN
treated in the following ways : (No. 9.)
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At No. 9, A, all the tones of the dominant seventh chord
are taken in similar motion. This is entirely satisfactory
here since the skip of the octave is essentially a binding
tone and the upper three voices all move degreewise, i. e.
diatonically. The leading tone might have progressed
upward to the tonic as at No. 10, A, but this leaves the
tonic triad without its fifth. While this is quite correct, it
is generally desirable to use the complete chord where
At No. 9, B, however, if all the voices moved downward
there would appear a somewhat unsatisfactory progression,
i. e. the consecutive fifths between the soprano and tenor.
( See 10, B.)
Now while these are not actually forbidden consecutives,
the second fifth being diminished, yet the solution at No.
9, B, is preferred by some good authorities.
At No. 9, C, the same fifths here spoken of appear, but
with no unpleasant.effect, the arrangement of the voices be-
ing especially favorable. This progression is very often
used as at No. 10, C, the seventh being delayed until after
the dominant triad has appeared. Such a progression is
indicated by the figures 8 7 over or under the same note.
In this case the passing seventh may be given to any voice
which gives a good arrangement of the following chord.
The figuring will generally suffice to make clear the
necessary solution, but the student must aim to become
familiar with the most usual and satisfactory progressions
so that he may early learn to write without any figuring, or
even to invent short exercises himself.
Here are three short melodies correctly harmonized.
a. V? n a V?
vii 06 i 6 iio i V 7
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V? n V 7 b. vii 06 i s
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It 06 j6 V?
c. VI V?
In 12, a, notice the open position. When the soprano is
high this is nearly always the better arrangement of the
In b, the open position changes to close quite naturally
through the progression of the outer voices. At N. B. the
cousecutives between alto and soprano are permitted, the
second fifth being diminished.
In c, note that the third must be doubled in the chord
on the sixth degree in order to approach the dominant
seventh chord without fault
Suggestions for the Exercises from this point on.
1. Write often in open position.
2. Write the tenor on the bass staff whether in open or
3. Write separate stems for each part, and turn the
stems up for soprano and tenor, and down for alto and
4. The alto must not be more than an octave from the
tenor or soprano. The tenor and bass may be farther
apart than this, but should rarely be more than two
octaves from each other.
In the following exercises, when no figure appears over
the first bass note, write two solutions beginning in differ-
ent positions. In one solution use the fifth in the domin-
ant seventh chord, in the other, omit it.
g~ I I r lh~__ ?_t
f. 3 6
g. 6 4 # h. 5 6 6 4 }f
i. Soprano. If V?
j. ii 06 if V?
k. n Ig V?
16 V V?
II 8 I V?