ninth with root omitted, in succeeding lessons.
In the major key the ninth is dissonant to both the root
and the third ; and in the minor key, to the root, third and
fifth. This makes it, like the seventh, a strong tendency-
tone requiring resolution one degree downward.
Resolution of the Complete Dominant Ninth Chord.
c - * - crt::2
g> i- -, rzrr/zsiu ~g mcrlZ
' r & &> rrt^Tj, ^ r ->y
H=_ _ _ __ __
Since most music is written in four parts, it is evident
that some interval of this chord must be omitted. The
fifth, being the least essential is the part generally left
out. (The .dominant ninth chord with the root omitted
will be treated in lessons XIX and XX.)
When in the fundamental position, this chord is figured
simply 9, or (in minor) ^ ^ etc., the sharp or natural re-
ferring as usual to the third above the bass.
INVERSIONS OF THE DOMINANT NINTH.
On account of the harshness of the ninth in certain posi-
tions, its use is subject to some important restrictions, as
1. The ninth (the third above the seventh) must never
appear less than a full ninth above the root. This makes
the fourth inversion impossible, 58, d, and always necessi-
tates care in the arrangement of the parts, 58, e.
2. Neither the seventh nor the third of the chord should
be omitted. This makes it impossible to write the second
inversion in four part harmony.
3. The chord always sounds best when the ninth is in
the soprano. For this reason the student is asked to use
the ninth in the highest voice only.
We are therefore limited, in four-part writing, to the
fundamental position, and the first and third inversions,
none of which violate the foregoing restrictions.
Resolutions of the Dominant Ninth, in four-part har-
mony, in its fundamental position and the two available
c. Third Inversion.
All of these positions bad.
Write and play the chord of the Dominant Ninth and its
admissible inversions with their resolutions in every
major and minor key. In some keys use close position, in
NOTE. Some schools of harmony, notably the English, consider not
only chords of the ninth, but also chords of the eleventh and thir-
teenth, as distinct chords ; while some of the highest German authorities
treat all combinations beyond the chord of the seventh as incidental choid
formations best explained as involving suspensions or passing tones. A
discussion of the relative merits of these views does not belong here, but in
advanced study the student can hardly afford to ignore either standpoint.
APPLICATION OF THE DOMINANT NINTH IN EXERCISES.
The chord of the ninth is best introduced in one of the
following two ways :
1. When the ninth is prepared, 59, a.
2. When the root is prepared and the ninth enters de-
greewise, 59, b and c.
SS II II ~C~ 33
^_JT .t t Il_tZI II t JJ
By using the chord of the ninth, the descending scale
may now be harmonized as follows :
Vlay No. 60 in every major key.
The descending minor scale, harmonic form, might be
harmonized in the same manner, but on account of the
augmented second which this presents, we shall not use it
Harmonize the following exercises in four parts, using
the chord of the ninth and its available inversions. A fig-
ure 9 in parenthesis calls for a chord of the ninth, but
leaves the pupil to select the fundamental position, or an
inversion, as he may think best. Where no figuring is
given, endeavor to locate the chord of the ninth in the most
k g F . f i .
d. 8 9 66 6
6 9 6 5^
THE CHORD OF THE SEVENTH ON THE LEADING TONE IN
The Chord of the Seventh on the Leading tone, in Major
(see example 37) comprises the upper four parts of the
chord of the major ninth. It is practically a dominant
ninth chord with the root omitted, and is treated as such
in every respect, although for the sake of simplicity it is
figured like a chord of the seventh.
It resolves to the tonic triad with doubled third. At N.
B. No. 62, the doubled third is avoided by a skip in the
tenor. With this particular arrangement of the chord the
effect is good, but this is clearly exceptional, and in every
other case the pupil is recommended to resolve each of the
four voices degreewise. Where the third lies above the
seventh, it may descend parallel with the seventh, avoiding
in this way the doubled third, but this arrangement of the
seventh chord is not altogether satisfactory.
The fifth may resolve degreewise upward where consecu-
tive fifths do not result. Ex. 63.
The seventh (the original ninth) ought always to appear
in the highest voice if the most satisfactory effect is to be
obtained. The examples under 62, a, are therefore prefer-
able to those at 6, although the latter are not forbidden.
The seventh (the original ninth) is wholly unsatisfactory
in the bass, thus making the third inversion valueless.
No tone in this chord is either doubled or omitted.
-~^i^m pr s: c C-^Jizz-r^qj
The pupil should not lose sight of the fact that the real
root, or generator, of this chord is the dominant, the tone
omitted. This view of the chord becomes e^ en clearer
through the following experiment at the piano :
Strike the chord of the seventh on the leading tone, and
sustain it, then add below it the dominant. This added
tone in no way contradicts the harmony of the other four
tones but rather serves to strengthen and support them,
supplying a tone which the ear welcomes as the omitted
In this chord neither seventh nor roc's requires prepara-
tion, but when there is no preparation approach them in
I I I I
^ JL -!L J .J-L :- : Ji +
-, l-r- 1 -HV-4-.-J
S _ * EJ?_. _*_iE. /Q ,_i_j3
THB CHORD OP THE DIMINISHED SEVENTH.
The chord of the seventh on the leading tone in the
major key, has shown itself as an incomplete form of the
dominant major ninth. The chord of the seventh on the
leading tone in the minor key, called the Chord of the Di-
minished Seventh, is an incomplete form of the dominant
minor ninth, and is in general, subject to the principles
already laid down in the previous lesson. Compare Nos.
66 and 67.
Chord of the Seventh on the lead-
" J ing tone in Major.
(Dominant Major Ninth with root
f Chord of the Diminished Seventh.
(Dominant Minor Ninth with root
The chord of the diminished seventh consisting, as it
does, of three minor thirds, presents no perfect consonance
between its intervals in any position or inversion. This
permits great freedom in its use and it is without question
one of the most important of the seventh chords. Neither
its seventh nor its root needs preparation, and it can be
approached in similar motion of all the voices without re-
striction. It is valuable in all of its inversions and with
any of its parts in the highest voice, but it is still to be ob-
served that the third inversion is the least adaptable in
practice, since it resolves to the tonic six-four, a chord
which always requires careful treatment. If the six-four
chord does not appear in the usual manner in the cadence,
it should at least enter with a degreewise progression of
the bass as in No. 68.
A few of the usual resolutions of the diminished seventh
chord are given in No. 69. It is unnecessary to multiply
examples. Resolve the seventh degreewise downward, the
root, degreewise upward, and lead the other parts so as to
avoid forbidden consecutive fifths.
&-* - g ~P
Play the chord of the Dimioished Seventh and all its
inversions with resolution in every minor key.
a. ^6 b.
5 3 4 ,
Add the A Ito and Tenor.
* -.g-*g j | - j- j
THE CHORDS OF THE SEVENTH ON THE REMAINING DEGREES
OF THE SCALE IN BOTH THE MAJOR AND MINOR KEYS.
THE PASSING SEVENTH.
The chords of the seventh which still remain unused in
these lessons are shown in No. 72.
a. In major.
III' 7 iv 7
Not all of this material is practical for our present use.
In fact with the exception of a brief general view of these
chords they may well be left until a study of the suspen-
sions, passing tones and passing chords gives the pupil a
In some works it is pointed out that all chords of the
seventh have the, so-called, cadencing resolution to the
chord dtuated a fourth higher, just as the dominant sev-
enth resolves, or cadences, to the tonic harmony, and the
supertotic, to the dominant. This is, however, only par-
REMAINING SEVENTH CHORDS IN MAJOR.
In the major key the chords, in 7 and vi 7 , take readily
this cadencing resolution, since their sevenths are minor,
but I 7 and IV 7 , containing, as they do, the harsh major
seventh, are less manageable and generally need the sup-
port of a sequence to make them satisfactory if they are to
cadence in this way. No. 73. (It must be understood that
the passing seventh is not at all considered in this connec-
C I V I 7 IV TII7 III VI 7 II V 7 I
Notice also that the chord of the seventh on the leading
tone does not take its regular resolution to the tonic as
heretofore, but cadences like the other seventh chords to
preserve the sequence, No. 73. Care is to be used everywhere
to see that all these sevenths are prepared and properly
Sequences of successive chords of the seventh are some-
times written. In this case the fifth is omitted in alternate
chords of the seventh, provided the chords are in their fun-
damental position, but not otherwise, No. 74. In such pro-.
gressions the third of one chord prepares the seventh in
the next and so on throughout.
C I IV 7 vn7 in 7 vi 7 n 7 V 7 I
In examples 73 and 74, the major sevenths in I 7 and IV 7
resolve downward, conforming to the general requirement
of the cadencing resolution, partly on account of the se-
quence. Except under circumstances of this kind the sev-
enth in these two chords is quite as likely to resolve up-
ward, when it becomes a retardation (to be treated later)
rather than a seventh,
The figures 8 7, 6 or 2, have often been applied to the
dominant harmony, and the student is familiar with the
dominant triad followed by the dominant seventh as a
passing tone (called passing seventh) first shown in these
lessons in example 10, C. In this manner the seventh may
be added to any triad, and when so used the harshness of
the seventh even in I 7 and IV 7 disappears. No new figur-
ing is needed for this. No. 75.
REMAINING SEVENTH CHORDS IN MINOR.
In the minor key the chords iv 7 and VI 7 can be given
the cadencing resolution, but they rarely so appear. In
neither case can the bass make the skip of a fourth upward
because this fourth is augmented, hence the skip of the
diminished fifth downward becomes a necessity.
a. iv? vii 07
These chords of tenest appear as mere triads to which the
passing seventh is added. See No. 77, measures 4 and 5.
The seventh in i 7 (72. &,) will only appear as a retarda-
tion not to be used at present. But when the seventh if
used as a passing seventh, which is often the case, the
original form of the minor scale is always used instead of
the leading tone, and this is a form of the tonic seventh
chord which is always useful. See No. 77, 3d measure.
The seventh chord on the third degree, III' 7 can be
given the cadencing resolution, but will oftener show itself
as formed through the use of the before mentioned sus-
pension and retardation.
IU' 7 i 6 111' 7 VI III'? VI
This chord, last shown and least valuable for our present
use, closes the list of seventh chords formed from the tones
of the diatonic scale. One might analyze many pages of
the best music without finding all of these chords, but an
acquaintance with the structure and treatment of each is
essential for successful further study.
3 6 ft 2 367
8 a 5
_.IZ.___ L-/0 1 U /^
7% - -
L.I H L| ^_
_. ja a
7 - $ t
Add Tenor and Alto.
I ^ w
z_t=_tz^t? ^_K_._. H
46 68 :i
25 5 7
REGAKDING GREATER FREEDOM IN THE TREATMENT OF
It was shown in No. 19, B, that any or all of the voices
may change their position freely without regard to a bind-
ing tone, so long as the chord remains the same This
remains true a/so with any triad to which its seventh is
afterward added as passing seventh, No. 80. In such a
case there is no objection to having the root taken by a
skip in similar motion with the seventh.
All the voices in a chord of the seventh may change their
position freely while the chord remains the same. In this
case the voice which has the seventh last must resolve it.
No. 81, a.
Instead of resolving in the usual manner, the seventh of
the dominant seventh may remain stationary if contained
in the following chord as in 81, b.
The seventh may ascend when the bass progresses de-
greewise upward to the tone of resolution (or its octave) as
in No. 82, a. Such a progression is to be considered ?s
vii 06 I 6 with which we are already familiar, the root of V 7
being looked upon as a stationary voice (organ point or
pedal in later lessons.)
In this progression, 82, 6, is forbidden, because it is in
poor taste to have any voice progress obliquely into the
unison as is done here by the tenor.
When the bass skips a third downward from the root of
a seventh chord as at 83, a, it is impossible to lead the
seventh down on account of the covered octaves which re-
sult. A common remedy for this is to lead the seventh di-
rectly upward as at 83, i, but even this is not fine The
voice having the seventh should be allowed to skip first to
the fifth of the first chord, 83, c. It is to be observed that
the covered octave in 83, a, is in all cases objectionable and
is to be avoided without exception.
b. Possible, c. Better.
-S 1 -
- ' -&-
In the following exercises there will be a few places to
use these less common progressions ; otherwise this lesson
and the two following consist of review exercises.
b. 8 6 756 7
!~ *~' r * r
:z3tm;zz ^ r^g ^
Select a stanza of a Long Meter Hymn and set it to suit-
able music as a choral for the usual four yokes. Close
the first line with a half cadence, the second with a ca-
dence in the dominant key, and the other two as you think
^T K I I ^
\\\ \ J
c. 6 65
Set a itanza of a Short Meter Hymn to suitable Music
for the usual four roices. Cadence the lines as you think
will be most interesting. Use no chords nor progressions
which you cannot clearly justify according to the
ciples already learned.
Tne choral here given is one of the easiest of that inter-
esting collection of figured chorals of Johann Seb. Bach,
taken from Schemelli's Gesangbuch. The collection con-
tains seventy -five chorals from Bach's own hand, with the
figures only to indicate what the alto and tenor should be.
We shall make the acquaintance of a number of these in
the next term's work. From the end of one line of a choral
to the beginning of the next, Bach disregards the appear-
ance of octaves and fifths, even though they be consecutive.
This is because in a sense each line is a complete idea, and
somewhat removed from what follows.
Adapted from Bach's figured chorals.
DIVISION I. MODULATION.
FROM THE TONIC OF THE OLD KEY TO THE DOMINANT
SEVENTH OF THE NEW KEY.
An interesting as well as practical means of modulation
is made by entering a key by way of its dominant seventh
CI G V 5
I 6 CI F V 7 I
This means of modulation is used by some authorities
in modulating from any key (major or minor), to any other
key (major or minor). This, however, is not possible when
the modulation is to be pure in mode. RULE: " A modu-
lation is pure in mode when the, third of the new tonic triad,
or its enharmonic equivalent, is contained in the old key"
Fig. 88. In minor keys the notation of either the original
or harmonic forms may be used.
C I eb Vg
There is but one exception to the above rule, that of
modulating from a major key to the sub-dominant minor
(C-f). Why this is pure will be explained under the head
of modulations to the sub-dominant keys.
The progression to the new dominant seventh is made
by going to the nearest chord tones. There are modulations
where a strict adherence to the above is not necessary
(Fig. 89 a), but in all cases the modulation is smoother
and the keys are better connected, when the nearest chord
tones are taken as in Fig. 89 b.
C I G VI I C I G V, I
The dominant seventh of the new key is best taken at
its first appearance, in one of its inversions, as in Fig. 89 b.
A dominant seventh foreign to HIP old key and regulaily
resolved, does not of itself constitute a modulation; it is
necessary to add still another, a final cadence. In other
words a modulation to be permanent, by this means, must
contain a preliminary and a final cadence as in Fig. 90
C I G V 2 T IV I| V 7 I
Cross relation is to be avoided; t. e., any tone that is to
be chromatically altered must not be doubled, and the
alteration must occur in the same voice.
There are exceptional cases, where it is good to double
the tone that is to be chromatically altered. Attention
will be called to these as they occur.
The modulation in the present lesson is to the dominant
key and is most frequently used in modulating from major
to major, or minor to minor keys. Fig. 91. It is, however,
good to interchange the modes as far as the rule permits.
He prepared to play and write modulations to the domi-
nant key, when a key is given; also selecting your own
MODULATING TO THE SUB-DOMINANT KEY.
Here also the modulation is most frequently used in
going from major to major or minor to minor keys. Fig.
98, a and 6.
The modulation from a major key to the sub-dominant
minor, is the only exception to the rule in Lesson XV. This
is good because the tonic triad of the old key is the domi-
nant triad of the new key, and only requires the addition
of its minor seventh to make it the dominant seventh of
the new key. Fig. 93 c.
_ I cif V, i C If V, i
Write and play this modulation as directed in Lesson I.
-t = s=^
COMBINING THE MODULATIONS IN LESSONS I AND II.
In this lesson a modulation is made to the dominant or
sub-dominant key and back again to the original key.
Fig. 95 a, b.
In combining modulations in exercises of the length
given in this lesson, the modulation to the new key is sel-
dom made permanent, but when the return to the original
key is made the final cadence must be used.
C I G V.
I 6 ICVjI
- S- 1. 1-,-, 1 J -J-r-l j 1,.
c i i 6 f VS i i c V, i e
Write and play these modulations as directed in Lesson
:gz:[ z-f - p - >g- -^
It " ^
^\ it* * I ^
r|-v It i
~rr 4- |
V w* i i
MODULATING A MAJOR SECOND UPWARD,
C I dV 7 i
In approaching the new dominant seventh in this modu-
lation, it is necessary for one of the roots of the old tonic
to skip down to the root, while the other moves up chro-
matically to the third of the new dominant seventh. Fig.
98 a, b. It is best not to make the skip in the soprano.
To make it in the bass is preferable. Fig. 98 b. This is
the only exception to the paragraph in Lesson XXV rela-
tive to cross relation.
The 5th of the old tonic triad may be doubled; the modu-
lation is then made as in 98 c. This is probably the most
beautiful way of approaching the new dominant seventh.
- J- ff-J-
C I d Vf i C I d V T i C I 6 d V} I
Write and play this modulation.
I EY -. J
MODULATING A MAJOR SECOND DOWNWARD.
In this modulation it is only necessary to proceed as
usual, by going to the nearest chord tones of the new domi-
nant seventh. Fig. 100.
5-*i &'~ l~* \ J.
Write and play this modulation.
COMBINING THE MODULATIONS IN LESSONS XXVIII AND
In this lesson a modulation is made to a key a major
second higher or lower and back again to the original key.
Fig. 102 a, b.
CI dV| i
c i B^Vf I c V 7 i
In this and succeeding combinations, to make the modu-
lations both going and returning conform to the rule in
Lesson XXV, they must be made only between major and
minor, or minor and major keys.
Write and play these modulations.
S\ 1 * 1 j
fm v j A &
^^ . ,-.
-ff-f 1 1 I fj
MODULATING A MINOR THIRD UPWARD. FIG. 104.
a i C Vf I
Write and play this modulation.
MODULATING A MINOR THIRD DOWNWARD. FIG. 106-
^* ' Wfc3
C I a V* i 6
Write and play this modulation.
i i I j- I I
COMBINE THE MODULATIONS IN LESSONS XXXT AND
In this lesson a modulation is made to a key a minor
third higher or lower and back again to the original key.
Fig. 108 a, b.
CV aV, i 6 CVi i
a I C V! I a V|
Write and play these modulations.
M i i^
MODULATING A MAJOR THIRD UPWARD. FIG. 110.
^3<2 xs it^zz ^ n.^-L^zJJ
C I e V 7 i
In modulating a major third upward it is best for the
student to double the third of the old tonic triad before
approaching the new dominant seventh, and use the root
position in both chords as in Fig. Ill a. When this form
of modulation is mastered, the student may use those at
111 6, and c. Faulty progressions as at 111 d, e, and f,
create the necessity for special care in progressing to the
dominant seventh, in this modulation.
CI eV r i
Write and play this modulation.
MODULATING A MAJOR THIRD DOWNWARD FIG. 113.
e i C V 2 I 6
Write and play this Modulation.