John Greig.

The musical educator; a library of musical instruction by eminent specialists (Volume 2) online

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is the third from the root, or the sixth from the bass note, which is the root itself. This chord
is generally followed by the second inversion of the tonic, or by the dominant seventh chord.



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The second inversion of this chord is sometimes used, but only very rarely.



Chromatic Chord on the Subdominant

This is just the subdominant of the major key made minor. It can be used in both in-
versions, just as an ordinary subdominant




A very fine example of this chord is found in the opening bars of the Overture to the
" Midsummer Night's Dream," by Mendelssohn.

There are four chromatic concordant triads that can be used in the major scale, namely,
the major chord on the supertonic, the major chord on the minor second of the key, the minor
chord on the subdominant, and the major chord on the minor sixth of the key ; these can all
be used in the major mode without leaving the key.



n8



THE MUSICAL EDUCATOR



Chromatic Chord on Supertonic of Major Key.

In the key of C this chord looks as if were threatening a modulation tc key of G, thus :






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But if we follow it with a chord that can only belong to the key of C, such as the dominant
seventh in the key of C, or by a chord which, while it might belong to several keys, points
preferentially to the key of C, such as the second inversion of the chord of C, it is clear that
there can be no modulation, thus :



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This last illustration shows the chord of D major, followed by the second inversion of the
chord of C, the F sharp rising to G ; also the same chord followed by dominant seventh in key
of C, where the F sharp falls to F natural, thus securing the key of C. Had we allowed the
passage to modulate, the chord would no longer have been chromatic ; it would have been
diatonic in the new key. The first inversion of this chord may be taken

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The third should never be doubled. The second inversion is rarely used.

Chromatic Chord on the Minor Sixth of the Scale.

This is a major chord built upon the minor sixth of the major scale ; and it can be followed
either by me tonic or some inversion of the dominant ; generally, however, it is followed by a
second inversion of the tonic chord.






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HARMONY



119



The first inversion of this chord may also be used (No. 25), and the second inversion
more rarely.

Another chord sometimes used chromatically in the major key is the first inversion of the
supertonic, with the diminished fifth. This is also generally followed by second inversion of
the tonic (No. 26).

In the minor key the chromatic chords are the major chord on the supertonic of the key,



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No. 26.



and the major chord on the minor second of the key. All the other chords mentioned, as
chromatic in the major, are really diatonic in the minor.

When the chord of the tonic or a dominant discord, whether in root position or inversions,
follows a chord seemingly foreign to the key, this chord seemingly foreign to the key will be
then identified as one of the chromatic chords.



Dominant Ninth and its Inversion.

To the chord of the dominant seventh we can add either a major or minor third, which is
the ninth from the root.



Major gth.



Minor gth.



Dominant Major Ninth.

This chord is used only in the major key, and can be taken without preparation. The
ninth may be resolved either on the root of the same chord, or on the third of the same chord,
or on another chord. It is figured . When resolved upon the root of the same chord, while
the rest of the chord remains, the root should not be heard in any of the upper parts at the same



No. 27.



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No. 28.



time, but only in the bass, in accordance with the rule that the note on which a discord resolves
should not be heard at the same time as the discord, except the root with the ninth, when that
root is in the bass (No. 27).

In four-part harmony the fifth is generally omitted. The ninth should not be placed below



120



THE MUSICAL EDUCATOR



the third, except when the third remains stationary, and the ninth proceeds to the root. When
resolved upon the third of its own root, the ninth either rises a second or falls a seventh. In
accordance with the above-mentioned rule, the third must be left out of the chord until heard
by the resolution of the ninth (No. 28).

By thus resolving on a note belonging to its own root, it becomes simply a chord, of the
dominant seventh.

The ninth may also be resolved by falling to the fifth of the tonic chord (No. 29).

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No. 29.



No. 30.



When the fifth of the chord is present, as in five parts, the third in the succeeding tonic
chord must either be doubled, or the fifth in the chord of the ninth be placed above the ninth,
in order to avoid consecutive fifths ; the first alternative which places the ninth above the
fifth and seventh, and doubles the third in the succeeding tonic chord being the preferable
one (No. 30).

In all the inversions of this chord the root is left out. The first inversion of the ninth with
the root left out will thus become a chord of the seventh, and is called the chord of the leading
seventh, because it starts from the leading note. This, like the direct chord, can be used in the
major key only (No. 31). It is figured 7.

It is impossible to mistake this chord of the leading seventh for the dominant seventh, as
the intervals are quite differently placed ; a dominant seventh consists of one major third and two
minor thirds, whereas this chord consists of two minor thirds and a major third. The domi-
nant seventh has a perfect fifth, while the chord of the leading seventh has a diminished fifth
(No. 32).




1 7

Dominant yth. Leading 7th.



No. 31. No. ya.

The leading seventh can fall one degree and resolve upon its own root, while the rest of the
chord remains, or it may fall one degree to the fifth of the tonic chord (No. 33). Care must
be taken to let the fifth, when below the ninth, as in previous example, ascend to the third of the
tonic chord, otherwise consecutive fifths will ensue. It is true this progression causes the third
of the tonic chord to be doubled, yet of two evils one must choose the less ; and the doubling
of the major third is unmistakably a much less evil than a consecutive fifth, in fact, no evil at
all in the circumstances.



No. 33.



HAKMOKY



121



Second Inversion of Dominant Major Ninth.

The root here is omitted altogether as in the first inversion, consequently this chord appears
as the first inversion of the leading seventh, figured | (No. 34.)




No. 34.



No. 35.



The ninth may, like the direct chord and first inversion, resolve on its own root while the
rest of the chord remains (No. 35), or it may fall one degree to the fifth of the tonic chord,
which, however, must be taken in the first inversion in order to avoid consecutive fifths (No. 36).



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No. 36.



No. 37.



It will be recollected that the one exception to the rule, that the dominant seventh should
descend one degree, was when the second inversion of the dominant seventh proceeded to the
first inversion of the tonic, when the seventh could then rise one degree. The same progression
of the seventh can take place when the second inversion of the ninth proceeds to the chord
of the tonic in the first inversion (No. 37).



Third Inversion of the Dominant Major Ninth.

This inversion of the dominant ninth has the seventh in the bass. The root is best omitted
here also, although it is sometimes heard in an upper part It is figured * or J, or with root 3
(No. 38).



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No. 38.



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No. 39.



The ninth here may also resolve on the root, while the rest of the chord remains
(No. 39), or it may proceed to the fifth of the tonic chord, while the seventh, which is in



122



THE MUSICAL EDUCATOR



the bass, takes its usual resolution and descends one degree to the first inversion of the tonic
(No. 40). Should the ninth be above the fifth, the third of the tonic chord will require to
be doubled in the resolution (No. 41), or the fifth of the dominant must leap to the fifth of
the tonic.



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No. 40.


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No. 41.



If the third of the chord be left out when the root is heard in an upper part, the ninth may
proceed to the third. This resolution then becomes simply the last inversion of the dominant
seventh resolving on the tonic chord, thus :



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Fourth Inversion of Dominant Major Ninth.

This being the last inversion, has the ninth in the bass ; but, owing to the harshness of the
ninth being heard below the third, it is very seldom, we may almost say never, used in this
inversion.



Dominant Minor Ninth.

The chord of the dominant minor ninth consists of the dominant seventh, with a minor
third added to it (No. 42.) It is figured >? in the major key of C, and in the minor key of C
a natural is used to show the leading note $ ; when accidentals occur in any part above the
bass they are shown as the figuring. This chord is freely used in the major key as well as in
the minor ; and there is no objection to the ninth being heard below the third, as the effect is
always good (No. 43.)



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No. 43.



HARMONY



123



The ninth may be resolved, while the rest of the chord remains, either upon the root or
third of the same chord, or it may resolve with the other notes upon another chord.

When it is resolved upon the root of the same chord, the root should not be heard in an
upper part, unless in very exceptional cases.




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When it is resolved upon the third of the same chord, the ninth may either rise a second
or fall a seventh ; and in this case the third must be left out, in accordance with the rule that
a discord should not be heard at the same time with its note of resolution. The ninth here
may rise an augmented second with good effect. Sometimes the root may be sounded in this
case in an upper part.




There is a very good example of the ninth falling to the third in Beethoven's Concerto in
C minor.

When the ninth is resolved with the other notes of the chord, it is usually upon the tonic,
when the ninth falls to the fifth of that chord.




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The root is left out in all the inversions.



First Inversion of Dominant Minor Ninth.

The root here being omitted, we have the notes standing in a series of minor thirds above
each other; thus in the key of C, by leaving out the dominant root G, we have the notes
B, D, F, A flat (No. 44.) The chord in this inversion is called the diminished seventh ; and
it can also be resolved on its own root, while the rest of the chord remains (No. 45.) It can
be used either in the major or minor keys.

Seeing that the bass note itself is the third, it cannot be resolved upon the third of the same
chord, as it can when the root of the chord is in the bass. It can also be resolved upon another
chord, and then its most natural and common resolution is upon the tonic ; and here, as in the
major chord, it is well that the fifth of the dominant should rise to the third of the tonic j for



i2 4 THE MUSICAL EDUCATOR

it is not good that a diminished fifth should be followed by a perfect fifth when the two notes




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No. 44.




No. 45.



forming the diminished fifth move downwards by one degree. Of course, in this inversion, the
fifth of the dominant could also skip to the fifth of the tonic (No. 46.) When a little further
on we come to deal with enharmonic changes and modulation, we shall see that some of the
most exquisite effects are got by enharmonically changing one or more notes of this chord so
as to alter the root and therefore changing the key to which this diminished seventh belongs.
For instance, if we take the notes B, D, F, A flat (No. 47), the root is G, the dominant





No. 46.



No. 47.



in the key of C; but if we enharmonically change the A flat to G sharp (No. 48), and
then place the chord in thirds, we get Gft B, D, F. (No. 49). We here bring about the first
inversion of the dominant minor ninth on E, which is the dominant of A major or minor; and

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No. 48.



No. 49.



it would accordingly resolve on that chord. The intervals of this chord are the minor third,
diminished fifth, and diminished seventh, from which last interval it takes its name.

Second Inversion of Dominant Minor Ninth.

The root is also here omitted, and the discord can be resolved either upon its own chord,
or upon a chord having another root (No. 50). Here it is resolved upon the root of its own



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No. 50.



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No. 51.



HARMONY



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chord, thus forming the second inversion of the dominant seventh.
upon the fifth of the tonic chord.



In No. 5 1 it is resolved



Third Inversion of Dominant Minor Ninth.

The root here is left out, and must not be sounded in any upper part along with the
minor ninth, as it can be in the case of the major ninth. In this inversion, the minor ninth
may also resolve upon its own chord, thus making the last inversion of the dominant
seventh (No. 52), or upon another chord, usually the first inversion of tonic. (No 53).








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No. 52.




No. 53.



No. 54.



There is another resolution of this inversion which seems a little strange, and which is yet
often used ; that is where the seventh, instead of as usual descending one degree to the first
inversion of the Tonic, leaps down to the root thus (No. 54). Examples of this resolution
will be found in Beethoven's Symphony in D, also in Mendelssohn's "Elijah."



Fourth Inversion of Dominant Minor Ninth.

This inversion has the ninth in the bass, and the root is omitted. Although the last
inversion of the major ninth was said to be very rarely used, owing to the harshness of the
ninth being below the third, yet the minor ninth can be freely used in the last inversion, and
always with a very fine effect It can also be resolved on its own chord, thus (No. 55)





No. 55.



No. 56.



or on a chord with another root, the most usual one being the tonic second inversion (No.
56). It is usually figured * or *. In the first example, the minor ninth proceeds to the root
of the chord, the other notes remaining. In the second example, the minor ninth is resolved
along with the other notes of the chord, on the second inversion of the tonic.



X2D



THE MUSICAL EDUCATOR



Secondary or Essential Chords of the Ninth.

These are just the same as the secondary or essential chords of the seventh before-
mentioned, with the addition of a ninth added ; and they follow the same rules. They are
resolved on a chord, the root of which is a fourth above their own root (No. 57). The
ninth being always a dissonant note should be prepared, and then resolved on the fifth of
the following chord. These ninths can be taken in root position on any note of the scale,

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No. 58.



provided that the chord, the root of which is a fourth above, is one that can be taken in root
position. If the fifth of the chord is written below the ninth, it must rise to the third of the
following chord to prevent consecutive fifths (No. 58). Any note that makes a discord
with the bass should be prepared. There are four inversions of this chord, the last
of which is not used. The root is left out in all the inversions. The first inversion of the
ninth will then, to all appearance, be a chord of the seventh ; but as the resolution of each is a
fourth above the root, these resolutions will be both on different chords, thus (No. 59). Here
we have the first inversion of the chord of the ninth, the root of which is C, resolving on the
chord of F, a fourth above. Our next example will illustrate the same notes, being a chord
of the seventh (No. 60). Here we have the same notes as in the first inversion of the
chord of the ninth ; but in this case it is a chord of the seventh on E, resolving on the fourth



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above, namely, on chord of A. It will be clear, then, that a chord of the seventh can be treated
and resolved in two different ways ; either as a chord of the seventh, resolving on the fourth
above, or as the first inversion of a chord of the ninth, resolving on the note above, which note
is the fourth above the root of the ninth.

The second inversion of the chord of the ninth is resolved on the first inversion of the
following chord. This inversion of the ninth has the fifth in the bass and the root left out.
If it were resolved on the root of the next chord, consecutive fifths would necessarily ensue
(No. 61). Here the second inversion of the root C resolves upon the first inversion of the
root F. This chord is also identical with the first inversion of the seventh, resolved on the



HARMONY



127



root a fourth above, thus (No. 62). Here is the first inversion of the chord of the seventh
on E, resolving on the root of the chord A, the fourth above E. The third inversion of the

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ninth has the seventh in the bass, and resolve on a first inversion (No. 63). This chord
is not used as the second inversion of the seventh on E. These resolutions of the
ninth explain one very common resolution of the dominant seventh, called the interrupted
cadence. Instead of resolving on the tonic, the dominant in the interrupted cadence re-
solves on the submediant




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No. 63.




with root left out.



No. 64.



If we take the chord of the ninth on the mediant, and leave out the root, we have the first
inversion of the ninth, which is just the dominant resolving on the fourth above the root of the
ninth, which is the submediant, as in foregoing example (No. 64). Thus the dominant
seventh can either resolve upon its own tonic according to the rule of the seventh, or upon
the chord of the submediant, according to the rule of the ninth.



Chromatic Discords of the Seventh and Ninth.

These are chords, consisting of exactly the same quality of intervals as the dominant
seventh and ninth, but used upon the supertonic and tonic without causing a change of key.
The supertonic is, in fact, the dominant of the dominant, and the tonic is the dominant of the
subdominant, but used without making a modulation into these keys. They can be used either
in the major or minor keys.

One of the most frequently used of these chords is the supertonic seventh. It is a minor
seventh added to the chromatic concord of the supertonic ; thus, in the key of C the chord
would be the following :




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128



THE MUSICAL EDUCATOR



This chord has all the appearance of the dominant seventh in the key of G, and did we
proceed to the triad of G, a modulation to that key would certainly be made. In order, there-
fore, to prevent modulation, this chord must be followed by another chord, specially belonging




No. 65.



to the original key, such as a dominant discord, or the tonic chord, either in root or inversions.
The foregoing is an example of the supertonic discord followed by the dominant discord
(No. 65). Another example of this will be found in Verdi's " II Trovatore," thus




Here the key is B flat, and the chromatic supertonic is C, with the major third, the acci-
dental E natural, which is the leading note of the dominant key of F, falls to the E flat, which
is the dominant seventh of the original key ; and the seventh of the supertonic according to
the usual rule falls a second to the third of the dominant. The other resolution of the super-
tonic discord is, when it proceeds to the chord of the tonic, generally to one of the inversions



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The seventh here remains to be a note of the following chord, and when this is the case,
the seventh may be doubled, and one of the two sevenths is free to leap as a concord, thus



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Here the seventh C is doubled, and one of them leaps to E, the third of the chord
of C, while the other remains. The supertonic seventh may, without being doubled, leap as a
concord, provided that the fifth in the chord of the seventh proceed to the same note in the
next chord that was the seventh in the chord it has just left, as in the following example t




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In this example, A, which is the fifth note of the supertonic discord, leaps to the C!, the
root of the tonic, which note was the seventh of the supertonic discord.

When this chord is followed by a dominant discord, the seventh of the supertonic may rise
to the fifth of the dominant, provided that the fifth of the supertonic also moves to the third of
the dominant, as in the following example :

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This chord may also be taken in the three inversions :

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In the first of the three above examples, the supertonic seventh is in the first inversion, and
is resolved first upon the last inversion of the dominant seventh, and next on the second in-
version of the tonic chord.

In the second example, the supertonic seventh is in the second inversion, and is resolved
first upon the root of the dominant seventh, and next, upon the second inversion of the tonic
chord.

VOL. u. I



130



THE MUSICAL EDUCATOR



In the third example, the supertonic seventh is in the last inversion, and is resolved first upon
the first inversion of the dominant seventh, and next, upon the root of the tonic chord which
last resolution is somewhat rare.

A chromatic discord of the seventh can also be used upon the tonic, both of major and
minor keys, the third of which chord must always be major. It is precisely the same chord as
the dominant of the subdominant ; only to prevent modulation, it must be followed either by
a dominant or a supertonic discord. The third and seventh in this chord must never be
doubled ; if it resolve upon a dominant discord, the third will rise a semitone, and the seventh
will also rise a chromatic semitone, thus (No. 66)



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No. 67.



If the tonic seventh resolve upon a supertonic discord, the third will rise a major second, and
the seventh will descend a minor second, as in example (No. 67).

A very clear example of the tonic seventh resolving on the dominant is to be found in
Beethoven's Quartet, Op. 59, No. 3, thus




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An exceptional resolution of the third is shown in the preceding example. When the


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