we have again another major triad on the sixth degree. C major therefore has

Major triads on C, G, and F, Minor triads on A, E, and D, and consequently upon all the tonic chords nearest related to it (page 25)—G major, F major, and the relative keys, A minor, E minor, and D minor. In the irregular minor mode this is exhibited irregularly and incompletely.

Let us turn, in conclusion, again to the chord of the dominant. We know now, at least in part, the peculiar importance of this chord, as the most sure sign of the scale, as the chord in common of major and minor, whereby it is to them as a bond of union, and as the foundation of both the chords of the ninth. For all these reasons it was not to be affected by the minor mode; its third (the seventh of the tonic) was not to become minor, as we have already said. And on these grounds (better than which are still to come) it is already manifest, as we endeavoured to show at page 24, why the fundamental tone of this important chord, the fifth of the tonic, has received the pre-eminent name of dominant, the governing or directing power.

REMARK.—An uncommonly ingenious and useful representation of the system of scales (keys) has appeared, by C. V. Decker, Berlin, at Mittler's. It is of great assistance in impressing on the mind the various scales, signatures, chords, modulations, &c., and we recommend it particularly to teachers of music in schools and seminaries.

This rule, however, cannot certainly apply to those intervals which are the chief signs by which the chords are known. If we left out the third from a triad, we should no longer distinguish whether it were major or minor. If the seventh were omitted in a chord of the seventh, or a ninth in a chord of the ninth, the former would become merely a triad, and the latter a chord of the seventh. Just so in leaving out the highest or the fundamental tone of a triad, it would become doubtful which of two chords was

intended, whether one without a fundamental tone, or one without a fifth :

251.88 88=

But in the chord of the dominant and chords of the ninth, the fundamental tone may be omitted with a peculiar effect. By this omission, a new triad arises from the chord of the dominant, consisting of minor third and minor fifth (already mentioned at page 67), and is called the diminished triad. Another chord of the seventh, (without any peculiar name), is produced from the major chord of the ninth, with minor third, fifth, and seventh; and from the minor chord of the ninth is produced another chord of the seventh, having a minor third and fifth, and a diminished seventh, which is called the

CHORD OF THE Diminished Seventh.

Here we have the three new chords with their root chords :

252. C'

We will only observe that they are nothing more than the previous chords without their fundamental tones. 3. TRANSPOSITION.

We say a chord is transposed, when its tones, as here at (a)

are removed from their position into other octaves; an alteration which (excepting in the following of thirds) makes no essential difference in the chord.

If in the doubling of the fundamental tone in a triad, the doubling tone or octave lie highest, the arrangement is called the

FIRST POSITION OR OCTAVE POSITION of the chord; if the third lie highest, it is called the SECOND POSITION, OR POSITION OF THE THIRD ; if the fifth lie highest, the

THIRD POSITION, OR POSITION OF THE FIFTH of the chord. Other teachers of music call the position in which the fifth is above, the first,-that where the octave is above, the second,—and where the third is above, the third. These names are of little or no consequence, provided that the expressions be reciprocally understood; but those which we have selected, seemed to us to deserve the preference, since they recognize the most important tone in the most important parts of the chord, as highest and lowest.

Changing the form of a chord will appear more striking, when the fundamental tone itself leaves its place, and ceases to be the lowest tone of the chord. This kind of transposition is called

4. INVERSION OF THE CHORD,

and gives it new names.

Let us examine, therefore, what inversions are possible, and how they are to be called.

When the fundamental tone ceases to be the deepest, some other tone of the chord must of course become so.

we see, by way of example, the two first inversions of a chord of the ninth; at (a), without inversion, and so confused as to be impracticable; at (b) separated from each other by virtue of transposition and practicable. The inversions of the chord of the ninth have received no peculiar name, as they are still more rarely employed than this chord itself. What we have here said of the inversion of one triad, chord of the seventh, and chord of the ninth, applies to every kind of triads and chords of the seventh and of the ninth. Every triad has its two inversions, the 6 and g chords. Every chord of the seventh has its three inversions, its g, 4, and , &c. Now, we can also mark every inverted chord in two ways: first according to its deepest tone; for example

secondly, according to its root, for exampleThe first position of the (major and minor) triad on c, &c.

The latter mode of indication is more circuitous, but more instructive to the scholar; for it shows us that an inversion is certainly a material and striking appearance in a chord, but that it is in no way a change of the chord. The chord

g_b_d_f

remains a chord of the dominant, g continues to be its fundamental tone, f continues to be its seventh, and everything that has been and will be said of it, will continue to be true, whether g, b, d, or f, be its deepest tone. But it may be confusing to retain all the names. The fundamental tone, as the invariable foundation of the chords, might everywhere retain its name. The other intervals we would measure (as is done above) from each lowest tone in the inversions; for instance, in the g chord, b-d-f-g, d (the former fifth) shall be called the third; f(the former seventh) shall be called the fifth; and we may call g (the fundamental tone) the sixth, that is, of the chord.

How are we to recognize a chord among all these transpositions and inversions? The tones must be arranged in higher or lower octaves, until they come to assume the position of thirds. By experiment, therefore, the original position of the chord in thirds is discovered. Tones already in the position of thirds, would not, of course, require altering. If we did not know, for example, by the first inversion of the chord of the ninth (Example 256, b), what to consider it what chord it might be, in the first place, bd and f-a must by all means remain together, for they are already thirds; but d-g and g-f are not so; g is therefore the questionable tone. We therefore place g below, and get this form:8

257.

We now see easily, that fa are to be placed lower. Had we not perceived the opposition of g, we might perhaps have transposed f-a

258.

but seeing the fault, immediately corrected it, by transposing b-d:

259.

With a little practice, the eye and ear soon hit upon the tones required.

We may use chords untransposed (as fundamental chords) or uninverted; and for this end they can be placed in

5. CLOSE OR DISPERSED POSITION,. as close or dispersed harmony. The harmony is called close, when all, or the greater part of the intervals are as near to each other as they can be ; as at (a)

260.

we see at (a) closes imperfect in melody-at (b) imperfect in rhythm-at (c) imperfect in harmony.

A perfect close is required to the true end of a phrase that is at the end of a subject. How then, should we close the opening phrase of a subject? The whole subject, or the closing phrase, was (as we have said above) to be closed from the dominant on the tonic. As therefore, the opening and closing phrases are opposite phrases, distinguished by the contrary motion of their melody, it is natural that the close of the opening phrase should be in contrariety to the close of the closing phrase, or of the whole subject; consequently the opening phrase will close from the tonic on the dominant

In the third place, by giving to the chord of the dominant, which governs the close, a resolution differing from its original direction:—

and thus, instead of going immediately to the closing chord, it deviates into a foreign scale, in order to begin the appendage therein, and thence return into the principal scale, wherein the real close of the phrase will be formed. Such a determination into a new scale, in lieu of the properly indicated and expected close, is called a

FALSE CADENCE.

8. THE PRelude.

It is sometimes advisable, for several reasons, to introduce the performance of music by a foretaste of the art, in order to arouse the attention of the audience, to give the singers the key-note of what they are about to sing, &c; such an introduction is called a prelude.

The most proper use of this performance, is to make known thereby the scale of the music about to be produced.

The simplest way of effecting this object, is to play the tonic chords two or three times in different positions or inversions—

281.

=8=8=8=8 美

with various doublings or repetitions, upwards or downwards, and progressions by gradual ascent or decline, &c.

A more determinate character can be given to a prelude, by the chord of the dominant and tonic triad, as in No. 273. Moreover, either or both of these chords may be interchangeably carried

The following section will give elucidations of the chords from foreign scales employed here and in No. 280. We cannot give in this book more than that which is absolutely essential to those who have not hitherto had, nor perhaps ever will have, time for the study of composition. Everything beyond, more elaborated and more beautiful, must be reserved for that study, or left to the good fortune of those who may seek for it. We will not, however, quit We will not, however, quit the subject, without giving one word of advice to the amateur, which may be sometimes useful to him, and spare him many errors. When he wishes to unite one chord to another, let him endeavour to "hold on" every tone which is common to both chords; and to give every new tone to that Part, which can most conveniently reach it; that is, to that Part whose present tone is nearest to that which is to come. By no means, however, is this hint to be considered as a universally directing rule of art. The accompanying phrases give some examples.

We therefore say: This composition is in such and such a scale, passes into this or that scale, returns into the principal scale. This is its modulation.

Moreover, in the widest sense, all harmonical construction is called modulation.

Some knowledge of modulation is useful to every practitioner of music, were it only to keep him aware of what scale he is playing in, and that thereby he may be able to read the notes and chords with greater ease and certainty. Here we can only mention that which is most necessary.

(A)

LAW OF MODULATION.

Whither, into what scales can we modulate? In general we may answer to this question-that regularly, the principal tone has the predominant power; that it embraces the whole compass of its dependencies, and must govern their manner of closing.

The nearest related scales of both dominant and subdominant, and the relative keys of the principal tone, and of the dominant and subdominant, may be first combined with the principal tone; after which only, and in smaller masses, more distant scales may be associated in the modulation. The latter, however, must be touched in passing only; while in the former we may remain some time to perform a considerable part of the whole composition.

The most important scale in composition in the major mode is (next to that of the principal tone) DOMINANT,

that of the

and in compositions in the minor mode, its RELATIVE MAJOR SCALE. We cannot here dilate on the numerous ex

ceptions to, and further exemplifications of, this rule. (B) MEANS OF MODULATION.

How is the passing to be effected? This question is easily answered if we reflect, that passing, means nothing but changing one scale for another; that is, changing the tones of one scale for the tones of another We pass from C major to Eb major, when we no longer use the succession of tones (or the scale)

c, d, e, f, g, a, b, c, but take the succession of tones (or scale)eb, f, g, ab, bb c, d, eb, as the materials of our composition.