Now, the scales mostly, do not differ in all, but in some only of their tones. E major, for example, agrees with C major in the tones f, g, c, d, and differs through the tones eb, ab, and bb. We need not therefore consider all the tones, but merely those which differ; that is, for example, for the passage from C major to Eb major, only the tones eb, ab, and bb.

But that seems not to be sufficient. The tones eb, ab, and bb, are not in Eb major only. They are also in Ab major, in D major, &c. Their appearance convinces us, probably, that we are not in major, but not that we are in Eb major. We seek, therefore, for a surer sign, and find it in the CHORD OF THE DOMINANT,

for the chord of the dominant of a scale (major and minor) is to be found in no other scale than in that in which its fundamental tone is the dominant; and it is therefore the surest sign of the scale of its tonic. We have seen, for example, page 68, that the chord of the dominant, g, b, d, f, is possible only in C major or minor. When this chord appears in a composition written in G, D, F, Bb major, &c., it indicates to us that we are no longer in the original scale, but in C major or minor. In like manner, if we are in C major, and the chord of the dominant, e, g, b, d, occurs, it shows us that C major is no longer the position of the music, but A major or minor.

Here are a few examples for verification. We pass from

It begins in C major, goes by (a), through the chord of the diminished seventh, to A minor; by (b) through the chord of the dominant, or rather through the

* Among all chords for modulation, none is more convenient than the diminished seventh. In order to be of some service to amateurs, who are generally fond of preluding and exercising their fancy before they study composition, we will say a few words upon this most serviceable caterer for modulation.

The diminished seventh has this peculiarity, that its inversions continuously reproduce the sound of a diminished seventh: for it consists of nothing but minor thirds. If the fundamental tone be placed over the seventh, an extreme second is formed:

287.

A minor. F minor.

thus, by the inversion of gb-df, the extreme second f, is formed. But this is enharmonically equal to a minor third, e consequently

a new diminished seventh has been produced, e- -b-d, which leads us into a new scale. We have then in every chord of the diminished seventh, the introduction to four different scales, that is, the scale in which we are, and three others by modulation. This chord in A minor for example (g-b-d-f), places under our hands, by enharmonic changes, the following modulations besides A minor:Eb

288.

A

C

We pass over many other kinds of changes. More complete directions and explanations are given in the Instructions for Composition.

From this circumstance the old theory connects the doctrine of modulation with the so-called leading tones. The leading tone was sometimes the seventh degree of the scale, as for example in the scale of C major, and e in F major. Hence its Latin name, subsemitonium modi. But if I wish to pass from C to F, is the tone e sufficient for me? or generally, is it a sign of the new scale, F major? Again at other times, the leading tone was to be considered as the tone which distinguished one scale from another. In order, therefore, to pass from C major to F major, bb would be the leading tone; but if it were wished to perform this operation, not bp but e was to be the leading tone, so that the attribute of leading tone was constantly wavering and uncertain. We may learn, however, in the Doctrine of Harmony, that single tones, without any influence in harmony and modulation, can be introduced, for example, as bb, in C major,-without passing into F. So then the doctrine of leading tones is quite unsatisfactory.

cluded chord before us-for example, in No. 290, first the chord c-e-g, then the chord g-b-d-f, &c.

This method of movement, therefore, requires for itself no further consideration. It furnishes us merely the contrary to the following.

3. UNEQUAL MOVEMENT IN THE CHORDS. This consists in the passage of one or more parts of a chord, to a second chord, while the others remain in the first. Here we must distinguish the following forms:

(4) SUSPENSION OR RETARDATION.

A suspension is a tone which moves from one chord into another to which it does not belong, but of which it afterwards forms a part. Here we see

296.

(b)

at (a) the tone g step out of the first chord into the triad f-a-c, and then only, enter into the tone of the chord f, or (technically speaking) resolve itself. At (b) (c) and (d) respectively, e, b, d and b, are cases of suspension. The latter resolve themselves upwards, and come, therefore, from under, and are hence called suspensions from beneath; the others, on the contrary, are called suspensions from above. At(e) (f) and (g) we see suspensions from above and beneath at the same time: f and a resolve themselves from above, b from beneath, d at (g) once from above and once from beneath.

293. 294.

,295.

2. EQUAL MOVEMENT IN THE CHORDS. By this is understood the equal progress of all the parts of a chord from the one to the other, which we have observed in all our harmonic examples, Nos. 250, 292, and others. Since all the parts go step by step with each other, we have every moment a con

Although nature herself has given us the self-originating tones. Cc-g-c-e-g, arising from the vibrations of a string. See page 47, in note, and the author's Composition-lehre, Part I. + For an explanation of this term, see page 83.

We now refer again to the pretended chords of the eleventh and thir teenth, mentioned at page 67, in note. They are nothing but suspensions, which make their appearance over one or more tones of the following chord. The pretended chord of the eleventh shows itself in No. 296, at (f), and the chord of the thirteenth at (g). When we know from the Instructions for Composition (Part I), that, regularly, a suspension tone cannot appear simultaneously with the tone of the chord, whose place it assumes for a time, we shall understand why these pretended chords cannot have a third-instead of this third, the suspension tones, (f and d above), present themselves. This circumstance shews precisely the impropriety of representing a form so easily explained as a chord, which ought indeed to be formed by thirds from the fundamental tone, but which, in this case, begins exactly with having no third at all. If, however, it were wished to explain the suspensions at (f) and (g), by admitting those imagined chords, how many more admissions would be still necessary to explain the other suspensions! Otherwise, most inconsequentially, we must allow some suspensions to be chords, while others are to remain considered as suspensions. And how many double, and therefore perplexing rules, would be necessary to explain such groups of notes-for example, in No. 296, at (a) and (c), the groups f-a-c (eb or e nat.)-g, and c-e-(g)-6), which at one time are real chords, at another, merely suspensions, which have the appearance of chordswhile according to the pure and clear doctrine of suspension, one single law governs all.

until a chord appears in which the sustained tone is contained, whereby it becomes reconciled and endurable to the ear, such a tone is technically called an Organ point.

It forms a strong band of combination to the suite of chords flowing over it, and is employed, occasionally, after an extensive and somewhat violent modulation, to impress and magnify the return of the principal tone. In this case the dominant in the bass is sustained during a more or less extended succession of harmony, to some of whose chords the sustained tone is related, and to others not related. Here is an example of this form of composition :

we see a simple example of such a procedure. The upper part, at (a), has tones in accordance with it; but at (b) tones continue and accompany it which by no means belong to it. It then meets a chord of which it is a harmony. From its manner of proceeding it is called a

PASSING OR TRANSIENT tone.

We can call the tone at (c) also a passing tone, and through it the chord becomes a chord. It is certain, however, that the tone at (d), namely e, does not belong to the chord under it. It begins with the chord, and hinders for a time the right harmonic tone, d, from assuming its place in the chord. Such passing tones as this latter, at (d), are also called EXCHANGING TONES.

Not only one tone alone and not diatonic tones alone, but two or more, and also chromatic tones, may be used as passing tones; as for example, here,

301.

W

The sustained tone g is related to the first chord g-b-d, not to the following chords, a and d-f-a. It is again related in g-b-d-f, in c-e-g, and g-b-d. Again, not related in -a-c, and so forth. The upper parts in such an Organ point generally make a greater display of This figure is melody than is attempted here. applied also to the closing tone of the bass: the tonic is sustained, and the upper parts allowed to wander in manifold harmonical configurations at pleasure. Moreover, in serious and important compositions, the beginning is at times ornamented by this kind of introduction. One of the most dignified examples of this method of beginning is that of the Matthäischen Passion, of Seb. Bach.† Sometimes, in lieu of the bass, an upper part or a middle part, or an upper part and the bass, are sustained. This last is most employed for the closing note; the previous ones, during the course of the composition: the two first (as before said) for the introduction and corroboration of the close.

* Or does it form, perhaps, with a-c-e, a chord of the dominant a-c-e-g? Such a chord would resolve itself into d-f (or f-a and the g as a seventh (page 71), pass to for f. But, as that does not take place here, we cannot consider g as a tone of the chord, as seventh of

e.

+ The beginning of most of the French overtures is a caricature of the Organ point. In these compositions from poverty of harmony, the bass is allowed to stand still.

we see at (a) the minor triad of c following the major; and the minor third, eb, appears in a different part from that which previously had the major third, e; the one part performs e-c, while the other produces c-e eb; therefore the one seems to be in C major and the other in C minor. Herein lies a contradiction, which, however unintelligibly, offends the ear. At (b) we have the same case, excepting that the contradictory tones are separated by passing tones, by means of which, the offence is moderated, if not entirely removed. Very frequently the false relation is occasioned simply by the neglect of the advice we gave at page 73-to let each part proceed by the nearest tone of the following chord. The above modulations might, according to the said advice, have been written thus,

307.

without any false relation.

That other false relations are less repulsive, and that many admitted successions of tones have a falsely related appearance, is quite indubitable. Here are a few examples thereof :

308.

* In this information upon passing tones, imperfect though it be, we think we see a sufficient justificatiou of our assertions in the note at page 74, upon the uncertainty of the so-called leading tones, as signs of

REFLECTIONS.

We see easily after these short elucidations, how immeasurably rich is the web of harmony, and how impossible it would be to include anything like a complete development of it in preparatory lessons, such as we can give in the General Musical Instruction. Such a task can be fulfilled by the Doctrine of Composition only, and is indeed the principal object of that study. In these sections we have pointed out merely so much as will enable the student to acquire a tolerable conception of the different forms he will meet with in composition.

We entertain hopes, however, that this introductory instruction will give him a sure insight into the elements and combination of musical productions, and also greater ease in reading the notation, in comprehension and in performance. But most assuredly a two-fold practice is essential, if this instruction is to produce a fine and abundant harvest.

In the first place, the student must be able to play every scale upon the instrument; then every chord in its positions, transpositions, inversions, and the indicated progressions. Conversely, he must learn to recognise by the ear any given chord, and not only in one, but in all the scales, by gradual and frequent repetition. It is very instructive to the musical perception to practise the tones of each chord separately, and the transition to the chord of the dominant, in such forms as these, for example :309.

and also vocal exercises on the chord of the ninth and its derivations, with clearness and precision. A man knows only that well which he can himself produce, unless hindered by deficiency of physical power and he who cannot recognise and produce by ear any chord or form of composition, so far as his voice will reach, knows it not at all—or at least, has but a very indistinct and imperfect knowledge of it.

In the second place the student must go through, (and, indeed, with indefatigable repetition), complete compositions with the utmost minuteness. In doing this, he must ask himself point by point

What scale do the signature and close indicate? What are its chords?

really and faithfully to read all the parts, and in each part all the notes, constantly, simultaneously, and in the right absolute time (tempo), at once from the book, in a large score. But he who is perfectly at home in the simple mysteries of chords, and in the construction and movements of the parts, is able from a few notes to seize the harmony, from one or two parts to guess in a measure at the others, and so by a swift glance to become master of the score.

But it is also impossible to play upon one instrument, literally, all the parts of an extensive score: nor, were it possible, would it be an advantage. The tones and parts, which in an orchestra flow distinctly and characteristically from the hands of several performers, would form a mass of confused perplexity upon a single instrument. The score

player, therefore, must before all things be able to distinguish the essential from the secondary; to grasp and enhance the former, and to subordinate, or if need be, to sacrifice the latter: but even this could not be done with any certainty of success, without a mature inspection into the inward construction of the composition.

Let every one, therefore, examine how far cultivation is necessary, for his inclination or propensity to music. The more grievously he is sensible of his deficiencies, the more noble and real he may consider his disposition for Art; and the more ardently he strives to supply these deficiencies, the more strongly, by consequent advantages, will his talent be confirmed.

The faculty of playing thorough bass is worth acquiring, because in many compositions, for example, recitatives (chorales also in many elder works) are accompanied by this invention only, without any harmonies in notation.

We will now give the most needful information on this point.

The first question in figuring basses is, what is to be indicated?

If it be merely a succession of intervals, such as octaves, thirds, or sixths, the indications,

all 8va. or alla 3za. or alla 6ta.

(as noted already at page 12) must be written as at (a); or also a simple 8, or 3, or 6, followed by little oblique lines, as at (b):

If a chord is to be signified, a distinction must be made between triads and all other chords.

Triads, as the most simple chords, are understood when no other indications, no other chord, no al unisono (all the parts in unison) no tasto solo, all' 8, &c. are expressly marked.

This case apart, every chord is signified according to its interval, from which its name is derived. Therefore,

6 signifies a chord of 6 (that is, of the bass tone over or under which the cipher is placed);

or signifies a chord of §;

7 signifies a chord of the seventh;
org signifies a chord of g;

or

signifies a chord of ;

2 signifies a chord of the second;
9 signifies a chord of the ninth.

If we wish to indicate a triad, we must employ a
3, or 3, 3
§, or or, or, and so forth;