210. Allegretto. The close of the fourth bar would be c in a value of three quavers; but c becomes immediately, the beginning of the repetition, which (in respect of rhythmical arrangement) must be considered as a second phrase; and moreover, in virtue of the sign of repetition, the same c serves as a close for the said second phrase (that is, the repetition); and for the beginning of a third one, quite new, of which only two bars are written above. There are no exterior marks, none at least which are satisfactory, for these greater rhythmical sections. Sometimes large sections, large divisions of the whole, are marked with closing lines (with or without the sign of repetition), or with the intervening words al fine. Sometimes, if the closing and recommencement is in tailed notes (quavers, semiquavers, &c.) the beginning of the second section is made perceptible, by writing separately the closing and beginning notes, which would otherwise be bound by a line of duration. For example, as at (a), not as at (b) :211. (a) (b) But these intimations are not always given, and are never sufficient for the rhythmic direction of a whole composition. After the knowledge of rhythm, at least so far as it is here communicated,* and of harmony and construction, of which we have something more to say, although complete satisfaction is to be had only in the doctrine of composition, the observant student is committed to his own judgment and attentive consideration, which will in most cases lead him aright. FOURTH SECTION.-MELODIC GRACES. We have now to speak concerning a few figures in melody, and to show the usual mode of marking them. We limit ourselves to essential and practical observations, casting aside those subtle distinctions, and that long list of names, with which it was the fashion during many years for professors to torment their scholars and themselves. 1. THE APPOGGIATURA. By appoggiatura is understood a note written in a small character, and placed before a note of a melody, as it were by accident or unnecessarily. There are two kinds of appoggiaturas, which must be distinguished, the long and the short THE LONG APPOGGIATURA is written, according to the value of the note before which it is placed, in a note of the same or half its And in the Appendix A. In the execution of a turn, the upper and under tones are taken as intimated by the signature; thus, in the foregoing cases, Nos. 218 and 220, not ƒ but f, because the latter is so signatured. If one or the other, or both the tones of the turn are to be raised or lowered, the requisite sign is placed over or under the sign of the turn, in the relative position in notation of the tone to be altered. These turns (the signature of F being always understood), for example 221. are performed thus:222 We have seen cursorily in No. 217, that turns may begin by the upper or by the under tone; that there are turns from above and from below. This distinction is not shown by the sign of the turn alone. The choice, therefore, of either is left to the executants, if the composer do not point out which he intends to be played. If several notes are placed over each other on the staff, the sign for a turn is placed either over the upper note or under the lowest. Here for example— Shakes upon two notes at once, thus h 231. h are called DOUBLE SHAKES. A series of shakes upon several tones, thus is called A CHAIN OF SHAKES. All these and similar melodic forms are comprised under the term of GRACES, because they are in general merely an arbitrary E BASS (the lowest part), which first became known to us (page 46) as the chief kinds of singing parts. When two or more successions of tones are to be heard simultaneously, they must be in some compatible relation towards each other, according to the rules of art. This relation of different tones is called harmony. We must seek how two, three, or more tones become thus harmoniously related. All harmonic combinations originate from thirds. Why this is so, and all its consequences, cannot be demonstrated here, but must be referred to the science of music and art of composition.* * We will, however, say thus much. Our conviction that we derive all our harmonic constructions from a combination of thirds, is not the result of arbitrary, accidental, or unenlightened observation, because it is founded on scientific demonstration. It has been proved that the tones nearest related to each other (as mentioned at page 17), are the octave, the fifth above it, the next octave, the third above-this latter, the octave of the previous fifth, and finally, a tone which we in our system must consider as the nearest flat seventh. Therefore, from C there are first the tones and then, one step further, C, c, g, c, e, g, C, c, g, c, e, g, bb which tones (as before said) are in the relation towards each other of of the chord, or of the fundamental tone. A chord of four tones is called,-from the fourth tone, which it is in reality from the fundamental tone, and by which it is distinguished from a triad,— THE CHORD OF THE SEVENTH. A chord of five tones, is called from the accruing fifth tone, by which it is distinguished from the chord of the seventh, THE CHORD OF THE NINTH.† 1:2:8:4:5:6:7 (estimating the relation by the number of vibrations in a given time.) Let us now omit the three first supernumerary tones (1:2:3) and assemble the following which lie nearest to each other, and we shall then have a structure in thirds, which comprises both the two principal chords : and c. e, g. c, e, g, bb (the great triad and the chord of the dominant), out of and according to which, all other chords are formed. All harmony is to be deduced from this one, or it may be said, these two root-chords, as the author thinks he has proved in his doctrine of composition, with full evidence of reason existing in the art itself, but not to be found in the books of instruction. Gott. Weber, among others, places a row of chords mechanically together, as they are found near each other in the scale: and of necessity, having lost the natural and scientific foundation, he is betrayed into numberless deviations and perplexing doubts, while-if what is essential alone were held in view-ONE SINGLE FUNDAMENTAL PRINCIPLE FOR ALL HARMONY is sufficient. And moreover, this principle is so simple and comprehensible, that a boy can understand and retain it. A new teacher of harmony has even ventured on the extraordinary idea of considering the minor triad, as the second fundamental chord. It is no wonder that such modes of teaching should drag the students along through years-whereas, a system founded on reason gives more, and safer, and better grounded knowledge in three months, nay, in twenty or thirty lessons. + Are there not chords of more than five tones? Some theorists have formed such. They say there are chords of two tones, thus :236. of three, four, and five tones, which they exhibit thus: 237. and further chords of six tones-chords of the eleventh : 238. If therefore we ask again, how two or more tones can become harmonically related to each other, we are answered First, by their forming a chord together. Which tones are susceptible of this combination, and how they are to retain their functions as parts of the union, we are now to examine more minutely. We know well so far, that to a fundamental tone, a third, fifth, &c. may be combined; but not what kind of a third, fifth, &c., since, as we are aware, the names of the intervals do not determine their quantities nor values. After we have considered the subject of chords, other forms of harmonic combination will come under review. This will be more conveniently done in separate sections. Otherwise, it is not the function of general musical instruction to elucidate completely all these forms (if that indeed were possible), but to introduce and exemplify the fundamental forms and their chief application. Beyond this, belongs to composition.* SIXTH SECTION. THE MOST IMPORTANT We seek now for the most important and nearest chords in major and minor, beginning with the triads as the most simple chords, in order to proceed from them to the more numerous and complex chords of the seventh and of the ninth. As the major and minor modes are each respectively similar among themselves, what we say with regard to one major mode, or to one minor mode, will avail for all the rest of the same modes. 1. THE MOST IMPORTANT TRIADS. Which are in general the most important tones in and of seven tones-chords of the thirteenth →→ 239. More there could not be; since the next third, the eighth tone, was nothing but the second octave of the fundamental tone, and therefore not a new tone. But they must themselves confess, that their chords of the eleventh and thirteenth, as they give them, are never employed, nor can be employed (we mean apparently cannot; see the author's Instruction for Composition, Part I), excepting they be essentially altered, by the omission of several of the tones. This scheme, therefore, is arbitrary, and contradictory to all the previous notions of harmony, long since acquired by the student. If it were desired to begin by two tones (which is quite useless), the first (or rather, indeed, the only one given by nature) would be the fifth and not the third. And in like manner, the first chord of the seventh (the only one produced by nature), is not c, e, g, b, but c, e, g, bb. And the first chord of the ninth (as well as the pretended chords of the eleventh and thirteenth), in the same manner, is not to be founded on c, e, g, b, but on c, e, g, bb. Moreover it is matter of history, that every development of harmony has been attained by following the path indicated by nature; as every real historical progress must have been conformable to reason. In short, these chords, as the theorists have displayed them, are merely mechanical contrivances; methodical indeed, but ill-imagined auxiliaries, in contradiction to the reality of art and to the true system of the connexion of tones; and apparently render the study of harmony more difficult and confused, in lieu of offering the facilitations for which they were invented. The chords of two tones are also a purely mechanical contrivance. The chord given to us by nature the first rational true chord-is a triad, the major triad. From this the chord of the dominant and of the ninth proceed; and only from this latter can the chord of the eleventh come into existence-therefore, from the dominant. In this sense the author was obliged to employ a chord of the eleventh (perhaps the first ever used) in his Mosé, (page 168 of the score), impelled by the feeling of the moment. More intimate details in this matter will be found in the Instructions for Composition, and in the Science of Music. * The chords, as well as the intervals, have been divided into consonant and dissonant. The major and minor triad, with their inversions, are called consonant-all other chords, dissonant, Here as formerly, and on the same grounds, we must banish all ideas of consonant and dissonant, and the distinction altogether, as idle and useless. In old books of instruction this is also called the perfect triad, although naturally it is not more perfect than any other chord, and also (as we shall hereafter find) can be imperfectly employed; that is, it can be deprived of one of its intervals, without becoming thereby another chord. This also, in the old language of teaching, was called the false triad, from its having a so-called false fifth; although, in its proper place, it is as correct as any other chord in its own place. 2. THE CHORD OF THE DOMINANT SEVENTH. If we add a third (the seventh of the fundamental tone) to the triad of the dominant major or minor, as it is found in the scale, we form a chord of the seventh, whose fundamental tone is the dominant, and which for shortness we call the CHORD OF THE DOMINANT,* and moreover to distinguish it from other chords of the seventh, which we shall become acquainted with hereafter. This chord has, besides the fundamental tone, A MAJOR THIRD, MAJOR FIFTH, and MINOR SEVENTH, and is the same in the major or minor modes. It has another peculiar property. Every chord of the dominant is to be found in its scale only: that is, it can be constructed out of the tones of its scale only. The chord of the dominant of C major or minor can be fonnd only in C major or minor; in no other major or minor scale. The triad c-e-g, for example, may appear as tonic triad in C major; as dominant triad in F major; as subdominant triad in G major; and in other combinations. How do we show that property of the chord of the dominant? Let us consider any major scale,-for instance, C major. On the one side, the scales with sharps are shut against it,-in the first instance, G major with f instead of f: on the other side, the scales with flats-first that of F major, with bb in lieu of b natural. Now, what constitutes the chord of the dominant of C major? g—b-d-f. Can this chord be constructed in G major? No, f is wanting-it is changed into f; therefore the chord, g-b-d-f cannot be formed in G major; therefore it cannot in any other scale with sharps, for in them all, f remains instead of ƒ natural. But can it be constructed in F major? Again, no; for in F major we have bb instead of b natural; consequently g-b-d-f cannot be found in any scale with flats, since they have all bb instead of b natural. The same proof might be gone through in the minor modes. This observation we consider important. Since the chord of the dominant is possible only in one scale, major and minor, it serves us as the most sure SIGN OF THE SCALE. The signature (as we have seen at page 23) cannot serve us for that purpose, since each signature is employed in common for two scales, the relative keys. A composition without signature may be either in C major or A minor. Also, the last deepest tone may be some other than the tonic. A two-part passage in C major may close thus:— 243. and is not always therefore a definite sign (page 23), It has been called also the chief chord of the seventh, because it certainly is the most important chord of the seventh. We prefer the shortest name. Some older theorists have called it the leading chord, because it leads to the tonic triad: but the name is inexact, because other chords also do the same, while the chord of the dominant leads not only into the tonic triad, but also into other chords.t It may not have been generally observed, that the chord of the dominant seventh is formed essentially of the dominant and subdominant. Hence its strong impulsion to the tonic to which it is thus doubly related.-TRANSLATOR. but the chord of the dominant always is so. The moment we hear, g-b-d-f, we are quite sure that the scale is C major or minor. So soon as we hear e—g—b—d, we know that the scale must be A major or minor. The chord of the dominant shows the scale, but not the mode, whether it be major or minor. What now is the surest INDICATION OF THE MODE? The tonic triad following the chord of the dominant at the close; for it gives us, besides the tonic, the decisive third. But this rule is not without exception; for sometimes compositions in a minor mode close with a major triad. This conclusion was a special favorite with the old ecclesiastical composers. Other chords of the seventh are constructed from the chord of the dominant by arbitrary changes of one or other of its tones; thus, by raising the seventh or depressing the third, these two chords are formed: 244. f g Lg E and others also. Upon what grounds and with what right these changes are made, and how such chords are to be employed, will be shown in the instruction for composition. 3. THE CHIEF CHORD OF THE NINTH. If we extend the chord of the dominant in major and minor, by the addition of a third (the ninth of the fundamental tone) we form chords of the ninth, but differing in mode. In C major, for instance (from the tones of C major), we find g-b-d-f—a to be the chord of the ninth |
