MUSIC.

Adjuncts. It is then, in some measure, indifferent to the earwhether a transition be made to the one or to the other of theseadjuncts, since each of them has equally two sounds in commonwith the principal mode. Yet the mode of sol seems a little moreeligible; for sol is heard amongst the harmonics of ut, and of con-sequence is implied and signified by ut; whereas ut does notcause fa to be heard, though ut is included in the same soundja.Hence the ear, affected by the mode of ut, is a little more prepos-sessed for the mode of sol than for that of fa. Nothing, likewise,is more frequent, nor more natural, than to pass from the mode ofvt to that of sol. For this reason, as well as to distinguish thetwo fifths one from the other, we call sol the filth above the gene-rator the Dominant sound, and the fifth fit beneath the generatorthe Subdominant. (See these articles.) As we have seen in thepreceding chapter, that, in the series of fifths, we may indiffer-ently pass from one sound to that which is contiguous; in the samemanner, and for the same reason, one may pass from the mode ofsol to the mode of re, after having made a transition from themode of ut to the mode of sol, as from the mode of fa to the modeof si b- But it is necessary to observe, that the ear which hasbeen immediately affected with the principal mode feels always astrong propensity to return to it. Thus the further the mode towhich we make a tumsition is removed from the principal mode,the less time we ought to dwell upon it; or rather, to speak in theterms of the art, the less ought the phrase of that mode to be pro-tracted.

Of the Formation of the Diatonic Scale as used by theGreeks and Moderns.

From this rule, that two sounds which are contiguous may beplaced in immediate succession in the series of fifths, fa, ut, sol, itfollows, that one may form this modulation, or this fundamentalbass, by fifths, sol, ut, sol, ut, fa, ut, fa. Each of the soundswhich forms this modulation, brings necessarily along with itself itsthird major, its fifth, and its octave; (see fig. 8,) insomuch that hewho, for instance, sings the note sol, may be reckoned to sing at thesame time the notes sol, si,re, sol: in the same manner the sound ut inthe fundamental bass brings along with it this modulation, ut, mi,sol, ut; and, in short, the same sound fa brings along with it fa, la,ut,fa. This modulation then, or this fundamental bass, sol, ut,sot, ut, fa, ut, fa, gives the following diatonic series, si, ut, re,mi, fa, sol, la; which is precisely the cnatonic scale of the Greeks.(See fig. 8.) We are ignorant upon what principles they hadformed this scale; but it may be sensibly perceived, that that se-ries arises from the bass,so/, ut, sol, ut,fa, ut,fa; and that of con-sequence this bass is justly called fundamental, as being the realprimitive modulation, that which conducts the ear, and.which itfeels to be implied in (he diatonic modulation, si, ut, re, mi, fa,sol, la. This scale of the Greeks is formed, by means of a funda-mental bass composed of three sounds only, fa, ut, sol: but toform the scale ut, re, mi, fa, sol, la, si, UT, which we use at pre-sent, we must necessarily add to the fundamental bass the note re,and form, with these four sounds,/!!, ut, sol, re, the following fun-damental bass: ut, sol, ut, fa, ut, sol, re, sol, ut; from whencewe deduce the modulation or scale, ut, re, mi, fa, sol, la. si, UT.In effect, ut in the scale belongs to the harmony of ut which cor-responds with it in the bass; re, which is the second note in thegamut, is included in the harmony of sol, the second note of thebass; mi, the third note of the gamut, is a natural harmonic of ut,which is the third sound in the bass, &c. Thence it follows, thatthe diatonic scale of the Greeks is, at least in some respects, moresimple than ours; since the scale of the Greeks may be formedalone from the mode proper to ut; whereas ours is originally andprimitively formed, not only from the mode of ut {fa, at, sol,)but likewise from the mode of sol, (ut, sol, re.) It likewise ap-pears, that this last scale consists of two parts; of which the one,ut, re, mi, fa, sol, is in the mode of ut; and the other, sot, la, si,ut, in that of sol. For this reason the note sol is found to be twicerepeated in immediate succession in this scale; once as the fifth ofut, which corresponds with it in the fundamental bass; and again,as the octave of sol, which immediately follows ut in the same bass.As to what remains, these two consecutive sols are otherwise inperfect unison. For this reason we are satisfied with singing onlyone of them when one modulates the scale ut, re, mi, fa, sol, la,si, UT: but this does not prevent us from employing a pause or

repose, expressed or understood, after the sotmdyii. There is noperson who does not perceive this whilst he himself sings the scale.The scale of the moderns then, may be considered as consisting oftwo tetrachords, disjunctive indeed, but perfectly similar one tothe other, ut, re, mi, fa, and sol, la, si, ut, one in the mode of ut,the other in that of sol. For what remains, we shall see in thesequel by what artifice one may cause the scale ut, re, mi, fa, sol,la, si, UT, to be regarded as belonging to the mode of ut alone.'Fhe introduction of the mode proper to sol in the fundamentalbass has this happy effect, that the notes fa, sol, la, si, may imme-diately succeed each other in ascending the scale, which cannotlake [dace in the diatonic series of the Greeks, because that seriesis formed from the mode of ui alone. From whence it follows; 1.That we change the mode at every time when we modulate three,notes in succession. 2. That if these three notes are sung in suc-cession in the scale ut, re, mi, fa, sol, la, si, UT, this cannot bedone but by the assistance of a pause expressed or understood afterthe note j'a ; insomuch, that the three tones fa, sol, la, si, (threeonly because tile; note sol which is repeated is not enumerated) aresupposed to belong to two different tetrachords. It. ought notthen to surprise us, that we feel some difficulty whilst we ascendthe scale in singing three tones in succession, because this is im-practicable without changing the mode ; and if one pauses in thesame mode, the fourth sound above the first note will never behigher than a semitone above that which immediately precedes it;as may be seen by til, re, mi, fa, and by sol, la, si, ut, wherethere is no more than a semitone between mi and/h, and between.si and ut.

Of Reposes, or Cadences.

Tn a fundamental bass whose procedure is by fifths, there alwaysis, or always may be, a repose, or crisis, in which the mind ac-quiesces in its transition from one sound to another: but a reposemay be more or less distinctly signified, and of consequence moreor less perfect.. If one should rise by fifths; if, for instance, wepass from ut to.sol; it is the generator which passes to one of thesefifths, and this fifth was already pre-existent in its generator: butthe generator exists no longer in this fifth ; and the ear, as this ge-nerator is the principle of all harmony, and of all melody, feels adesire to it. Thus the transition from a sound lo its fifth inascent, is termed an imperfect repose, or imperfect cadence ; hutthe transition from any sound to its fifth in descent, is denominateda perfect cadence, or an absolute repose: it is the offspring whichreturns to its generator, and, as it were, recovers its existence oncemore in. that generator itself, with which when sounding it re-sounds. Amongst absolute reposes, there are some more absolute,that is to say, more perfect, than others. Thus in the fund a-,mental bass ut, sol, ut,fa, ut, sol, re, sol, ut, which forms the dia-tonic scale of the moderns, there is an absolute repose from re tosol, as from sol to ut: yet this last absolute repose is more perfectthan the preceding, because the ear, prepossessed with the modeof ut by the multiplied impression of the sound ut which it hasalready heard thrice before, feels a desire to return to the gene-rator ut; and it accordingly does so by the absolute repose sol, ut.What is commonly called cadence in melody, ought not to be.confounded with what we name cadence in harmony. In the firstcase, this word only signifies an agreeable and rapid alteration be-tween two contiguous sounds, called likewise trill or shake ; in thesecond, it signifies a repose or close. It is, however, true, thatthis shake implies, or at least frequently enough presages, a repose,either present or impending, in the fundamental bass. (See ■Trill.) Since there is a repose in passing from one sound to an-other in the fundamental bass, there is also a repose in passing fromone note to another in the diatonic scale, which is formed from it,and which this bass represents; and as the absolute repose sol ut,is of all others the most perfect in the fundamental bliss, the re-pose from si to ut, which answers to it in the scale, and which islikewise terminated by the generator, is for that reason the mostperfect of all others in the diatonic scale ascending. It j s then,alaw dictated by nature itself, that if you would ascend diatonic?,11 vto the generator of a mode, you. can only do this by means of, thethird major from the fifth of that very generator. This third ma-jor, which, with the generator, forms a semitone, has for that rea-son been called the sensible note, as introducing the generator,and preparing us for the most perfect repose. As the fundamental,

+ bass