S C A
[ 26 ]
S C A
the Sura of Octave and lbme lefs Concord ; 'tis evident^ That if we would have the Series of Degrees continued beyond Octave, they are to be continued in the fame Order through a Second as through the Firft Octave, and fo on through a Third and Fourth Octave, l£c. and iuch a Series is what we call the Scale of Mufick. Whereof there are two different Species ; according as the lefs or greater 3d. or the leis or greater 6th. are taken in j for both can never ftand together in relation to the lame Key or Fundamental, i'a as to make a harmonical Scale.
in immediate Succeffion, much lefs in Conionarice, Thus in the firft ^Series, or Scale above-delivered, though the Progreilion be melodious, as the Terms refer to one conv mon Fundamental, yet are there feveral Difcords amoiij. the mutual Relations of the Terms ; e.gr. from 4th to 7th is '32 : 45, and from the greater 2d to the greater <$tb j', 27 : 40, and from the grearer id to 4th is 27 : 32V which are all Dilcords ; and the lame will happen m the fecond Series, See Discord.
From whar we have obferved here, and under the
But if, either ot thele Ways, we afcend from a Funda- Article Key, it appears, That the Seals (uppoles no de"-
mental or given Sound, to an Octave, the Succeffion will terminate Pitch ot Tune; but that being affign d to any
be melodious; tho' the Two make two different Species Key, it marks out the Tune of all the red, wjth relation
ct Melody. Indeed, every Note is Dilcord with regard to it, (hews what Notes can be naturally joyned to any
to the next; but each of them is Concord to the Funda- Key, and thereby teaches the juft and natural Limitations
mental, except the 2d and 7th. In continuing the Series, of Melody: And when the Song is arrived through level
there are two Ways of compounding the Names of thi fimpLe Interval with the Octave. Thu<; A greater or letter Tone or Semi-tone above an Octave, or two Octaves, %£c. or to call them by the Number of Degrees from the Fun- damental, as 9th, 10th, &c. In the two Scales above, the feveral Terms of the Scale are expreffed by the pro- portionable Sections of a Line, represented by 1, the Key or Fundamental of the Series : If we would have the Series exprefled in the whole Numbers ; they will ftand as follows; in each whereof, the greateft Number
1 Keys, yet 'tis ftill the fame natural Scale, only ap- plied to different Fundamentals. If a Series of Sounds be fixed to the Relations of the Scale, 'twill be found ex- ceedingly defective; but this Imperfection is not any Defect in the Scale-, but follows accidentally from its beinp confined to this Condition, which is foreign to the Natute and Office of the Scale of Mufick.
This is the Cafe in mufical Instruments ; and in this confifts their great Deficiency, For, fuppole a Series of Sounds, as thole of an Organ or Harpficord, fixed
thefe Proportions of Length, they will exprefs the true Degrees and Intervals of the Scale of Mufick, as contained in an Octave concinnoufly divided in the Two different Species abovementioncd.
540 :
great Tone
iO = 43 2 : 405
left femi
Tone Tone
great Tone
360 : 324 : 2
lefs great Tone Tone
8 : 270 lefs Tone
216 : 192
great Tone
femi Tone
80 : 162
leis
Tone
great Tone
144 : 135
femi Tone
great Tone
lefs Tone
cxpreffes the longeft Chord, and the other Numbers the the Order of this Scale, and the Ioweft taken at any relt in Order; So that if any Number of Chords be in Pitch of Tune; 'tis evident, i Q . that we can proceed
from any Note, only by one particular Order of Degrees: Since from every Note of the Scde to its Octave is con- tained a different Order of the Tones and Semi-tones, Hence, 2 . we cannot find any Interval required from any Note upwards or downwards; fince the Intervals from every Note to every other, are alfo limited. And hence, 3 . a Song may be fo contrived, that, beginning at a particular Note of the Inftrument, all the Interval^ or other Notes, (hall be found exactly on the Inftrument or in the fixed Series; yet were the Song, though per- fectly Diatonic, begun in any other Note", it would not proceed. In effect, 'tis demonftrable, there can be no I'uch thing as a perfect Scale fixed on Inftruments, i, e. no (uch Scale as from any Note upwards or downwards, (hall contain any harmonical or cencinnous Interval re- quired. The only Remedy for this Defect of Inftruments whole Notes are fixed, muft be by inferring other Notes and Degrees betwixt thofe of the Diatonic Series. Hence lbme Authors fpeak of dividing the Octave into \$ t ig, 20, 24, 26, 31, and other Number of Degrees; but 'tis ealy to conceive, how hard it muft be to perform on Iuch an Inftrument. The belt on't is, we have a Remedy on eafier Terms : For a Scale proceeding by Twelve • Degrees, that is. Thirteen Notes, including the Ex- tremes, to an Octave, makes our Inftruments fo perfect, that we have little Reafon to complain. This, then, is the prefent Scale for Inftruments, viz. Between the Extremes of every Tone of the natural Scale is put a Note, which divides it into two unequal Parts, called Semi-tones ; whence the whole may be called the Semitonic Scale; as containing Twelve Semi-tones betwixt Thirteen Notes, within the Compafs of an Octave. And to preierve the Diafonic Series diftinct, thefe inferted Notes take either the Name of the natural Note next below, with the Mark # called a Sharp ; or the Name of the natural . Note next above, with this Mark k called a Flat. See Flat and Sharp : See alio Semi-tome.
This Scale the Ancients called the Diatonic Scale, be- caufe proceeding by Tones and Semi-tones. See Dia- tonic. The Moderns call it, Amply, The Scale, as be- ing the only one now in Ufe ; and fometimes The natural Scale, becaufe its Degrees and their Order are the moil agreeable and concinnous, and preferable, by the Conient both of Senle and Realbn, to all other Divifions ever inftituted. Thole others, • are the Chromatic and En- harmonic Scales, which, with the Diatonic, made the Three Scales or Genera of Melody of the Ancients. See Genera : See alfo Enharmonic and Chromatic.
Office and Ufe of the Scale of Mufick.
The Defign of the Scale of Mufick, is, To (hew how a Voice may nie and fall, lefs than any harmonical Interval, and thtrtby move from the one Extreme of any Interval to the other, in the moll agreeable Succefiion ot Sounds. The Scale therefore, is a Syftem, exhibiting the whole Principles of Mufick ; which are either harmonical In- tervals (commonly called Concords) or Concinnous Jn- tervals ; the firft are the effential Principles, the others, fubfervient to them, to make the greater Variety. See Concord and Intervals. Accordingly, in the Scale, we Have all the Concords, with their concinnous Degrees, (0 placed, as to make the moll perfect Succeffion of Sounds from any given Fundamental or Key, which is fuppofed to be reprelcnted by 1. 'Tis not to be fuppofed, that the Voice is never to move up and down by any other more immediate Distances than thole of the concinnous Degrees: For though that be the nioft ufiial Movement, yet to move by harmonical Diftanccs, as Concords at once, is not excluded, but is even abfblutely neceffary. In effect, the Degrees were only invented for Variety lake, and that we might not always move up and down by harmonic In- tervals, though thofe are the moft perfect ; the others deriving all their Agreeablenefs from their SuMerviency to them. See Diastem. And that, befides the harmo- nical and concinnous Intervals, which are the immediate
Principles of Mufick, and are directly applied in Praftice; Geometry Fig. J into any Number of equal Parts, there are other difcord Relations, which happen unavoid- 5 or ro, and 'then fubdividing oneof them, as a b, into ably in Mufick, in a kind of accidental and indirect 10 left Parts. This done, if 'one of the larger Divifions Manner: For, in the Succeffion of the feveral Notes of reprefent 10 of any Meafu're ; e.g. 10 Miles, 10 Chains, the Scale, there are to be confidered not only the Relations IO Poles, 10 Feet or 16 Inches; each of the leffer will of thofe that fucceed others immediately ; but alio of reprefent One Mile, or One Chain, Pole, Foot or Inch. thofe betwixt which other Notes intervene. Now the The Ufe of this Scale is very obvious, exemp.gr. To immediate Succeffion may be conducted fo, as to produce lay down a Diftance by it of 32 Miles or 32 Poles, £#- good Melody; and yet among the diftant Notes there I take in my Compaffcs the Interval of three of the may be very grofs Difcords, that would not be allowed larger Divifions, which contain 30, and two of the
fmaller,
See
"Semitonic Scale ' Gamut. Diagram.
For the Scale of Semi-tones For GteiaVs Scale, common- 1
ly called the Gamut
For the Scale of the An-,
cienrs, -commonly called *
the Diagram • * * ■
Scale, a Mathematical Inftrument, coniifting of one or more Lines drawn on Wood, Metal or other Matter, divided into equal or unequal Parts, of great Ufe in laying down Diftances in Proportion; or in mcaiuring Diftances already laid down.
There are Scales of feveral Kinds, accommodated to the feveral Ufes : The principal are the c Plain Scale, the Diagonal Scale, Ouster's Scale, and the Plotting Scale.
'Pla/n Scale, is made, by dividing a Line, as A B {'Tab.
