( 699 ):

sente .) And thefe two put together, make up that of an OB ave ( or Diu'fason, ) that of 4 to z, ( or z to i.?) And the Difference of thofe two, that

os a TW, or 9 to 8. Äs will plainly appear in the ordinary Method of

4 ^

Muhiflying and Divicling Fraftzons, That is, -f- ———-~ —. And

3 i z i

Xhus in the comttion S«/e (or Gam-vt) takingan OBave, in .thefe Notes,Ia, fa,fil, la, missa, sol, ia ; fiippofe, from E to e ( placing mi, B-fa-b-mi :which is called the 'Natur al Scah ;) the Lengths for the Extremes i a, ia, anOBave, are as i to i, or iz to 6. Thofe for ia, la , ( in ia,fa,fil , la, ) ormi, la, ( in mi, fa,sol, la,) a Fcurtb, as 4 to 3, or rz to 9, or 8 to 6. Thofe

for la, mi, (in la,fa,Jol, la,rnlf) or la, la, ( in la, mi, fa, sol, la,) a Fifth, 'as3 to z, or i z to 8, or 9 to 6. Thofe for la, mi, the Dia^euticsTone. ( orDifference of a F ourth and Fifth,) as 9 to 8. Sohave \ve for thofe four Notes

ia, la, mi, la, their Proportionatc Lcngth in the Numbers iz, 9,8,6.

Then if we prcceed in lilte tnanner, to Divide a Fifth ( or Dia-pente ) la,fa,sol, la, mi, or ia, mi, f a, sol, la, or the Proportion of 3 to z, into near E-quals, ( taking double Numbers in the ferne Proportion, 6 , 4; and interpo-fing the middleNuruber 54 ) of these three Numbers, 6, 5, 4; that of 6 to y.

is the Proportion of a Leser Third, ( called a Tri-hemitone, or Tone and half, )as la, fa, ( in ia, mi, fa. ) And that of y to 4, is the Proportion of the

Grcater Third, ( commonly call’d a Ditons , or two Tones,) assa, la, (in fa,

(j C

sol,la,) which two put together make a. Fifth, as 3 to z j that is — x -4—

5 4

And their Difference is, as zy to Z4: That is

So have we for thefe 3 Notes la, fa, la, their Proportionale Lengths in Num-bers, as 6, y, 4.

In like manner, if we divide a Ditonc, ( or Grcater Third, ) as fa, la, ( infa, sol, la, ) whofe Proportion is as y to 4, ( or 10 to 8,) into two near E-quals ( by help of a ntiddlc Nurnber 9 ,1 then havewe (in thefe. three Num-bers 1 o, 9, 8,) that of 1 o to 9, for ( what they cali ) the Lcjscr Tone ; 1 andthat of 9 to 8, for ( what they call y ,the Gr.eatcr Tone.

But, whether fa,fil, fhall be made the Leffer (as 10 to 9,) and sol, 'a, ,th<Grcater, ( as 9 to 8 ; ) or, This the Leser, (as 10 to 9,) and That theGreater, (as 9 to 8,) or forne time, This, fonte time That, as there isOccafion, (to avoid what they.call a Schis, n ; ) is somewhat indifferent .For, either way, the Compound will be, as y to, 4; and the Differenc e :

which they call a Comma, ) as 81 to 80. That is x —

8 V 80'

U u u u z

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