I

( 7 °° )

Lastly, if from that of the Tri-hcmitonc ( or Lejscr Third ) la, mi, f n .whose Proportion is as 6 to 5; wc take that os the 'Lene, la, mi ( which isthe Difference of a F ottrth and Fifth ) as 9 to 8; thcre remains for the

9 _, 6 ,48

Bemi-tone, jni, fa, (or la,fa,) that of 16 to iy. That is

Or, the Tri-hemitone ( or Lejscr T hirci') whose Proportion is as 6 to y,tnay be divided into three. near Equals, (by taking Triple Nnmbers, in the(äme Proportion 18, 1 5; and interpofmg the two Intermediäres 17, 16; )which will therefore bc as 18 to 17, and as 17 to j 6, and as \6 to iy.j

That is.

Where also the Grcatcr Tone, whose Proportion is as 9 to 8, or 18 to 16,is divided into ifs two near Equals ( commonly called Hemitones, ) that 0 £

18 to 17, and that of 17 to 16: That is, — x —— —-— — —

17 16 16 8

And the Lcffer Tone, that of I o to 9, or io to 18, may be in likemannet Divided into that of 2.0 to 19, and that of 19 to 18: That is,

2.0 19 i.o. 1Q

Which Divisions of the Grcatcr and Lejscr Tene, answcr to wbat is wont.be designed by Fiats and -Sharps.

So that (by this Komputation, ) of these Eight Notes, la, fa, sol, la, mi,

fa,Jol, la ; .their Proportion« stand thus j that of ia, fm ( or mi,fa) is asi6to iy.. That of fa sol as io to 9, and that of sä la as 9 to 8 : (or eile.that of fa sl, as'9 to 8, and that of Jol la, as. 10 to 9,) That of la, mi,as 9 to 8. And if either of the Tonci (Grcatcr or Leser chance ro be divi-

ded ( by Flati or Sharps ) into (what they call) I-femi- tones, their Propor-tion« are to be stich as is already mentioned*

There may be a like Division of a Fcurih, for Dia-tcfscron) into Tro Nearequals : And of forne others of these, into-three Near-rquals. Whieh mightbe of use for ( what they werc wont to call) the Climiu.ick and Enarmonicis

Mustek. But those forts of Mustek, having been lovig fince laid aside, thereis now no need of these Divisions, as to the Mustek now in use:

TU mperfelFton IV. I tliink ’tis Evident that eaehi/tye ^1 the Organ is intended to Express

c f an Organ ;by Dr. J. Walfis. n. 342,

f. 348 *

;aa j . a Distinct Sound at loch a Pitch ; that is, in such a Determinate Degree of-

Gravity or AcutcneJ } j or ( as it is now called ) Flatnefs or Sharpness And theRelative or Comparative Consideratiori of Two ( or more) such Sounds orDegreesof Flatnefs and Sliarpncfs, is the Ground of ( what we call J Concord,and Difetrd ; that is, a Soft, or HarCh,.Coincidencc..

Now,