. C 75 ) 
cords are iimired, Difcords infinite. Among all which 
he has herein treated only of fuch as are ufefui in Mu- 
fick, and given their feveral Proportions, Caufes^ P^e- 
lations, and Conipofitions, by defined Numbers, where- 
in doth lye the EfTence of Harmony and Mufick. He 
therefore judged this much preferrable to the Ari- 
ftoxenian way of dividing a Tone major into Twel'/e 
equal Parts , of which 3 made a Diejis^ 6 Hemitone , 
30 Diatefferotj &c. For that neither this^ nor Mr. Mer- 
catorSy nor any other like late Attempts could produce 
true Intervals, though they did approach them, nor 
give the true Grounds and Caufes of Harmony, which 
are afforded by this Rational way of true Proportions. 
Nor could they without mofiftrous Difficulty be imita- 
ted by the Voice, but the Voice endeavouring at them 
will naturally fall into the true Intervals that are pretty 
near them ; as the Voice endeavouring at the Ancient 
D/V(?;/^ of two Tones major will fall into that of 5 
to 4, or Tone major and Tone minor : Befides that 'tis 
unreafonable to meafure Irrtervals by irrational Num» 
bers, when they may fo eafily, naturally, and intelli- 
gibly be adjufted by fmaller Numbers, and more eaOe 
to be comprehended. 
It was not his Defign to meddle with the Metrick 
part of Mufick, concerning Compofition, Air, and Hu- 
mour ( which afford infinite Curious Difquifitions con- 
cerning it ; as to its EfTeds upon the PafTions caufed by 
different Scales of Tones, as flats and ftiarps ; or dif- 
ferent varieties of Times, as quicker or flower ; or dif- 
ferences of Inftruments for the produdions of them , 
aod why fome are more adapt for the purpofes tbaa 
others ) Nor to treat of the Receptive Faculties of Per» 
fons from the diiferent Conflitution of. their Organs of 
Hearing; nor to fliew why fome have and others want 
Mufical Ears ; nor to treat of other curious Speculations 
; concerning Mufick^which will afford the acuteft Philofo» 
phet 
