C 717 3 
nous ( 10 ) ; and hence the diateflaron could not be di- 
vided into more than three ratios, nor the diapente into 
more than four j and again, the exceffes of the ratios, 
or intervals in fucceffion, were affigned bv the doc- 
trine of the genera ; fo that in the confonances, each 
of the three limitations had a feparate caufe ; but in 
applying the fame limitations to the tones, there was 
a connection between them ; fo that the determining 
the firft, determined the reft. Thus, for inftance, 
if the interval diateflaron, or fequitertian ratio, lhould 
be affigned for the limitation of the extreme tones, 
the other limitations could only be fuch, as were 
affigned for that confonance ; that is, the component 
ratios muft be three, and the exceffes of thofe ratios 
fuch, as were eftabliffied for the diateflaron by the 
doCtrine of the genera. But the not knowing the 
neceffity of this confequence, he tells us, had occa- 
fioned a great difagreement amongft the harmonicians 
in determining thefe points, fome making the inter- 
val of the extreme tones lefs than a diapafon, others 
equal to it, and others again exceeding it ; the later 
harmonicians, in particular, being fond of adding 
fomething to what had been admitted by thofe, who 
went before them. To bring thefe various opinions 
to fome determination, he propofes the reftitution of 
fimilitude in the hermofmenon, or harmonifed melos, 
as the chief circumftance, by which to regulate the 
(10) ’Ey ttavt) <N yivet atsro 'zrctVTof odoyfx J'ia tcov i'Hf tJ yzh ( 
dybyivov, >9 W/ to £a?v, sy to >1 tov tWa(]ov to </V- 
TZasdfUV, ») TOV ' 73 ‘iy.TfloV S'ta.-TSifli (TVfJ.ZUVOV KAyCstV^jAI. 6) J’ CtV [li- 
J'iTi^L TbT « W aV/xC dll'll, ZKy.Z A«'|f If® Si"0> OTgpf AUAVTAf, ZV Otf <7V[xC r .- 
Cr.Kzv davuydn'M div&t kata Tvf eipHfKit'xs dc.td-y.nf, Ariftox. p. 5-;. 
edit. Meibom. 
firft 
2 Z 2 
