[ 7 20 3 
The number of the fpecles of diapafon was equal to 
that of the fpecies of the two hr ft confonances taken 
together, and the fpecies of thefe laft were taken ac- 
cording to the condition of the ratios in each, the 
number of which the very nature of them would 
not permit to be either increafed or dimmiflied. Now 
the tones contained within the diapafon following 
the nature of the confonances, and being indeed efta- 
blilhed on their account, viz. that the whole lyltems 
might have confonant differences, he argues, that 
thofe, who were either for admitting more than feven, 
which was the number both of the fpecies and of the 
ratios in the diapafon, or for making all the excefles 
of the tones equal, were not to be afiented to, fince 
they could not affign any fatisfadory reafon either 
for the equality of the increments in general, which, in 
the harmonic genus, was particularly inconvenient, 
or for fixing either on the tone, hemitone, or dielis, 
in particular, for the common excefs, (from the fup- 
pofition of one or other of which, they determined 
the number of tones, according to the number of 
fuch intervals contained within the diapafon). roi 
what was there to determine fuch a preference, when 
the confonance (meaning the diapafon) was, as they 
themfelves allowed, fufceptible not only of all thefe 
excefles, but of many others, in the orders both of 
the genera and of the diftances? Nor could they fay, 
that fuch a magnitude divides the diapafon exadly, 
and fuch another not exadly, or one, perhaps, into 
an even number of parts, and another into an uneven : 
for though the diapafon was divided into fix by the 
tone, into twelve by the hemitone, into eighteen by 
the third of the tone, and into twenty-four by the 
quarter. 
