C 7*9 3 
author fupports this argument dill farther, by an 
appeal to the circumdance of the fpecies of diapafon, 
the founds of which were eight, but the number of 
the fpecies feven only, anfwering not to the number 
of terms in the divifion, but to that of the component 
ratios : for that the diapafon taken from the graved 
found towards the grave, yielded the fame fpecies 
with the firft diapafon taken from the acuted found 
towards the fame parts, was out of difpute, it hold- 
ing true univerfally, that whatever takes its beginning 
in the fame manner from either of the extremes of the 
diapafon, produces the fame power. And here he 
leaves the fird limitation, without exprefly afligning 
the interval for the extreme tones ; for the title of the 
chapter, which' feems to fix it to a diapafon, ought 
to be underdood only in this fenfe, that it fhould not 
exceed it 5 which agrees with the reafoning in the 
chapter itfelf. As to the conclufion, which depended 
on the two other limitations, if I may venture to 
draw it for him, it will dand thus, that into what 
number foever of terms the diapafon be divided, the 
didance for the extreme tones fhould be the interval 
between the fird term and the lad but one. 
The fird limitation being thus far confidered, he 
proceeds to determine the next, upon which de- 
pended the number of the tones ; and here he again 
oppofes the Aridoxenians, rejecting, by his theory of 
this limitation, five of their thirteen modes, befides 
the Hyperphrygian, which flood condemned by the 
former one, and leaving only feven, according to the 
number of the fpecies of diapafon, which he pro- 
pofes as the properefl rule, by which to govern this 
limitation 3 and affigns for this the following reafons. 
The- 
