[ 7*8 ] 
flrft limitation ; and this, he fays, is effe&ed by the 
diapafon, for, at that diftance, there was always a 
return of fimilar harmony ; fo that the tone, that was 
a diapafon diftant from that flrft taken, was a repeti- 
tion of it ; and the tone ftill farther diftant, as for in- 
ftance, at a diapafon and diateflaron, the fame with 
the tone diftant a diateflaron only, and fo of the reft. 
For a proof of this, he appeals to the practice of 
mufic ; where it was well known, that in fuch mu- 
tations, as were at the interval of a diapafon, no one of 
the firings required new tuning, though in all other 
mutations fome alterations were neceflary. And 
hence he concludes, that thofe, who make the diftance 
of the extreme tones lefs than the diapafon, do not 
reftitute the hermofmenon, there being ftill other 
tones beyond the limit they aflign, unlike to thofe 
before taken 5 and that thofe, who exceed the diapa- 
fon, admit redundancies, by repeating fome of the 
harmonies before taken ; and further inftfts, that even 
they, who proceeded no farther than the diapafon, 
were yet to blame, inafmuch as they took in the 
tone, that was a diapafon diftant from the firft, fince, 
in fo doing, they admitted one redundancy, and 
thereby gave a handle to thofe, whom they charged 
with pafling the proper limits for the modes, to accufe 
them, in turn, with being really the authors of this 
licence, fince, if one ufelefs tone be admitted, the 
fame privilege may be fairly claimed for a greater 
number. This laft argument feems levelled at the 
Ariftoxenians, who admitted no more than thirteen 
modes ; bccaufe they would not exceed the diapafon; 
but whofe Hyperphrygian was, according to this 
argument, a repetition of the Hypodorian. The 
author 
