C 742 ] 
tilde of fenfe. And this might be the reafon why they 
omitted taking notice of that circumftance attending 
this mode j though we might perhaps* with fafety to 
the argument, go a ftep farther, and fuppofe, that 
the Ariftoxenians might think a difference of an 
odtave in pitch worthy of a diftindt denomination, 
though they would not allow it to that of a femi- 
tone. And this is the more probable,, as we find they 
did not abfolutely rejedt thefe modes, as Ptolemey 
did, but admitted them upon the principles of the 
harmonic dodtrine, though, by their denominating 
five of them from the genuine modes, it is plain 
they acknowleged them to be fuperfluous, in reipedt 
to the mufical. I cannot fay more to this point, 
without defrauding the fubfequent ones j and I fhall 
therefore leave it, with this rerfiark, that whatever is 
proved of the fubfequent points, and efpecially of the 
fifth, muft hold true of this, a fortiori ; fo that it 
may really be faid to have the fupport of the whole 
teftimony. 
2. To the fecond point, the firft diagram fpeaks 
very firongly ; for had the two dodtrines no relation 
to each other, no fuch coincidence, as is there found, 
could have been expedted, in the rel'ult of their com- 
bination ; and this proof, from the coincidence of the 
dodtrines in the diagram, becomes much ftronger, if 
we attend to thefe two circumftances. Firft, That in 
the canon, upon which the diagram has been con- 
ftrudted, there is no ftrain of either dodtrine, but a 
plain and natural combination of them, as they are 
ftated feparately by the antient writers. And fecondly, 
That the fpecies of diapafon, as brought out by this 
combination, all Fill upon the firings of the old 
odtachord 
