[ 6 9 8 ] 
leaft more methodically than any other, of which we 
can now form a judgment j and hence we find their 
divifions often adopted by antient writers, who might 
not, perhaps, be ready to admit all their principles. 
In confidering the phyficai properties of found, and 
the ratios of intervals, the Ariftoxenians appear to 
have been lefs exadt than the Pythagoreans, the doc- 
trines of the former being more adapted to the grofs 
and familiar notions of the practical mulician, than 
to the accurate fpeculations of the philofopher. But, 
however exceptionable their treatifes may have been 
in this refpedt, they are the more valuable to us, on 
this very account, as they give more light into the an- 
tient practice of mufic ; which is what is chiefly de- 
fired, the philofophic principles of the fcience being 
better underftood. By this fchool harmonic was di- 
vided into thefe feven parts ; I . of founds, 2 . of in- 
tervals, 3. of genera, 4* fyftems, tones, 
6. of mutations, 7. of melopceia. The propriety of 
their adding this laft divifion I (hall have occafion to 
confider. Of thefe divifions, it was the fifth, which 
contained the dodtrine in cjueftion j but, to complete 
it, the fixth muft alfo be taken in ; for, amongft 
other mutations, that of the tones was there treated 
of, and was indeed the mod confiderable objedf of 
that divifion. This dodtrine taught, that the dif- 
ference between one tone and another lay in the ten- 
don or pitch of the fyftem. dhe fyftem (by which 
I mean the greater perfedt one, exclufive of the lets, 
of which I fhall have little occafion to fpeak) con- 
lifted of fifteen founds, extending to a difdiapafon, or 
double odtave. Plow thefe founds were denominated, 
* and at what intervals they fucceeded each other, in 
the 
