i '° 4 1 
in the harmonic writers ; but as in the Ariftoxenian 
treatifes, they are not found under the fifth divifion, 
of tones ; nor under the fixth, of mutations, where 
it was natural to exped them ; but under the fourth, 
of fyftems j and it not being there exprefly affirmed, 
that the fpecies had a relation to the tones, though, 
from their denominations, and other circumftances, 
it might well be inferred, this has created a difficulty 
in admitting their connexion with the fubjed. The 
obviating of this objection I fliall referve for my fifth 
head ; where I ffiall take occafion, particularly, to 
juftify this dodrine, and the ule I ffiall have made 
of it ; and I ffiall therefore proceed to explain it, as 
I find it in the harmonic writers. 
To underftand how this dodrine of the fpecies of 
diapafon came to be treated under the head of fyftems, 
it will be neceflary to confider the definition given 
of the term fyftem by the Ariftoxenians, and their 
fubdivifion of this branch of harmonic. 
With this fchool, whatever confided of more than 
one interval, was a fyftem. So comprehenfive a de- 
finition could not but make this branch a very large 
one ; and fo we accordingly find it. It was fubdivided 
in the manner following : fyftems were there con- 
fidered as differing in refped, firft, to magnitude ; 
fecondly, to genus ; thirdly, to the being confonant 
or diffonant; fourthly, to the being rational or irra- 
tional ; fifthly, to the being fequent or tranfgreffive ; 
fixthly, to the being conjund ordisjund; feventhly, 
to the being mutable or immutable. Now, of thefe 
feven differences, it was under the third that the doc- 
trine of the fpecies of diapafon came to be treated, 
the confonant fyftems being there enumerated, and 
explained. 
