[ 74 ° ]: 
particular proofs, to lupport the explanations I have 
«riven of thefe two doctrines feparately. What imme- 
diately lies upon me is, to prove, that the dodrine ot 
the fpecies of diapafon had a connedion with the 
modes ; and to juftify the manner, in which I have 
combined the two dodrines in the canon, and in the 
diagrams framed from it. With this view, therefore, 
I (hall dired my arguments to the proving of the five 
following points. 
i. That the dodrine of the fpecies of diapafon 
was a dodrine of the modes. 
a. That this dodrine was not diftind from, nor 
independent of, the harmonic, but fo conneded with 
it, that a mutation, according to the one, produced 
the alteration required by. the other. 
3. That the fpecies of diapafon, as taken pradi- 
cally on the lyre, lay all at the fame pitch. 
4. That this pitch was the diapafon, between the 
firings hypate mefon and nete diezeugmenon, as they 
ftand in the diagram. 
y. I {hall endeavour to drew, that it was the mufi- 
cal dodrine, and not the harmonic, that exhibited 
the true charader of the modes, as confidered in re- 
fped to their eflfeds. 
To begin with the firft point. That the dodrine 
of the fpecies of diapafon was a dodrine of the 
modes, might,, perhaps, be inferred from fome of 
the definitions given of a mode ; but as thefe defini- 
tions are moftly intermixed with, if not drawn folely 
from, the harmonic dodrine, and hence have given 
room for difputes, I fhall reft this point upon three 
arguments, in which the definitions are not con- 
cerned. 
Firft.;, 
