[ 724 ] 
Now, thefe being the tones we have eftablifhed, 
it is plain, that. a certain found of the diapafon is ap- 
propriated to the mefe, in power of each, by reafon 
of their being equal in number to the fpecies. For a 
diapafon being feleded out of the middle parts of the 
perfed fyftem ; that is, the parts from hypate mefon 
m pofition to nete diezeugmenon, (becaufe the voice 
is mofl pleafed to be exercifed about the middle me- 
lodies, feldom running to the extremes, becaufe ot 
the difficulty and conftraint in immoderate intentions 
and remiffions), the mefe in power of the Mixo- 
lydian will be fitted to the place of paranete diezeug- 
menon, that the tone may, in this diapafon, make 
the fir ft fpecies ; that of the Lydian, to the place of 
trite diezeugmenon, according to the fecond fpecies ; 
that of the Phrygian, to the place of paramefe, ac- 
cording to the third fpecies; that of the Dorian, to 
the place of the mefe, making the fourth and middle 
fpaces of the diapafon; that of the Hypolydian to 
the place of lichanos mefon, according to the fifth 
fpecies; that of the Hypophrygian, to the place of 
parhvpate mefon, according to the fixth fpecies ; that 
of the Hypodorian, to the place of hypate mefon, ac- 
cording to the feventh fpecies ; that fo it may be pof- 
fible, in the alterations required for the tones, to keep 
fome of the founds of the fyftem unmoved, for pre- 
ferving the magnitude of the voice (meaning the pitch 
of the diapafon), it being impoflible for the lame 
powers, in different tones, to fall upon the places o 
the fame founds. But, fhould we admit more tones 
than thefe, as they do, who augment their excefles 
by hemitones, the mefes of two tones muft, of ne- 
ceflity, be applied to the place of one found ; fo that, 
