t 7+t ] 
Firft, Becaufe the fpecies are denominated after 
feven of the modes, which could hardly have arifen 
from any other caufe, than their connection with 
them. 
2dly, Becaufe the whole reafoning of Ptolemey, 
in the fixth, feventh, eighth, ninth, tenth, and ele- 
venth chapters, of his fecond book, tends to 1 educe 
the modes to the number of the fpecies of the dia- 
pafonj which, as far as his opinion goes, is an ex- 
prefs confirmation, that the mufical doCtrine was a 
doCtrine of the modes. 
3dly, Becaufe Ptolemey is not fingle in this opi- 
nion, as fome may have thought, but is fupported 
in it by the Ariftoxenian writers, who, though they 
admitted thirteen modes, upon the falfe principle of 
the harmonic doCtrine, did, in faCt, reduce them to 
eight, on the very principle of Ptolemey, calling the 
Hyperionian mode, which gave the fame fpecies with 
the Mixolydian, the acuter Mixolydian j and calling 
alfo the ALolian, the graver Lydian j the Ionian, the 
graver Phrygian ; the Hypoasolian, the graver Hypo- 
lydian ; and the Hypoionian, the graver Hypophry- 
gian ; the former of all which modes gave, re- 
fpeCtively, the fame fpecies with the latter. So that, 
to make their doCtrine anfwer to that of Ptolemey, 
there wanted but the reduction of one mode moie, 
which was their Hyperphrygian. And it is not to be 
conceived, but that they faw this mode alfo to be a re- 
petition of the Hypodorian ; but as this repetition was 
at the diftance of an oftave, and the other five were 
repeated at the difference only of a femitone in pitch, 
they could not have called this the acuter Hypodorian, 
without ufing the fame expreffion in too great a lati- 
3 C 2 fade 
