[ 727 ] 
fyftem. That the force of his arguments in this 
chapter, and the refult of admitting the eight modes, 
may be more plainly feen, I have annexed a fecond 
diagram of the fpecies, as they lay in the fpurious 
modes ; by which it will appear, to which fpecies in 
the genuine ones they feverally anfwered 5 and the 
objection, raifed againll each of them by Ptolemey 
will become intelligible. 
There is, however, an objection, to which this 
fecond diagram feems liable. It may be afked, if 
the Hypoionian mode, inftanced by Ptolemey, could 
give either Hypodorian or Hypophrygian harmony, 
according as either the eighth or the ninth firing was 
employed for its mefe ? and if the reft of the fpurious 
modes were liable to a like alternative, what was it 
determined me in my choice of the two fpecies, in 
the conftrudtion of the diagram ? To which I an- 
fwer, that the antients have decided for me as to five 
of them j for we find (12), that the Hypoionian was 
called the graver Hypophrygian ; the Hypoasolian, 
the graver Hypolydian ; the Ionian, the graver Phry- 
gian j the ALolian, the graver Lydian ; and the Hy- 
perionian, the acuter Mixolydian. And this, by the 
way, furnifhes us with an unanfwerable argument of 
the antiquity of the dodtrine enforced by Ptolemey, 
that the number of the modes ought not to exceed 
that of the fpecies of the diapafon ; for thefe appella- 
tions, which were given to the modes long enough 
before Ptolemey flourifhed, can be accounted for on 
no other principle, but the fuppofing the fpecies of 
(12) Vide Euclid. Introduft, Harm. p. 19. v. 29. & feq. Arift. 
Quint, p. 23. v. 7. & feq. 
diapafon 
