[ 74 § ] 
firings hypate mefon and nete diezeugmenon fall out 
fo, as to give the proper fpecies for every mode ; 
which circumftance will not attend any other boun- 
daries, common or varying, without altering the po- 
rtions of the mefe, and thereby difturbing the har- 
monic dodrine. But we have from Ptolemey fuf- 
ficient teftimony to this point. In the eleventh chap- 
ter of his fecond book, of which I have given a tranl- 
lation above, we fee, that the diapafon in queltion is 
chofen by him, to exhibit the divifions, that belong 
to the feveral fpecies. ’Tis true, he feems to in- 
sinuate, that any other diapafon might have been 
chofen, were it not for the difficulty the voice finds 
in running to the extremes : and in this, as a theoritt, 
he is right j for mufical relations and proportions, 
confidered as objeds of mere fpeculation, may be 
conceived at any pitch ; but in the cafe before us, it 
was die pradice of the inflrument, that governed 
the theory. The pitch of the lyre had been made 
to anfwer to the double odave of the human voice; 
the pitch of the fyftem, in the Dorian mode, anfvvered 
to that of the lyre; and, in every other mode, the 
difference in pitch from that of the Dorian was de- 
termined. Now, under luch limitations, that tooK 
their rife from pradical mufic, it is evident, that no 
other diapafon, but that inflanced by Ptolemey, could 
have ferved his purpofe. , 
But that the boundary of the fpecies is rightly at - 
iufled in the diagram, there is yet another ftrong teiti- 
mony, from the tables of Ptolemey, annexed to the 
fifteenth chapter of book fecond. 1 o make this piooi 
evident, it will be neceffary to give fome account o 
this part of his work. 
In 
