C 725 3 
in interchanging the tunings of thofe two tones, Ac 
whole fyftem in each muft be removed, not pre- 
ferving any one of the preceding tenfions in common, 
by which to regulate the proper [pitch] of the voice. 
For the mefe in power of the Hypodorian, for in- 
ftance, being fixed to hypate mefon by pofition, and 
that of the Hypophrygian to parhypate mefon, the 
tone taken between thefe two, and called by them 
the graver Hypophrygian, to diftinguifh it from the 
other acuter one, muft have its mefe either in hypate, 
as the Hypodorian, or in parhypate, as the acuter 
Hypophrygian ; which being the cafe, when we in- 
terchange the tuning of two fuch tones, which ufe 
one common found, this found is indeed altered a 
hemitone in pitch, by intention or remifiion; but 
having the fame power in each of the tones, viz. 
that of the mefe, all the reft of the founds are in- 
tended or remitted in like manner, for the fake of 
preferving the ratios to the mefe, the fame with thofe 
taken before the mutation, according to the genus 
common to both tones ; fo that this tone is not to be 
held different in fpecies from the former, but the 
Hypodorian again, or the fame Hypophrygian, only 
fomewhat acuter or graver in its pitch. That thefe 
feven tones, therefore, are fufficient, and fuch as the 
ratios require, be it thus far declared (1 1). 
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