[ 7 6 7 ] 
but, in this chapter, the author means only to fix 
the numerical firing allotted for each mefe, without 
regard to its pitch, which was to be regulated by 
the diftances afligned for the tones in the tenth 
chapter. And by thefe difiances, and all other con- 
curring circumftances, it is manifeft, that the two 
firings in queftion were, in thefe modes, to be made 
a femitone, more acute than their natural fituation, 
as I have already obferved, in explaining the har- 
monic dodtrine. How, therefore, the dodtor could 
fo far wander from the true theory, which lay before 
him in the text of his author’s tenth chapter, as to 
fubfiitute a different method, and deliver it. with 
great prolixity of explanation, as the method of his 
author, is what I know not how to account for, 
much lefs reconcile to his accufiomed care and fide- 
lity. What is ftill more extraordinary, is, that, after 
finifhing the diredtions and explanations of his own 
method, he, in the very next paragraph, cites the 
very tenth chapter of Ptolemey, where the method 
is given (5 1), in order to infer with his author, that 
the Mixolydian tone was diftant from the Lydian a 
hemitone ; the Lydian from the Phrygian, a tone, 
&c. though this inference, which is true only from 
Ptolemey’s method, diredtly contradidts all he had 
been delivering. Could he overlook the falfenefs of 
this inference, whilfi he was taking fo much pains 
(51) His pofitis, inde colligitur (ut cap. 10.) toni Mixolydii 
a Lydso diftantiam limma, feu craflius loquendo hemitonium ; 
hujus a Phrygio, tonum; hujus a Dorio, tonum ; Dorii ab Hypo- 
lydio limma; Hypolydii ab Hypophrygio, tonum; hujufque ab 
Hypodorio, itidem tonum. App. p. 315. Jin. 21, 
with 
