Lydian - 
j^Eolean - 
Middle Phrygian 
Ionian - 
Dorian - 
[ 7*4 ] 
- - in c# 
- - - c 
- - - b 
_ _ A 
Hypolydian - - 
- m g 
# 
Grave / 
g 
/# 
/ 
- 
Hypoaeolian - - - - - 
Hypophrygian ------ 
Hypoionian ------ 
Hypodorian - - - - - 
Having now fhewn, how thefe fifteen modes were 
iituated according to the harmonic doctrine, I come 
to the objections raifed by Ptolemey againfl: the eight 
laft explained. For the right underfianding of which, 
it will be neceflary to give an account of all that he 
lias delivered on the lubjeCt of the modes, a talk of 
fome difficulty i for though his reafoning appears to 
me moft clear and methodical, it is rather too pro ix 
to be given exaCtly in his own words, as this, with 
the neceflary explanations of thofe paflages, of which 
the fenle is lefs obvious, would carry me to too great 
a length. I muft therefore endeavour to abridge his 
dodtnnes, though at the hazard of leaving out lorne 
of the fubftantial parts, and thereby doing lnjuftice 
to his argument. 
It will be expedient to premife fomething con- 
cerning his apparent intention, and method of reafon- 
ing in this part of his work, which will ferve as a 
key to his argument : and this leems ^ the more 
neceflary, as he has been thought by fome (9) to 
Co) So obfcurely has the beft of all the antient writers (Ptolcnu ) ) 
delivered himfelf on this article (the tones), that de ferve o ave 
.been moft clearly handled. Malcolm’s Trcatife on Mulic, p. 5o9- 
