[ 7°3 ] 
1 thought this remark the more neceffary, as I 
lufpedt it was the not attending to this circumflance, 
that led Dr. Wallis to affign c and g natural, for the 
places of the mefe in the Lydian and Hypolydian 
modes, inftead of c# and^#, where I have placed 
them (4). But, to return. 
We are now to give the places of the mefe for 
thefe feven modes upon the lyre, which are thus 
fettled by Ptolemey (.5)* 
Mixolydian 
Lydian 
Phrygian 
Dorian 
Hypolydian 
Hypophrygian 
Hypodorian 
"Paranetediezeugmenon 
Tritediezeugmenon 
Paramefe - - - - 
} Mefe in( Mefe - - 
Lichanos mefon - - 
Parhypate mefon - - 
Hypate mefon - - - 
String 
3 1 
10 
9 
8 
7 
6 
The portions affigned for the mefes of thefe feven- 
modes, by the harmonic dodtrine, being thus fettled r 
both in our modern fcale, and upon the lyre, I come 
now,. 
Secondly, To explain the mufical dodtrine of tha 
fame modes, and fhew its agreement with the 
harmonic. 
The mufical dodtrine taught, that the difference 
between one mode and another confided in the man- 
ner of dividing an odtave,. or, as the antients- exprefs 
it, in the different fpecies of diapafcn. The ele- 
mentary principles of thefe fpecies we find delivered' 
(4) See his edition of Ptolemey, p, 137 
(5) Ibidem, 
