[ /Oi ] 
for though many of the harmonic writers treat of the 
thirteen or fifteen modes all together, without difiin- 
guifhing the feven in queftion, yet they have given 
them in fuch order, and at fuch diftances, that the 
feven fiand at the fame intervals from each other, as 
are afligned for them by thofe, who have treated of 
them feparately ; fo that all the accounts agree in this 
particular. The direction we may conveniently take 
from Bacchius (3), where it is clearly and concifely 
delivered ; and where it appears, that the Mixolydian 
was the moll acute 5 the Lydian, graver by a femi- 
tone; the Phrygian, graver than the Lydian by a 
tone ; the Dorian, graver than the Phrygian by a 
tone j the Hypolydian, graver than the Dorian by a 
femitone j the Hypophrygian, graver than the Hypo- 
lydian by a tone ; and the Hypodorian, graver than 
the Hypophrygian by a tone. Now, as the Guido- 
nian fcale, in ufe amongft the moderns, when ftripped 
of Guido’s additions, anfwers to the fyftem of the 
antients, in its natural fituation, which was in the 
Dorian mode, and our Alamire confequently an- 
fwers to the pitch of the Dorian mefe, we have a 
plain dire&ion for finding the abfolute pitch of the 
mefes, for all the feven in our modern notes, and 
they will be found to fiand thus : 
Mixolydian mefe in d 
Lydian in - - - c# 
Phrygian in - - b 
Dorian in - - - a 
Hypolydian in - - g# 
Hypophrygian in - 
Hypodorian in - - e 
But to underfiand this dodtrine, as it is delivered by 
the antients, it will be necefiary alfo to examine, how 
(3) Pa g- edit. Meibom. 
4X2 
the 
