[ 7°9 ] 
and it may not be amifs therefore, in order to pre- 
vent any limited conception of thefe fpecies, to date 
generally the order of the intervals, of which each is 
compofed ; which will be as follows, proceeding in 
each from grave to acute. 
Mixolydian. 
Lydian. 
Phrygian. 
Dorian. 
Hypolydian.’ 
Hypophrygian. 
Hypodorian. 
Semitone, tone, tone, femitone, tone, tone, tone. 
Tone, tone, femitone, tone, tone, tone, femitone. 
Tone, femitone, tone, tone, tone, femitone, tone. 
Semitone, tone, tone, tone, femitone, tone, tone. 
Tone, tone, tone, femitone, tone, tone, femitone. 
Tone, tone, femitone, tone, tone, femitone, tone. 
Tone, femitone, tone, tone, femitone, tone, tone. 
Befides the manner above-mentioned of explaining 
the fpecies of diapafon, the antients have given us 
another, the refult of which is the fame j and that 
is, by the pofition of the diazeudtic tone, or interval 
from mefe to paramefe. In the Mixolydian fpecies, 
the diazeudtic tone was the firft interval, reckoning 
from acute to grave ; in the Lydian, it was the fe- 
cond j in the Phrygian, the third ; in the Dorian, 
the fourth $ in the Hypolydian, the fifth j in the 
Hypophrygian, the fixthj and in the Hypodorian, 
the laft. 
Now, either of thefe methods fixes the fucceffion 
of intervals peculiar to each fpecies j but as the 
examples are taken from a fyftem, whofe pitch was 
variable, we are ftill to feek, at what abfolute pitch 
the feveral fpecies were taken in the modes, to which 
we fuppofe them to have been refpedtively fubfer- 
vient ; and it is, perhaps, the feeming difficulty of 
fettling this, that has induced fo many to rejedt this 
dodtrine entirely, and fall in with the harmonic 
writers, who confidered the modes as differing only 
