[ 706 ] 
Concerning thefe, I find no difagreement amongft 
the writers of antiquity: they all agree, that they 
were feven in number, and had the denominations 
of Mixolydian, Lydian, Phrygian, Dorian, Hypo- 
lydian, Hypophrygian, and Hypodonan ; circum- 
ftances, which leave no doubt of their connexion 
with the modes. The fucceflion of intervals, or 
manner of dividing the diapafon for each fpecies, has 
been varioufly explained by the antient waters ; but 
the refult of thefe explanations is the fame,. except- 
jn g the generic differences. It will be fufficient here 
to give what refpedts the diatonic genus only, as the 
queftion concerning the tones does not turn upon the 
diftindtion of the genera. 
In the diatonic genus, the diapafon con lilting 
of five tonic and two femitonic intervals, the Ari- 
ftoxenians fixed the fucceffion for each fpecies, by 
the polition of the two femitones; (hewing, at 
the fame time, between which of the lounds of 
the immutable fyftem the fpecies in queftion was 
comprehended: for this fyftem conhftmg of fifteen 
founds, contained eight odtaves, two of which 
viz. that from proflambanomenos to mele, and 
that from mefe again to netehyperboleon, were 
divided after the fame manner, and therefore con- 
ftituted the fame fpecies: but the fix others were 
all differently divided j fo that the fyftem con- 
tained within itfelf the feven fpecies of diapafon, 
and thence obtained the denomination of perfect 5 
the leffer perfedt fyftem, which reached only to 
a diapafon and diateffaron, being improperly fo 
called for want of this qualification, as Ptolen ^ 
