[ 6 99 ] 
the diatonic genus, to which I fhall confine this ex- 
planation, is fo well known, that I need fay no more 
concerning the ftrudture of the fyftem, than that it 
anfwered to that of our natural fcale, beginning with 
Are, and ending with Alamire. This fyftem was 
held immutable, as to the relation of its parts one to 
another j that is, the order of founds and intervals, 
by which it proceeded, was in the fame genus to be 
always the fame; but the tenfion or pitch of the 
whole was variable, a different one being affigned 
for each mode. The explanation, therefore, ufually 
given of the fyftem, by comparing it, as I have done, 
to a double odtave, from A in our natural fcale, is 
not to be underftood as fixing its pitch, but as {hew- 
ing its fucceffion only; which might as well be done 
by a double odtave from B, taking C# and F# into 
the fcale, or from any other note, taking in the flats 
and /harps neceflary to make the tones and femitones 
follow in the fame order. 
The relation of the parts to each other in the fyftem 
being immutable, the fixing the pitch of any one 
found in it, for any mode, was fufficient to deter- 
mine that of all the reft. For this purpofe, the found 
mefe was commonly ufed ; which, by its fituation, 
was well adapted to it, being the middle found of 
the fyftem. If, therefore, we fettle the pofition of 
the mefe for each mode, we fhall do all, that is re- 
quifite for the clearing up and eftablifhing the har- 
monic dodtrine, which confidered the modes as dif- 
fering only in the pitch of the fyftem. 
The modes admitted by the Ariftoxenians were 
thirteen in number ; to which two more were added 
by later harmonicians ; and to the mefe of each of 
Vol. LI. 4 X thefe 
