[ 72 2 ] 
the Dorian graver than it by a diate Aaron, that the 
reft of the four might be attended with the like cir- 
cumftance, they eftabhfhed the Hypolydian, Hypo- 
phrygian, and Hypodorian, a diateflaron giavei rc- 
fpedavely than the Lydian, Phrygian, and Dorian ; 
and laftly, they placed the Hypermixolydian at a 
diapafon from the Hypodorian, towards the acute, 
o-iving it that denomination from its pofition above 
the Mixolydian, mifufing, as he tells us, the prepo- 
lition hypo to fignify the grave, and hyper to exprels 
the acute. But though the refult of this method is 
the fame with that of his own, excepting as to the 
Hypermixolydian, (which he excludes for the reafon 
afligned in treating of the firft limitation) yet he ob- 
jedts to it ; becaufe the concinnous intervals are firft 
afiumed, which ought to be taken by the confo- 
nances ; and gives his own, which is by the con- 
tinual addition of the confonance diateftaron, but, 
however, within the compafs of the diapafon. 
Wherefore, when fuch addition would exceed it, he 
diredts taking the diapente in its ftead, the contraiy 
way j whereby the divifion will be kept within the 
limits afiigned. This method, and its refult, will 
perhaps be better underftood, and will alfo be more 
fuccindtly couched in our modern expiefiions, in 
which I firall therefore give it, applying to it the cor- 
refponding charadters of the Guidonian leale. 
Having firft taken the Mixolydian tone, which 
was the acuteft of the feven, fuppofe in D, fall a 
fourth to A, for the Dorian $ another fourth to L, 
for the Hypodorian \ then, to avoid paffing the 
bounds of the diapafon, rife a fifth to B, foi t ic 
Phrygian i fall a fourth again to/#, for the Hypo- 
J phrygian ; 
3 
