[ 7 ” ] 
of the diapafon is brought out by the canon for each 
of the feven modes. As in the conftruCtion of this 
diagram, the directions of the canon have, been 
flriCtly purfued, fo it will appear, that the refult of 
it is, in all refpeCts, conformable to the principles of 
both doCtrines. Thus in the Dorian, for inftance, it 
will be feen, that the mefe is placed in Alamire, and 
that the reft of the founds exhibited in that diapafon, 
are placed at the proper diftances, for preferving the 
order of the fyftem, as required by the harmonic 
doCtrine. It will be alfo feen, that the diapafon fe- 
leCted lies between hypate mefon and nete diezeug- 
menon; that the femitones are the firft interval in 1 
the grave, and third in the acute ; and that the dia- 
zeuCtic tone is in the fourth interval, reckoning from 1 
the acute; all which circumftances were alfo required 
by the mufical doCtrine for this mode ; and, in the 
reft of the modes, all the circumftances required by 
each doCtrine will, in like manner, be found to ob- 
tain : fo that no objection can well be raifed to the 
principles, on which the diagram has been framed, by 
the favourers of either doCtrine feparately; and the 
very coincidence of the two doCtrines therein, might 
furnifh a probable argument in juftification of the 
manner, in which I have combined them in the 
canon. But as I propofe to confider this under the 
fifth head, where the proofs will be collected, I fhall 
leave this argument for the prefent, and proceed to 
explain, , 
1 Thirdly , The eight harmonic modes rejected by 
Ptolemey, and give at large his reafons for ex- 
cluding them,. 
Six 
