[ 696 ] 
je<ft ; for fome, not aware of the diftinCtion, have 
charged the antients with contradictions j and others, 
who perceived the two doCtrines, not being able to 
reconcile them, have either adopted one, and rejected 
the other, - or given up the fubjeCt as hopelefs : but, 
as they were both admitted by the antients, they mull; 
both have been true, in fome fenfe. What, therefore, 
I have principally in view in thefe fheets, is to drew, 
that the difference between the doCtrines arofe only 
from the different way of confidering one and the 
fame objeCt ; and that therefore there was fuch an 
agreement betwixt them, as that, under certain re- 
ftriCtions, they may be embraced under one common 
interpretation. 
For diftinCtion fake, I fhall call one of thefe doc- 
trines the harmonic, and the other the mufical doc- 
trine ; the reafon of which will fufficiently appear, 
when I come to treat of the diftinCtion between the 
fcience of harmonic and that of melopceia or mufical 
compofition. 
According to the harmonic doCtrine, the number 
of the modes had been augmented to fifteen ; but as 
Ptolemey, who appears to have favoured the mufical, 
reduces them to feven, and as it is on the principles 
of that writer, that I propofe to fhew an agreement 
between the doCtrines, it will be neceffary for me, in 
treating of the harmonic modes, to diftinguifli the 
feven he admits from the eight he has excluded. 
This being premifed, I fhall be underftood in 
making the diftribution of what I have to offer upon 
this fubjeCt, which I propofe to treat under the fol- 
io wine fix heads. 
Firft, 
