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Firfi, To explain the harmonic dodtrine, as far as 
concerns the feven modes admitted by Pto- 
lemey. 
Secondly , To explain the mufical dodtrine of the 
fame modes, and fhew its agreement with the 
harmonic. 
- Thirdly , To explain the eight harmonic modes re- 
jected by Ptolemey, and give at large his reafons 
for excluding them. 
Fourthly , To point out fomething of the origin of 
the two doctrines. 
Fifthly , To drew how far the preceding explana- 
tions may be fupported by arguments, or war- 
ranted by the teftimony of antient writers. 
Laflly, To confider how this fubjedt has been un- 
derftood by Meibomius, Wallis, and fome few 
others that have wrote fince, and in what refpedt 
their explanations differ from my own. 
I now proceed to the firff head ; viz. 
Ftrft, To explain the harmonic doctrine, as far as 
concerns the feven modes admitted by Pto- 
lemey. 
The harmonic doctrine of the tones we find ex- 
prelly delivered in the harmonic treatifes - y which, 
probably, is the reafon, why, among the moderns, the 
later writers at lead; have, for the mod; part, deter- 
mined themfelves in its favour : how juffly it is in- 
titled to the preference, I diall have fufficient occafion 
to examine. The treatifes on harmonic, that are come 
down to us, are moftly Aridoxenian, which fchool 
feems to have treated the fcience, if not better, at 
lead 
