[ 737 ] 
to think, that the flrudture of it was not fettled, till 
the inflrument had been again extended to the com- 
pafs of a difdiapafon, by the additions of the tetra- 
chords hyperbolaeon and hypaton, and of the found 
proflambanomenos : for this change the age of Ale- 
xander the Great may, perhaps, be a probable asra ; 
for, in the mufical problems of Ariflotle, I obferve 
no mention of the new tetrachords, though many of 
the queflions concern the firings of the lyre; and 
yet there is no doubt of their being in ufe in the time 
of Arifloxenus, his difciple. Should I be near the 
truth in this, the mufical dodlrine will then appear 
to have been earlier than the harmonic, by the whole 
period from Pythagoras to Alexander. But, without 
being follicitous about the precife time when the har- 
monic dodlrine was introduced, I fhall, with more 
certainty, endeavour to point <3ut what mufl have 
given occafion to it. 
The fludy of the mufic of the antients, though 
they feem not to have much ufed compofition in 
parts, mufl yet have been very perplexing, from the 
variety only of the tones and genera ; and fome help 
might well be thought neceffary, even in the time of 
the odtachord lyre. But when feven new firings were 
given to the inflrument, and thefe placed not all at 
one end, but three at the acute, and four at the 
grave, the eight old firings, upon which the cha- 
radleriflic fpecies of melody for each mode had 
been always exhibited, became confounded by thefe 
additions ; and poffeffing now the center of the lyre, 
it was difficult to diflinguifh them, and to preferve for 
each mode its proper charadter as before. This dif- 
ficulty mull alfo have been increafed, by the change 
introduced 
