Till his time music was so vague and uncertain, that 

 it required an extraordinary effort of genius to reduce 

 it to method and order. He precisely determined 

 the proportions which sounds bear one to another, 

 and regulated harmony upon mathematical principles. 

 But he let the precision of his mind carry him too 

 far, in subjecting music to the judgment of reason 

 alone, and admitting no pauses or rests, but such as 

 had an arithmetical or geometric proportion in them. 

 Aristoxenes, the disciple of Aristotle thought, on the 

 contrary, that this subject came entirely within the 

 verge of hearing, and that the ear was the only judge 

 of pounds. He therefore regulated the order, the 

 unison and break in tones, solely by the judgment of 

 the car ; and his system prevailed for some time in 

 Greece. Olympus, a Phrygian, came soon after to 

 Athens, who invented a stringed instrument which 

 gave the semi-tones, whereby he introduced so many 

 new graces into music, as gave it entirely another air. 

 He joined Aristoxenes, appealing for the merit of his 

 system to the decision of the ear. At length the fa- 

 rnous Ptolemy appeared, and with superior spirit 

 equally disclaimed the partiality of both sides. He 

 took a middle course, asserting that sense and reason 

 bad a joint right to judge of sounds. He accused 

 the Pythagoreans of fallacy in their speculations, 

 "with respect to proportions \ as well as of folly in so 

 disregarding the decisions of the ear, as to refuse it 

 that kind of harmony which was agreeable to it, mere- 

 ly because the proportions of it did not correspond 

 with their arbitrary rules. And he charged the parti- 

 sans of Aristoxenes with an absurd neglect of rea. 

 zoning, in that though they were convinced of the 

 difference of grave and acute tones, and of the pro- 

 portions subsisting between them ; and that those 

 proportions invariably depended upon the several 

 lengths of the musical chords ; yet they never took 

 the trouble of considering this, so as to enter, into the 

 reason of it. He therefore determined in deciding upon 

 the principles of harmony ? to make use not only of 



