ehap.XIII. ANTIENT METAPHYSICS, 259 



Before fuch an art could be invented, the tune or fong muft firft be 

 analyfed into its elementarv notes ; and then we mull difcover what 

 the ratio is of thofe notes to one another; that is in other wcr' 

 we muft apply arithmetic and the doctrine of ratios to the diiff . '. 

 tones of the human voice, or of any inftruaient of muiic. To do 

 this, and likewiie to make the analyfis, which muft neceffarily pre- 

 cede it, muft appear, at tirft fight, a matter of great art and fcience. 

 But even this is not all ; for as the acute notes rife above the grave 

 in an infinite progreffion, to which nature has fet no bounds, in the 

 fame manner as numbers increafe in iiifinitiim^ it was the bufinefs of 

 fcience to fet bounds to infinity in this as well as in other things. 

 And this it has done by ftoppmg at what is called the odave., (that is 

 when the acute note is to the grave, as tisjo to cne^ which is the firft 

 multiple ratio), and making it a new fundamental, and from it count- 

 ing upwards as we did from the firft fundamental, and fo going on 

 from one odtave to another: In the fame manner as in numeration we 

 go on till we come to the decade, and there we ftop, and reckon from 

 it, as we did from unity, faying 10 and i, 10 and 2, &c. ; and fo v,'e 

 go on till we come to another decade; and in this manner we reckon, 

 proceeding, from decade to decade, to numbers, which we denominate 

 by the names of hundreds, that is, ten decades ; and then from hun- 

 dreds to thoufands, which are compofed of ten hundreds ; and fo 

 on. To explain fuch a progreffion at more length, in the matter of 

 mufic, does not belong to a work of this kind. But, I think, I 

 have faid enough to {how, that mufic could not be reduced to an 

 art, and what is called a gamut, or fcale of mufic, formed, except in a 

 country fuch as Egypt, where there was a body of the beft men of 

 the nation fet apart for the cultivation of arts and fciences, and where 

 fo many other arts and fciences were difcovered. 



The mufic of the Greeks, while they were yet barbarians, rofe 

 no higher than the mufic of the Hurons in North America, that is to a 



K k 2 fourth. 



