230 ANTIENT METAPHYSICS. Book III. 



fcicnce of It ; and from the feveral dlvifions of the firing was formed 

 the gamut or fcak of mufic : So that the whole fyftem of this fine 

 art is comprehended in a fingle ftring and its feveral divifions ; 

 which fhows us, that from the meaneft things, properly confidcr- 

 ed, the greateft confequences may be drawn and the fineft arts 

 produced. Before Pythagoras, the Greek mufic rofe no higher than 

 the mufic of the Hurons, that is to 2l fourth^ which was the mufic 

 oi\X\^n tctrachord ox fom--Jlringed\)'Xt. It is true that before Py- 

 thagoras gave them the cxfiave they had invented a feven-Jlrlnged 

 lyre. But that only doubled xht fourth of their four-ftringed lyre, 

 by making the fourth ftring of their feven-ftringed lyre, which con- 

 cluded the firft fourth upon that lyre, the fundamental of another 

 fourth, which was concluded by the laft ftring of the feven-ftringed 

 lyre. But this, as I have fi\id, only gave them an additional yo///-//?, 

 but no oSlave. 



And here it may be obferved, as a peculiarity of the art of mufic, 

 that none of the tones, of which it is compofed, have an exlftence 

 by themfelves, as tones of mufic, but each of them exlfts by rela- 

 tion to fome other tone. This is to be explained by the nature of 

 the tones, which are all acute or grave. Now no tone Is by Itfelf 

 acute, but only in reference to another tone, which is lefs acute : 

 For every acute tone muft be more acute than another tone ; as 

 otherwife it Is impoflible that it can be faid to be acute. And, with 

 refped to grave tones, it is impoflible to conceive any, but In refe- 

 rence to acute tones ; for if there were no acute tones, there could 

 be no grave tones : And the grave tones muft differ from one ano- 

 ther in the degree of gravity. Now every tone, that is acutef than 

 another, muft contain in it the tone lefs acute ; and a graver tone 

 muft contain In It a tone lefs grave : And this accounts for all the 

 mufical tones being geometrical ratios, that Is, two numbers, of 

 which the one contains the other. 



Thus 



