Chap. XVII. ANTIENT METAPHYSICS. 229 



acutenefs or gravity, which alfo differs from the quicknefs or flow- 

 nefs of the found. Thefe make what the anticnts called the rhythm 

 of their mufic, and what we call tlie timc^ but are quite diftercut 

 from the acutenefs or gravity of the found. 



Having thus fhown what acutenefs or gravity in mufical founds 

 is, and how all the notes of mufic differ from one another as to 

 acutenefs and gravity, and have to one another certain ratios of 

 thai kind, we are now to coniider what thefe ratios are, and how 

 they are connecled with one another. And this inflrudion Py- 

 thagoras gave his countrymen by a fingle firing, or monochcrd as 

 he called it, which he divided into certain parts. The firfi: and 

 mofl natural divifion of every thing is into two parts ; and in that 

 ■way Pythagoras made the firfl divifion of the firing. By that di- 

 vifion he gave his countrymen the idea of the Odlave ; for as the 

 greater or lefs acutenefs of the note depends, as I have faid, upon 

 the length or fhortnefs of the firing, the note produced by the 

 half of the firing, is twice as acute as the note produced by 

 the whole firing ; and this is the ratio of the cclavc to its funda- 

 mental. If a greater divifion of the firing be taken than a half, fup- 

 poie t^vo thirds^ then the note is what is called a fifths being in the 

 ratio, to the note produced by the whole firing, of two to three ; 

 but if three fourths of the firing be taken, then the ratio of that note 

 to the note founded by the whole firing, is as three tofo/er^ and the 

 note is called a fourth. And by dividing, in this way, the firing 

 into parts, greater and lefl"er, all the feveral notes, from the funda- 

 mental tone^ with which the diatonic fcale begins, up to the o^ave, 

 with which it concludes, are performed. 



From what is faid, it is evident that the Greeks had no fcience 

 of raufic, till Pythagoras brought to them, from Egypt, the 

 octave, which fets bounds to mufic, and confequently makes a 



fcience 



