228 ANTIENT METAPHYSICS. Book III. 



the tones of the human voice or of any mufical inftrument ; and 

 not only fimple numbers, but numbers in geometrical ratio to one 

 another, that is, containing or being contained in one another : For 

 all the notes have that ratio to one another ; and if we do not per- 

 ceive the ratio, which a mufical note, that we hear, has to another 

 note, we only hear a found, but do not perceive that it is a mufi- 

 cal note. 



Thus it appears that mufic confifls of certain founds called Notes, 

 differing from one another in acutenefs or gravity ; for it is the dif- 

 ference in that refpedt, which makes, as I have faid, the fubjed of 

 mufic ; fo that all the notes have certain ratios of acutenefs or gra- 

 vity to one another : And we are now to inquire what thefe ratios 

 are, and how they are conneded with one another. 



But before we proceed to that, we are to inquire what it is that 

 makes acutenefs or gravity in mufical founds. And I fay it is the 

 motion of the air, produced by the vibratory motion of any 

 body ; and the greater number of vibrations there is in the fame 

 time, the more acute is the found ; and the fewer the vibrations, the 

 more grave. This is befl: illuftrated by a ftring, of which a greater 

 number of vibrations produces a more acute found than a leffer 

 number does in the fame time ; the confequence of which is, that a 

 iliorter firing, when by impulfe made to vibrate, produces more vi- 

 brations in the fame time than a longer ftring. 



And here we muft diftlngulfli betwixt the loudnefs of the found, 

 and the acutenefs or the gravity of it : If the ftring be impelled by 

 a great force, and confequently make great vibrations, the found 

 will be louder, but not more acute, unlefs the number of vibrations 

 in the fame time be increafed. We muft alfo diftinguifti betwixt 

 the length of the note, that is the duration of the found, and its 



acutenefs 



