Chap. XVII. ANTIENT METAPHYSICS. 227 



which it is compofed ; for analyfis is the fouudaticn of all arts and 

 fcicnces. 



The fubjciSl: of mufic is the tones of the human voice or of any mu- 

 fical inftrument, differing from one another in acutenefs and gravity : 

 Thefe are called tones and femitones in our fcale of mufic, which make 

 the different notes to the number oi/even, rifing above one another in 

 acutenefs; and, with the addition of an eighth note, which is called 

 the Octave, the fcale of mufic, or the Gamut as we call it, iscompleat- 

 cd. And here the progrefs of the tones of mufic ends ; for if we have 

 a mind to form an acuter found, we make a fecond odavc, of which 

 the firft odtave is the fundamental; and fo on from 0(ftave to octave, as 

 far as the human voice or any inftrument can go. But upon this fub- 

 jedl I have fpoken at fomc length in the IV. vol. of tliis work, (p. 25 S. 

 and following), where I have fliown that the Greeks, by dividing the 

 tone not only into halves or femitones, but into the third and fourth 

 parts of tones, made two other kinds of mufic : One of thefe they 

 called the Chromatic^ by which the note was divided into three parts; 

 and the other they called the Enharmonic^ by which the note was 

 divided into four parts : Whereas by the Diatonic fcale, which is the 

 mufic we ufe, and which was the common mufic in Greece, the tone 

 is only divided into halves or femitones. In the fame paffage I have 

 alfo mentioned the great antiquity of mufic in Egypt, and fhown 

 that the Egyptians employed it for the two beft purpofes, devotion 

 and the education of youth. (Ibid. p. 257. and 25S.) 



And thus I have explained how mufic is anallzed into its ele- 

 mental founds, and how it rifes from the loweft to the highefl 

 notes. 



And here we are come to what is the greateft and moft wonder- 

 ful part of the art of mufic, and that is, the applying of numbers to 



F f 2 the 



