352 VIBRATIONS OF MUSICAL NOTES. 



octave is produced by double the number of vibra 

 tions which produce the corresponding note in th< 

 preceding lower octave ; and if the intervals betweei 

 c! and e f , c r and /', c' and g', are characterised b\ 

 saying that e r is the third, /' the fourth, and g' the fifth 

 of the fundamental note, then notes which have th 

 same intervals with respect to other notes will be re 

 spectively thirds, fourths, and fifths of these notes, th 

 latter being considered as fundamental notes, and i 

 follows that the number of vibrations which produce 



each note in the musical scale can be calculated. Thu 



3 

 g f , the fifth of c', makes of 264 = 396 vibrations; e 



the third of c', makes of 264 = 330 vibrations p( 



second. Again, /' is the fourth of c', and the ratio of tl: 

 numbers of vibrations which produce these notes must 1 

 the same as that between c" and g f , the latter being tl 

 fourth of the former; but the number of holes in tl 



outer circle is 96 = -- of 72, hence the number of v 



u 



brations which produce f is of 264 =352. Sim 



o 



5 



larly a', the third of /', is produced by - of 352= 4<i 

 vibrations; J', the third of /, by | of 396 = 495, ai 

 finally d", the fifth of /, by | of 396 = 594 vibratior 



The lower octave of d", viz. d', is therefore produc 



by - = 297 vibrations. We have thus obtained t 

 2 



complete series for the whole scale : 



