THE HOMEMADE ORCHESTRA 333 



We have chosen a musical scale in which the rate of vibration 

 starting from middle C is as follows : 



CDEFGABC 



256 288 320 34i 384 426! 480 512 



The intervals between the notes corresponding to these 

 numbers of vibrations are pleasing to our ears. These numbers 

 are in the ratio of 



24 27 30 32 36 40 45 48 



Or we may say that D has nine-eighths of the number of vibra- 

 tions of C, E five-fourths as many, and so on, the series of fractions 

 being 



CDEFGABC 



I I \ - i I I V 2 



So in making Pan's pipes or the flute (see Field and Laboratory 

 Guide in Physical Nature-Study, p. 95), these relations must 

 be maintained between the lengths of the pipes used or the dis- 

 tances of successive holes from the mouth opening of the flute. 



In making an instrument like the piano the manufacturer 

 is confronted with a difficulty, for one may want to play on other 

 keys besides C. Suppose, for instance, it is desired to start the 

 scale with D or with E. Now the number of vibrations of the 

 successive notes in the scale must bear to those of D or E the 

 same ratio which the number of vibrations producing the notes 

 of the C scale bear to the number of the C string. The num- 

 ber of vibrations needed for the notes of these new scales as 

 compared with the number needed for the notes of the C scale 

 is indicated below. 



When C begins the scale: 



CDEFGAB CD E 



256 288 320 341^ 384 426! 480 512 576 640 

 When D begins the scale : 



288 324 360 384 432 480 540 576 648 

 When E begins the scale: 



320 360 400 426! 480 53 1 600 640 



