HERMANN VON HELMHOLTZ 



when Pythagoras is said to have discovered the arrange- 

 ment of tones in an octave, by observing that the 

 sounds of the blacksmith's hammer in the forge pro- 

 duce a fourth, a fifth and an octave, and was then led 

 to obtain harmonic proportion between the strings of 

 the heptachord, all who investigate musical tones 

 know that, although these are fleeting sensations, they 

 depend physically on numerical relations between 

 various kinds of movements j but it was Helmholtz, 

 more than any other philosopher, who examined the 

 whole range of the phenomena, physical as well as 

 physiological, and whose work will for generations 

 remain an enduring monument to his genius. 



168 



