192 Dr. Charles J. Hall on 



difference between the tone of a violin and a flute ; they 

 knew, possibly, that a couple of similar organ pipes produc- 

 ing the same note, if placed in juxtaposition, might neutralise 

 and not reinforce each other ; but of the laws which ex- 

 plained these phenomena they were absolutely ignorant. 

 From the time of Pythagoras physicists have known some- 

 thing about musical consonances in relation to arithmetical 

 ratios, and musical theorists have had vague notions about 

 harmonics and resultant tones ; but it was reserved for 

 Helmholtz to weld into a compositewhole physical acoustics, 

 on the one hand, and musical theory, on the other. How 

 splendidly he has accomplished his task I need not say. 

 But the existence of his book is, I submit, a complete 

 answer to any who would doubt the propriety of my intro- 

 ducing here the subject of music. This close connection 

 between the art of music and the science of acoustics is, I 

 think, now universally recognized by musicians ; but the 

 recognition has been somewhat tardily and grudgingly 

 given. I remember an eminent musician, who has not long 

 gone to his last resting place, saying that acoustics had 

 no more to do with music than astronomy. The simile 

 was entirely unfortunate, for astronomy, as studied by the 

 Greeks, was only a branch of music. The motion of 

 the planets was regulated, they imagined, by musical in- 

 tervals, and it is thus that the expression " music of the 

 spheres " has crept into common use. Again, writing as 

 late as 1874, an accomplished musical antiquarian showed 

 an extraordinary want of appreciation of Helmholtz and 

 his theories. Of one, he says " Were it so, there would indeed 

 be a jargon" and "They (the scientists) attribute the various 

 qualities of tone in musical instruments to differences in their 

 harmonics." Nothing is so misleading as half the truth. 

 What Helmholtz contended for, and what any one who has 

 taken the trouble to test his experiments can prove to 

 demonstration is, that the quality of tone is dependent upon 



