Jantjabt 29, 1909] 



SCIENCE 



165 



instance, be due to the superior intensity of one 

 or another harmonic? 



Many other quotations might be given 

 of opinions expressed by Rameau, Chladni, 

 Wheatstone and others; but enough has 

 been said to show that the ideas as to qual- 

 ity were well understood before Ohm put 

 forth his law, which is almost misnamed. 



Helmholtz (1862) defended and devel- 

 oped Ohm's theorem, and gave elaborate 

 proof of it, chiefly by the use of resonators. 

 Melde (1864) made visible, by his beautiful 

 tuning-fork monoehord, the simultaneous 

 existence of two or more harmonic vibra- 

 tions in a string. Koenig (1872) showed 

 the simultaneous coexistence of two sets of 

 waves in the same organ pipe by means of 

 his manometrie flames. 



The theories of Ohm and Helmholtz seem 

 so simple that they have generally been 

 accepted as expressing the whole physical 

 condition, and few investigators have suc- 

 cessfully combated them. Seebeck (1844) 

 argued that the quality of tone must be 

 decided by the ear, and he concluded that 

 the definition of a simple tone given by 

 Ohm is too limited; he believes that other 

 forms of vibration besides the pendular are 

 capable of giving the sensations of a single 

 simple tone, and that simple tones may 

 have different qualities among themselves. 

 Seebeck greatly improved the siren, and 

 used it to produce the fundamental and 

 partial tones with which he experimented. 

 Helmholtz admits the experimental results 

 of Seebeck, and after extended argument, 

 he claims that Seebeck did not give proper 

 attention to the hearing of the partials. 



Another investigator to oppose Helm- 

 holtz was Koenig ; he was not satisfied with 

 the statement as to the cause of tone-qual- 

 ity. Koenig invented the wave siren, a 

 very beautiful piece of demonstration ap- 

 paratus, with which he showed that qual- 

 ity is not accounted for solely by the pres- 

 ence and relative intensity of the partials ; 



but that phase is a factor too important to 

 be left out of account. If changes in the 

 number and intensity of the partials give 

 rise to such differences in quality as we 

 observe in instruments belonging to differ- 

 ent families, Koenig says the changes in 

 the difference of phase for the same par- 

 tials are competent to produce differences 

 of quality at least as sensible as those 

 which are noticed in instruments of the 

 same kind. 



Helmholtz says distinctly that if we dis- 

 regard the noise of rushing wind, the 

 proper musical quality of the tone pro- 

 duced by blowing over the mouth of a 

 bottle is really the same as that produced 

 by a tuning fork; and that the tone of a 

 flute, which according to Helmholtz is 

 practically devoid of over-tones, is the same 

 as that of a tuning fork. Since we agree 

 to some extent with Seebeck, that tone qual- 

 ity must be decided by the ear, we hesitate 

 to adopt the conclusion that the bottle and 

 the fork both give simple tones of the same 

 musical quality. 



"When this address was first thought of, 

 it was hoped that some conclusions might 

 be reached regarding this general question. 

 But, for reasons referred to later, it seems 

 best to limit our further consideration to 

 certain particular instances, about which 

 it is believed some definite conclusions can 

 be drawn. 



Perhaps the points to be investigated 

 will be most clearly presented by a some- 

 Avhat personal statement of the incidents 

 that led to this enquiry. 



In connection with the study of the flute 

 as a musical instrument there arose the 

 question which may be specifically stated: 



Is the tone quality of a ilute, the tube of which 

 is made of gold, superior to that of a similar flute 

 having a tube of silver or of wood? If there is a 

 diiTerenee, what is its cause? 



Probably many will be inclined at once 

 to dismiss the subject as not a question. 



