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SCIENCE. 



[N. S. Vol. XIV. No. 358. 



ways to work at some disadvantage. He 

 had an abiding faith in experiment, and 

 was not afraid to proclaim the results of 

 his careful, painstaking work, even if it 

 seemed to contravene the conclusions of 

 those whose theoretic preparation was 

 better than his. The subject of musical 

 quality was one which he attacked with 

 characteristic patience. With the mathe- 

 matical theory of combination tones, as 

 brought out by Helmholtz, and the two 

 subdivisions of difference tones and sum- 

 mation tones, Koenig was not prepared to 

 grapple. With his naturally acute and 

 highly trained ear he sought in vain to 

 perceive the summation tones for which 

 theory provided, and he reached the con- 

 clusion that they had no objective exist- 

 ence. Difference tones, or beat tones, as 

 he called them, are easily perceived, and he 

 spent much time in the investigation of 

 such tones due to the interference of upper 

 partials. It was in furtherance of this in- 

 vestigation that he invented the wave 

 siren ; and as a result of experiment with 

 it he concluded, in opposition to the view 

 of Helmholtz, that musical quality is deter- 

 mined not only by the number, the orders 

 and the relative intensities of the upper 

 partials which accompany a given funda- 

 mental tone, but also by their mode of 

 phase combiuation. To test this the wave 

 siren was certainly better than the appa- 

 ratus employed by Helmholtz ; but the 

 perception of the result requires an experi- 

 enced ear. The experiment is more psy- 

 chological than physical. Upon the present 

 writer, while cooperating with Koenig in 

 his laboratory, and upon others also, the 

 decided impression was that Koenig's con- 

 clusion was correct. But the subject is 

 still one for investigation. 



A monumental piece of mechanical work 

 accomplished by Koenig was his great 

 tonometer, consisting of hundreds of ac- 

 curately adjusted and properly labeled 



tuning forks arranged in a series, each 

 making a definite and small number of 

 beats with the preceding and following ones, 

 so that the frequency of any source of sound 

 approximately simple can be at once as- 

 certained by direct comparison. The range 

 extends through all the tones ordinarily 

 employed in music. To have access to this 

 tonometer the late Professor A. M. Mayer 

 spent the summer of 1892 in Paris, where 

 he secured the cooperation of Koenig 

 in his research on the variation of the 

 modulus of elasticity of different metals 

 with change of temperature, as indicated 

 by the pitch obtained by transverse vibra- 

 tion of bars. Koenig's keen ear was applied 

 also in Mayer's investigation regarding the 

 duration of the residual auditory sensation 

 when beats are produced by neighboring 

 tones in different parts of the musical scale. 

 The author's conclusion was that, between 

 the limits of 100 and 4,000 vibrations per 

 second, there was closer accordance be- 

 tween the results of calculation and ob- 

 servation than in the case of any other 

 physiological law for which the attempt 

 had been made to express sensation mathe- 

 matically. So well trained was Koenig's 

 ear that in the tuning of the standard 

 forks issued from his laboratory there was 

 little need for any better guide than his own 

 auditory sensation. After the pitch had 

 been provisionally attained in this way it 

 was corrected by other and more exact 

 methods, but the correction was always 

 very small. 



It seems scarcely probable that Koenig 

 will have any successor. For a man now 

 to devote his whole life to the science of 

 acoustics would be a piece of specialization 

 for which but little reward can be expected. 

 The progress of science has its phases of 

 relative importance and that of acoustics 

 seems now to be past. Koenig is dead, and 

 his friends will remember him with afiec- 

 tion and respect. His devotion to acous- 



