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XL. Researches in Acoustics. By Alfred M. Mayer*. — No. VI. 

 [Continued from vol. xlviii. p. 525.] 



Contents. 



1 . The Determination of the Law connecting the Pitch of a Sound with 



the Duration of its Residual Sensation. 



2. The Determination of the numbers of Beats, throughout the musical 



scale, which produce the greatest dissonances. 



3. Application of these Laws (1 and 2) in a New Method of Sonorous 



Analysis, by means of a perforated rotating disk. 



4. Deductions from these Laws leading to new Facts in the Physiology of 



Audition. 



5. Quantitative Applications of these Laws to the fundamental facts of 



Musical Harmony. 



" Consonanz ist eine continuirliche, Dissonanz eine intermittirende Ton- 

 empfindung." — Helmholtz. 



1 . The Determination of the Law connecting the Pitch of a Sound 

 with the Duration of its Residual Sensation. 



WHILE the durations of the residual sensations on the eye, 

 corresponding to lights of various colours and intensi- 

 ties, have been the subjects of many masterly memoirs, I know 

 of no attempts to determine the durations of the residual sono- 

 rous sensations. Helmholtz founds indeed his Physiological 

 Theory of Music on the facts that a certain number of beats per 

 second produce in the ear a maximum dissonant sensation, 

 while a greater number may blend into a smooth continuous 

 sound; and in discussing the position in his scaleof the "damping- 

 powers " of the covibrating parts of the organ of Corti, Helmholtz 

 (Tonempf. p. 212 et seq.) infers, from the difficulty of trilling on 

 the bass notes, that the covibrating parts of the ear set in motion 

 by sounds of low pitch maintain their vibrations longer than 

 those excited by sounds belonging to higher portions of the 

 musical scale. He says :— " Trills of this kind, of ten notes per 

 second, are of a sharp and clear execution in the greatest portion 

 of the musical scale ; below the la of 110 vibrations in the grand 

 and contra octaves, however, they sound bad, harsh, and the 

 sounds begin to blend." Yet it does not appear that Helmholtz 

 ever attempted to determine that quantitative relation existing 

 between the pitch of a sound and the duration of its residual 

 sensation which I will now endeavour to establish. This law 

 in its further applications will render quantitative many of the 

 qualitative statements contained in HelmhohVs renowned work. 

 The method of obtaining the facts (of which our law expresses 

 the general relation) is similar to the method used in the study 

 of the analogical phenomena of light. A simple sound was ob- 

 tained by vibrating a fork before the mouth of its corresponding 

 resonator; and this sound was broken up into flashes, or explo- 

 sions by alternately screening and unscreening the mouth of the 

 * Communicated by the Author. 



