PROCEEDINGS 



OF THE 



AMERICAN ACADEMY 



OF 



ARTS AND SCIENCES. 



VOL. XXVII. 

 PAPERS READ BEFORE THE ACADEMY. 



I. 



CONTRIBUTIONS FROM THE PHYSICAL LABORATORY OF THE 

 MASSACHUSETTS INSTITUTE OF TECHNOLOGY. 



XXXVII. — SOME CONSIDERATIONS REGARDING 

 HELMHOLTZ'S THEORY OF CONSONANCE. 



By Charles R. Cross and Harry M. Goodwin. 



Presented June 10, 1891. 



The present paper contains the results of a number of experiments 

 relating to certain aspects of the theory of consonance and dissonance 

 put forth by Helmholtz in the Tonempfindungen. In that work 

 the author gives as the number of beats producing the maximum of 

 harshness from thirty to forty per second, reaching this conclusion 

 from a consideration of the amount of dissonance of various different 

 chords in different octaves. 



Ma}*er * studied the relation of the number of beats causing the 

 greatest harshness to the absolute pitch, and showed that there is 

 a marked rise in this number as the pitch becomes higher. The 

 beats studied by Mayer, however, as he himself pointed out, are 

 in several respects different from those which occur in the case of 

 mistimed unisons. They were caused by rotating a disk, which 



* American Journal of Science, Vol. CVIII. p. 211 ; Vol. CIX. p. 267. 



VOL. XXVII. (N. 8. XIX.) 1 



