222 PROCEEDINGS OF THE AMERICAN ACADEMY 



XV. 



CONTRIBUTIONS FROM THE PHYSICAL LABORATORY OF THE 

 MASSACHUSETTS INSTITUTE OF TECHNOLOGY. 



XXXVIII. —ON THE LEAST NUMBER OF VIBRATIONS 

 NECESSARY TO DETERMINE PITCH. 



By Charles R. Cross and Margaret E. Maltby. 



Presented May 24, 1892. 



The present paper is an extension of one by the same authors 

 read at the meeting of this Academy held on June 10, 1891, but not 

 hitherto published. In the investigation described in it a method 

 was employed which was originally proposed by one of the writers 

 a number of years since in a paper read at the Philadelphia Meeting 

 of the American Association for the Advancement of Science, and 

 published in abstract in the Proceedings for 1884, Vol. XXXIII. 

 p. 114. 



In that paper attention was called to a defect in the method em- 

 ployed by Savart and Kohlrausch, from which they concluded that 

 at least two complete vibrations are necessary to characterize pitch. 

 This defect is a consequence of the character of the vibrations im- 

 pressed upon the air by the blows produced by the teeth of the 

 wheel of Savart or the comb of Kohlrausch. 



The statement of this difficulty in the paper referred to is as 

 follows : — 



"A cardinal defect in these methods of investigating the point 

 in question is that the sound produced by a toothed wheel is very 

 impure; first, because the noise of each separate impulse is mingled 

 with the note produced by the coalescence of the separate impulses; 

 and second, because the proper note, determined by the number of 

 impulses, is itself far from simple in its character. To obtain re- 

 sults that are fully satisfactory the vibrations utilized should be 

 pendular (sinusoidal) in their character. I see no reason in the 

 nature of things why, if a single such simple vibration could be 

 caused to fall upon the ear, it should not produce the sensation of 

 a definite pitch. Rather, under the known action of the separate 



