62 Mr. S. Taylor on Variations of Pitch in Beats. 



wave-lengtlis will therefore be all equal, each having the value 



2 



. Hence, in this case, there will be no variation of pitch 



whatever, the number of vibrations per second remaining con- 

 stant, and equal to ^ ^ 



In passing to the experimental verification of the above theo- 

 retical conclusions, I may mention a confirmatory instance which 

 is interesting from its undesigned character. Helmholtz has 

 given* a copy of a curve representing the movement of a mem- 

 brane resonating under the action of two beating organ-pipes, 

 drawn by means of Konig^s phonautograph. In this instru- 

 ment a small steel pointer is connected with the membrane and 

 registers the vibrations of the latter on a rotating cylinder which 

 has previously been covered with lampblack-coated paper. The 

 figure is intended by Helmholtz to illustrate variations of inten- 

 sity alone ; nevertheless the roughest measurement suffices to 

 show that the wave-lengths near the minimum of intensity are 

 shorter than those near the maximum, and therefore that 4)itch- 

 variations are also present. It is clear, by what has been shown 

 in the present paper, that in the experiment thus recorded the 

 more acute of the two organ sounds must have been likewise the 

 louder. 



As another example of how easy it is to miss a phenomenon 

 lying directly under our eyes, when we are not specially on the 

 look-out for it, I may be allowed to relate a conversation with an 

 organ- and pianoforte-tunist of much experience, Mr. Ling, of 

 Cambridge. I asked him whether he had ever noticed changes 

 of pitch in slow beats. He replied in the negative, and expressed 

 a decided opinion that no such changes occurred. On trying the 

 experiment, however, upon a pianoforte in my rooms, he at once 

 perceived the variations in question, though remarking that he 

 would not have accepted the fact save on the testimony of his 

 own ears, so convinced was he that the alternations of intensity, 

 to which he had hitherto exclusively attended, constituted the 

 whole of the phenomenon. 



I had afterwards the advantage of Mr. Ling^s assistance in 

 some experiments made on the organ in the chapel of Trinity 

 College. A stopped diapason, At?, having been flattened until 

 it gave slow beats with the neighbouring G, we found, in accord- 

 ance with the result obtained above for sounds of equal intensity, 

 that the pitch of the beating tone was perfectly steady. On 

 combining, however, the same G with an Al? belonging to a 

 softer stop on another manual, which had first been similarly 



*P.26L 



