Prof. J. D. Everett on Resultant Tones. 203 



measure will be the frequency of the complete cycle of change. 

 This cycle will not be conspicuous in the curve if the ratio of 

 n—m to ^(n + m) is very small, but will assert itself more and 

 more as this ratio increases ; and these remarks will apply to 

 the comparison of the fundamental with the first difference- 

 tone. 



10. If the ear is able so to alter the form of waves 

 impinging upon it as to generate resultant tones, it is natural 

 to seek for some instance of a similar action in external bodies. 

 A violin is very susceptible, like the ear, to vibrations of all 

 frequencies between wide limits, and the sound-post serves, 

 like the ossicles of the ear, to transmit vibrations from one 

 portion to another. It is easy to produce resultant tones by 

 bowing two strings of a violin together. For example, in 

 the ordinary process of tuning, when the fourth and third 

 strings with frequencies as 2 : 3 are combined, the resultant 

 tone 1 is very observable if attention be directed towards it. 

 But more striking effects are obtained when the resultant is 

 at a larger interval from the primaries. The major sixth 3 : 5, 

 the major second 8 : 9, and the minor seventh 5 : 9, are suitable 

 intervals for calling out the fundamental 1, the strings em- 

 ployed being either the first and second or the second and 

 third. The deep resultant tone thus obtained can not only 

 be heard by the ear but felt as a tremor by the hand which 

 holds the instrument. This is clear evidence of its objective 

 existence, and I have succeeded in confirming the fact by 

 means of a Helmholtz resonance-globe, the largest of the 

 ordinary set, responding to C of 128 vibrations. When held 

 with the edge of its mouth resting against the side of the 

 violin, it responds to the combination C of 256 and G of 384 

 on the 4th and 3rd strings, or to the combination C of 512 

 and E of 640 on the 2nd and 1st ; or, still better, to the 3rd 

 and 2nd open strings each flattened one note, so as to be C of 

 256 and G of 384. Here, then, we have distinct evidence 

 that the violin possesses the power which I have ascribed to 

 the ear — the power of manufacturing the fundamental when 

 the two primaries are supplied. 



11. Sir John Herschel, in his treatise on Sound (Enc. 

 Met. arts. 238, 239), mentions the fact that the common 

 fundamental can be called out by sounding two or more of 

 its harmonics on very accurately tuned strings or pipes, and 

 says that the effect cannot be obtained from a pianoforte tuned 

 in the ordinary way, because the intervals are tempered. I 

 find, however, on trying the experiment with an upright 

 Broadwood of date about 1860, that C of 64 is easily called 

 out by simultaneously striking eight or ten of its harmonics ; 



P2 



