be made yet perhaps to supply.

* * * * *




RECENT EXPERIMENTS AFFECTING THE RECEIVED THEORY OF MUSIC.


To prove the incorrectness of Helmholtz's statement that beats do not
colesce into musical sounds, but that the ear will distinguish them as a
rumbling noise, even when their number rises as high as 132 vibrations
per second, Rudolph Koenig has constructed a series of tuning forks,
recently presented by President Morton to the Stevens Institute of
Technology. The following table exhibits the number of vibrations per
second of these forks, the ratios of their vibrations when two are
sounded together, the number of beats produced, and the resultant sound:

Vibrations per second. Ratio. Beats. Sounds.

3840 :4096 15:16 128 Ut_{2}
3904 : " 61:64 96 Sol_{1}
3936 : " 123:128 80 Mi_{1}
3968 : " 31:32 64 Ut_{1}
3976 : " 497:512 60 Si_{-1}
3989.3 : " 187:192 53.3 La_{-1}
4000 : " 125:128 48 Sol_{1}
4010.7 : " 47:48 42.7 Fa_{-1}
4016 : " 251:256 40 Mi_{-1}