830 AN AMERICAN TEXT-BOOK OF PHYSIOLOGY. 



Inharmonic Overtones. It will be remembered that all the overtones con- 

 tained in a musical note are produced by vibrations which are simple multiples 

 of the rate of the fundamental tone. These overtones are properly called 

 harmonic upper partials ; they are, according to Helmholtz, particularly charac- 

 teristic of stretched strings and narrow organ-pipes. But most elastic bodies 

 have proper tones which are not exact multiples of the fundamental, and 

 which may be termed inharmonic upper partials. The high-pitched jingle 

 heard when a tuning-fork is first struck represents the inharmonic upper par- 

 tials of the fork. Stretched membranes have a great number of such inhar- 

 monic overtones. Inharmonic upper partials, as might be expected, rapidly 

 die out in a note of which they form a part. It is evident that inharmonic 

 proper tones, when nearly of the same pitch, must interfere with one another 

 and repress the development of a well-marked fundamental tone. 



Production of Beats. When two tones of slightly different pitch are 

 sounded together, the more rapid vibrations overtake the slower, so that at 

 certain periods the crests, or phases of condensation, of two waves fall together, 

 and the result is a phase of increased condensation and louder sound. The 

 waves immediately cease to correspond, and diverge more and more until the 

 crest of one falls upon the trough of another, the result being silence, or at 

 least great diminution in the intensity of the sound. Such alternate augmenta- 

 tion and diminution of the waves give rise to pulses in the sound, known 

 technically as beats. This is one of the most familiar and important phenom- 

 ena of musical art. If two tuning-forks on resonance-boxes vibrate in unison, 

 a piece of wax stuck to the prong of one fork will lower its tone and give rise 

 to beats. The undulating sound caused by striking a bell or the rim of a thin 

 glass tumbler is due to beats. When two notes not included in a perfect chord 

 are sounded on the piano, beats are heard not only from the interference of the 

 fundamental tones, but of the upper partials as well. It is the absence of beats 

 in notes which should be in harmony, as those of the major chord, that deter- 

 mines the instrument to be in tune. When two tones produce beats, the 

 number of beats in a given time is equal to the difference between the number 

 of vibrations involved in the two tones in the same time. For example, a tone 

 produced by 256 vibrations in a second sounded with one of 228 vibrations 

 would give 28 beats in a second. It is evident that the frequency of beats 

 may be increased either by increasing the interval between the tones or by 

 striking tones of the same interval in a higher part of the scale. Beats which are 

 not too frequent from four to six in a second have important musical value, 

 but when they number thirty or forty in a second they become' exceedingly dis- 

 agreeable, irritating the ear in a manner analogous to the effect of a flickering 

 light on the eye. When sufficiently near together the beats no longer produce 

 an intermittent sensation. The number of beats in a second required to result 

 in this fusion increases as we ascend the musical scale, varying from 16 beats 

 at c of 64 vibrations per second to 136 beats at c'" of 1024 vibrations. 1 The 

 reason for this variation lies in the progressive shortening of the waves as the 



1 Mayer : Sound, 1891. 



