EAR AS AN ORGAN FOR SOUND SENSATIONS. 381 



however, that a vibration too slow to be perceived by the ear will 

 give overtones of sufficient strength to be recognized. An inter- 

 esting example in physiology of this fact is furnished by the tone 

 of the contracting muscle. As heard, this tone corresponds to a 

 vibration of 40 per second; but other data lead us to believe that 

 the vibrations of the contracting muscle, due to the single con- 

 tractions of which the compound contraction is composed, occur 

 at the rate of only 10 per second; so that what is heard is, in reality, 

 the second octave of the fundamental. The high limit of audibility, 

 on the other hand, is usually placed at 40,000 double vibrations 

 per second, although the various estimates published vary so 

 widely that in this respect there must be great individual differences. 

 The shrill notes of insects are said to be inaudible to some ears. 

 Konig, making use of Kundt's method of light powders, succeeded 

 in tuning a series of forks to an estimated rate of 90,000 double 

 vibrations per second. It was found that those between c 7 and c 9 

 (8192 to 32,768) were generally audible, while the c 10 (65,536) was 

 inaudible. The limit, therefore, lay between c 9 and c 10 . Notes 

 near this high limit are not, however, usable in ordinary music; 

 the sensations produced have a disagreeable, if not actually painful 

 shrillness. The range of vibrations employed in music is illustrated 

 by the seven octaves of the piano, the notes varying from the lowest 

 c of 32 vibrations to c e of 4096 vibrations. The intervening series 

 is divided into tones whose serial relations to each other are ex- 

 pressed by the ratios f or V and semitones of the ratio yf or ff ; 

 thus, c"= 256 vibrations and the d" of the same octave corresponds 

 to 256 X f = 288 vibrations.* 



"See Helmholtz, Popular Scientific Lectures, "Ueberdie physiologischen 

 Ursachen des musikalischen Harmonic," Bonn, 1857. 



