EAR AS AN ORGAN FOR SOUND SENSATIONS. 403 



is larger. The lowest rate of vibration that can cause a musical 

 sensation is usually placed at 24 to 30 per second, although some 

 ears can still respond to an octave lower about 16 per second. To 

 most ears vibrations below 16 per second are felt, if perceived at all, 

 as single pulses that stimulate the sensory nerves of the tympanic 

 membrane itself, giving pressure sensations rather than auditory 

 sensations. It may happen, however, that vibrations too slow 

 to be perceived by the ear as an auditory sensation will give 

 overtones of a higher pitch and of sufficient strength to be recog- 

 nized. 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, how- 

 ever, 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 6 of 4096 vibrations. The intervening series is divided into 

 tones whose serial relations to each other are expressed by the 

 ratios -f or V and semitones of the ratio yf or \ f ; thus, c" = 256 

 vibrations and the d" of the same octave corresponds to 256 X f= 

 288 vibrations.* 



* See Helmholtz, Popular Scientific Lectures, "Ueber die physiologischen 

 Ursachen des musikalischen Harmonic," Bonn, 1857. 



