THE SENSE OF HEARING. 827 



ment of tactile nerves in the tympanic membrane or of the auditory filaments 

 in the internal ear is yet uncertain. 1 Such sensations probably form an import- 

 ant quota of that complex system of sensations which do not obtrude themselves 

 on consciousness, but which, nevertheless, bring information from the outer 

 world, and have an intimate association with the more or less reflex move- 

 ments that preserve the equilibrium of the body. 



Overtones and Quality of Sound. We have thus far considered only 

 simple tones produced by simple vibrations of elastic bodies. Thus, a stretched 

 string plucked at its middle vibrates throughout its whole length, the greatest 

 amplitude of movement being at the middle point, which moves to and fro 

 like a pendulum. It is very rare that a body set vibrating confines itself to 

 a single pendular movement. Thus, a stretched string when struck not only 

 moves as a single cord, but the string may break up, as it were, into two halves, 

 each vibrating independently, but with twice the rate of movement of the 

 whole length of string. Not only is this the case, but the string in its vibra- 

 tion also breaks up into chords of one-third, one-fourth, one-fifth, etc. of its 

 original length, giving rise to vibrations three, four, and five times as rapid as 

 those produced by the whole string. In musical phrase, the middle c of the 

 piano, when this key is struck, gives not only a note c representing 132 vibra- 

 tions, but also its octave c' of 264 vibrations, the fifth above this of 396 

 vibrations, the second octave, 528, the third above this, 660, and so on. The 

 vibration of a string, then, sends to the ear a complex series of tones each of 

 which represents a simple pendular motion of the air. The lowest tone, that 

 produced by the slowest rate of vibration of the string as a whole, is known 

 as the fundamental tone. 



The pitch of the fundamental tone determines our estimate of the pitch 

 of the whole complex note. The other tones produced by segmental vibration 

 of the string are known as partial tones, upper partials, or overtones. The 

 fundamental tone is usually stronger than its accompanying overtones, the 

 successively higher upper partials diminishing rapidly in intensity. Some 

 musical instruments produce notes with a longer series of overtones than do 

 others ; the human voice is particularly rich in overtones. Instruments differ 

 also in the greater or lesser strength and in the relative prominence of the 

 individual overtones accompanying the fundamental. It is the number and the 

 relative prominence of the overtones in a musical note that determine its quality. 

 Thus, a violin, a cornet, and a piano, though sounding a note of the same 

 pitch, would never be mistaken the one for the other ; our discrimination of 

 their notes depends simply upon the difference in the relative strength and the 

 number of their overtones, the fundamental tone being the same throughout. 

 The brilliancy and richness of musical notes is dependent on their wealth of 

 upper partials. It is believed that a sound-producing body, like a stretched 

 string, does not send to the ear a separate set of waves representing each of its 

 segmental vibrations, but that all the waves aroused by it fuse together into 

 a single series of waves of peculiar form. Such a composite wave may be 

 1 W. James : Psychology, 1890, vol ii. p. 140. 



