392 THE SPECIAL SENSES. 



that vary in pitch with the rate of excitation and in intensity with 

 the amphtude of the vibratory movement. A third property of 

 musical sounds is their variations in quahty or timbre. The same 

 note of the same amphtude, when given by different musical instru- 

 ments, varies in quality, so that we have no difficulty in recognizing 

 the note of a piano from the same note when given by a violin or 

 the human voice. The underlying physical cause of variations in 

 timbre is found in the form of the sound waves produced, and im- 

 mediately, therefore, in the form of vibratory movement communi- 

 cated to the perilymph. Examination of the forms of sound waves 

 produced by different musical instruments shows that they may be 

 divided into two great groups : (1) The simple or pendular form ; (2) 

 the compound or non-pendular form. The simple or pendular form 

 of wave is given, for instance, by tuning forks. A graphic repre- 

 sentation of this wave form may be obtained by attaching a bristle 

 to the end of the fork and allowing it to write upon a piece of black- 

 ened paper moving with uniform velocity, — the blackened surface, 

 for instance, of a kymograpliion. The form of the wave obtained 

 is represented in Fig. 174. The vibrating body swings symmetrically 

 to each side of the Une of rest, and, inasmuch as this is also the form 

 of movement that would be traced by a swinging pendulum, this 

 form of wave is designated frequently as pendular. It is sometimes 

 called also the sinusoidal wave, since the distance of the vibrating 

 point to each side of the line of rest is equal to the sine of an arc 

 increasing proportionally for the time of the phase. A compound 

 (or non-pendular or non-sinusoidal) wave may have a very great 

 variety of forms. The different phases follow periodically, but the 

 movement of the vibrating body to each side of the line of rest is not 



Fig. 174. — Form of wave made by tuning fork. 



perfectly symmetrical. Fourier has shown that any periodical vibra- 

 tory movement, whatever may be its form, may be considered as 

 being composed of a series of simple or pendular movements whose 

 periods of vibrations are 1, 2, 3, 4, etc., times as great as the vibra- 

 tion period of the given movement. That is, every so-called com- 

 pound wave form may be considered as being caused by the fusion 

 of a number of simple waves. Representing the wave movement 

 of the air graphically as water waves, this composition of simple 

 waves into compound ones is illustrated by the curves given in Fig. 

 175. In this figure A and B represent two simple vibrations such 

 as would be given by two tuning-forks, the vibrations in B being 

 double those of A. If these two waves are communicated to the air 



