Chap, iv.] HEARING. 999 



energy which is expended in producing the vibratory move- 

 ments ; the greater the disturbance of the air (or other medium) 

 the louder the sound. Using the term ' wave ' to denote the 

 characters of the vibrations, the loudness of a sound is indicated 

 by the height of the wave. 



In the second place we recognize a character which we call 

 pitch. This is determined by the frequency of repetition of the 

 vibrations, by the time taken up by each vibration ; the greater 

 the number of consecutive vibrations which fall upon the ear in 

 a second, the shorter the time of each vibration, the higher the 

 pitch. Hence the pitch of a sound is indicated by the length of 

 the wave, a low note having a long, a high note a short wave- 

 length. We are able to distinguish a whole series of musical 

 sounds of different pitch, from the lowest to the highest audible 

 note. 



In the third place, we distinguish musical sounds by what is 

 usually called their quality (timbre) ; the same note sounded on 

 a piano and on a violin produces very different sensations, even 

 though the two instruments give rise to vibrations having the 

 same period of repetition. This arises from the fact that the 

 musical sounds generated by most musical instruments are not 

 simple but compound vibration ; the instrument sets going in 

 the surrounding air not one series only of vibrations of one 

 wave-length, but several series of different wave-lengths ; as we 

 shall see however, the several vibrations travel through the air, 

 not as a group of waves but as one compound wave. When the 

 note C in the bass clef is struck on the piano, and we analyze 

 the total sound, we find that it can be resolved partly into a 

 series of vibrations with a period characteristic of the pure tone 

 of C of the bass clef, and partly into other series of vibrations 

 with periods characteristic of the C in the octave above (middle 

 C), of the G above that, of the C of the next octave, and of the 

 E above that. And the sensation which we associate with the 

 sound of the C in the bass clef on the piano is determined by 

 the characters of the complex vibration arising out of these 

 several constitutent simple vibrations. Almost all musical 

 sounds are thus composed of what is called & fundamental tone 

 accompanied by a number of partial tones. When a violin 

 string gives out a musical note, the fundamental tone is pro- 

 duced by the string vibrating along its whole length, the par- 

 tial tones by the string vibrating at the same time in segments 

 or definite parts of the whole length ; and so with other instru- 

 ments; hence the name 'partial.' Since these partial tones 

 have a higher pitch than the fundamental tone they are fre- 

 quently spoken of as ' partial uppertones or overtones ' or simply 

 as ' overtones.' The partial tones vary in number and relative 

 prominence in different instruments and thus give rise to a dif- 

 ference in the sensation caused by the whole sound. Hence 



