224 AUDITORY SENSATIONS. [BOOK in. 



the amplitude of the vibrations, by the amount of energy which is 

 expended in producing the vibratory movements ; 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 vibrations ; 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 analyse 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 G 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 rising out 

 of these several constituent simple vibrations. Almost all musical 

 sounds are thus composed of what "is called a fundamental tone 

 accompanied by a number of partial tones. When a violin string 

 gives out a musical note, the fundamental tone is produced by the 

 string vibrating along its whole length, the partial tones by the 

 string vibrating at the same time in segments or definite parts of 

 the whole length ; and so with other instruments ; hence the name 

 ' partial.' Since these partial tones have a higher pitch than the 

 fundamental tone they are frequently spoken of as ' partial upper- 

 tones or overtones ' or simply as ' overtones.' The partial tones 

 vary in number and relative prominence in different instruments 

 and thus give rise to a difference in the sensation caused by the 

 whole sound. Hence while a ' tone ' is a single series of simple 

 vibrations, a ' note ' may be and generally is a number of series of 



