560 A UDITOR Y SENS A TIONS. [BOOK HI. 



the vibrations; the greater the disturbance of the air (or other 

 medium) the louder the sound. In a musical sound we recognise 

 also a character which we call pitch. This is determined by the 

 wave-length of the vibrations; the shorter the wave-length, the 

 larger the number of consecutive vibrations which fall upon the ear 

 in a second, the higher the pitch. We are able to speak of a whole 

 series of tones or musical sounds of different pitch, from the lowest 

 to the highest audible tone. And even in many noises we can, to 

 a certain extent, recognise a pitch, indicating that among the 

 multifarious vibrations there is a periodicity of certain groups of 

 vibrations. 



Lastly, we distinguish musical sounds by their quality; the 

 same note sounded on a piano and on a violin produce very 

 different sensations, even when a series of vibrations having in each 

 case the same period of repetition is set going. This arises from 

 the fact that the musical sounds generated by most musical in- 

 struments are not simple but compound vibrations. When the 

 note C in the treble for instance 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 the treble 0, and partly into other series of vibrations with 

 periods characteristic of the C in the octave above, of the G above 

 that, of the C in the next octave, and of the E above that. And 

 the sensation which we associate with the sound of the treble C on 

 the piano is determined by the characters of the complex vibration 

 arising out of these several constituent simple vibrations. Almost 

 all musical sounds are thus composed of what is called a 'funda- 

 mental tone' accompanied by a number of 'overtones.' And the 

 overtones varying in number and relative prominence in different 

 instruments, give rise to a difference in the sensation caused by the 

 whole tone. So that while the fundamental tone determines the 

 pitch of the sound, the quality of the sound is determined by the 

 number and relative prominence of the overtones. In a somewhat 

 similar way we distinguish the quality of noises, such as a banging, 

 crackling, or rustling noise, by an appreciation of sudden or 

 irregular changes in the amplitude and period of the constituent 

 vibrations. 



Since we have a very considerable appreciation, capable by 

 exercise of astonishing enlargement, of the loudness, pitch, and 

 quality of a wide range of noises and musical sounds, it is clear 

 that, within the limits of hearing, each vibration or series of 

 vibrations must produce its effect on the auditory nerves, according 

 to the measure of its intensity and period. Out of those effects, out 

 of the sensory impulses to which the several vibrations thus give 

 rise, are generated our sensations of the noise or of the sound. 



The vibrations of a musical sound (and since noises are so im- 

 perfectly understood-, we may, with benefit, chiefly confine ourselves 

 to musical sounds), as they pass through the air (or other medium) 



