182 SPECIAL SENSES. 



the timbre, producing, usually, a certain roughness, such as 

 the grating of a violin-bow, the friction of the columns of 

 air against the angles in wind-instruments, etc. All of these 

 conditions have their effect upon the quality of tones ; and 

 these discordant sounds may exist in infinite number and va- 

 riety. These sounds are composed of irregular vibrations, 

 and are consequently inharmonious. Nearly all tones that 

 we speak of in general terms as musical are composed of mu- 

 sical, or harmonic partial tones, and the discordant elements 

 to which we just alluded. 



Aside from the relations of the various component parts 

 of musical tones, the quality depends largely on the form of 

 the vibrations. To quote the words of Helmholtz, " the 

 more uniformly rounded the .form of the wave, the softer 

 and milder is the quality of the tone. The more jerking and 

 angular the wave-form, the more piercing the quality. Tun- 

 ing-forks, with their rounded forms of wave, have an extraor- 

 dinarily soft quality ; and the qualities of tone generated by 

 the zither and violin resemble in harshness the angularity of 

 their wave-forms." - 1 



Harmonics, or Overtones. As we have stated in the fore- 

 going paragraphs, nearly all tones are composite, but some 

 contain many more partial,, or secondary vibrations than oth- 

 ers. The tones of vibrating strings are peculiarly rich in 

 harmonics, and these may be used for illustration, remember- 

 ing that the phenomena here observed have their analogies in 

 nearly all varieties of musical sounds. If a stretched string be 

 made to vibrate, the secondary tones, which qualify, as it 

 were, the fundamental, are called harmonics, or, in German, 

 overtones, a term which is now much used by English 

 writers. 



While it is difficult at all times to distinguish by the ear 

 the individual overtones of vibrating strings, their existence 

 can be demonstrated by a few simple experiments. Let us 



1 HELMHOLTZ, Popular Lectures on Scientific Subjects, New York, 1873, p. 77. 



