PHYSICS OF SOUND 727 



fied, and with these modifications in form, the quality, or timbre of the 

 note is changed. 



From what has just been stated, it follows that nearly all musical 

 notes consist, not only of a fundamental sound, but of harmonic vibra- 

 tions subordinate to the fundamental and qualifying it in a particular 

 way. These harmonics may be feeble or intense ; certain of them may 

 predominate over others ; some that usually are present may be elimi- 

 nated ; and, in short, there may be a great diversity in their arrangement, 

 and thus the timbre may present an infinite variety. This is one of the 

 elements entering into the composition of notes, and it affords a partial 

 explanation of quality. 



Another element in the quality of notes depends on their reenforce- 

 ment by resonance. The vibrations of a stretched string not connected 

 with a resonant body are almost inaudible. In musical instruments the 

 sound is taken up by some mechanical arrangement, as the sound- 

 board of the organ, piano, violin, harp or guitar. In the violin, for 

 example, the sweetness of the notes depends mainly on the construction 

 of the resonant part of the instrument and but little on the strings them- 

 selves, which latter are frequently changed ; and the same is in a 

 measure true of the human voice. 



In addition to the harmonic tones of sonorous bodies, various discord- 

 ant sounds usually are present, which modify the timbre, producing 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 

 these conditions have their effect on the quality of tones ; and these dis- 

 cordant sounds may exist in infinite number and variety. These sounds 

 are composed of irregular vibrations and consequently are inharmonious. 

 Nearly all notes that are spoken of in general terms as musical are com- 

 posed of musical, or harmonic aliquot tones, with the discordant ele- 

 ments to which allusion has just been made. 



Aside from the relations of the various component parts of musical 

 notes, 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 sound. The 

 more jerking and angular the wave-form, the more piercing the quality. 

 Tuning-forks, with their rounded form of waves, have a remarkably soft 

 quality ; and the qualities of sound produced by the zither and violin 

 resemble in harshness the angularity of their wave-forms." 



Harmonics, or Overtones, As before stated, nearly all sounds are 

 composite ; but some contain many more aliquot, or secondary vibrations 

 than others. The notes of vibrating strings are peculiarly rich in har- 

 monics ; and these may be used for illustration, remembering that the 



