LAWS OF SONOROUS VIBRATIONS. 829 



If we diminish the third by a semitone, we still have for the predominant note, but 

 the quality of the chord is changed to the minor. In this rough illustration, the ear can 

 readily detect the harmonious tones ; but, in the note of a single string, this cannot be 

 done without practice and close attention. Still, in the notes of single strings, the ear 

 can distinguish the harmonics ; and, what is more satisfactory, the existence of harmon- 

 ics can be actually demonstrated in various ways. 



From what we have just stated, it follows that nearly all musical tones consist, not 

 only of a fundamental sound, but of harmonic vibrations, subordinate to the fundamental 

 and qualifying it in a particular way. These harmonics may be feeble or intense ; cer- 

 tain of them may predominate over others ; some, that are usually present, may be 

 eliminated ; 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 upon their reinforcement by reso- 

 nance. The vibrations of a stretched string, not connected with a resonant body, are 

 almost inaudible. In musical instruments, we have the sound taken up by some mechani- 

 cal arrangement, as the sound-board of the organ, piano, violin, harp, guitar, etc. In 

 the violin, for example, the sweetness of the tone depends chiefly upon the construction 

 of the resonant part of the instrument, and but little upon the strings themselves, which 

 are frequently changed. The same is true of the human voice, of wind-instruments, etc. ; 

 but we could not discuss these points elaborately, without giving a full description of the 

 various musical instruments in common use, which would be out of place in a work upon 

 physiology. 



In addition to the harmonic tones of sonorous bodies, various discordant sounds are 

 generally present, which modify 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 variety. These 

 sounds are composed of irregular vibrations and are consequently inharmonious. Nearly 

 all notes that we speak of in general terms as musical are composed of musical, or har- 

 monic aliquot tones with the discordant elements to which we just alluded. 



Aside from the relations of the various component parts of musical notes, the quality 

 depends largely upon the form of the vibrations. To quote the words of Helmholtz, u 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 forms of wave, have an extraordinarily soft quality ; 

 and the qualities of sound generated by the zither and violin resemble in harshness the 

 angularity of their wave-forms." 



Harmonics, or Overtones. As we have stated in the foregoing discussion, 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 harmonics, and these may 

 be used for illustration, remembering that the phenomena here observed have their analo- 

 gies 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 suppose, for example, that we have a string, the fundamental tone of which is 0. We 

 damp this string with a feather at one-fourth of its length and draw a violin-bow across 

 the smaller section. We then sound, not only the fourth part of the string across which 

 the bow is drawn, but the remaining three-fourths ; but, if we have placed little riders of 

 paper upon the longer segment, at distances equal to one-fourth the entire string, they 



