438 PHYSIOLOGICAL PHYSICS. [Cha P . xxxn. 



tracing of it is obtained it does not exhibit smoothly 

 rounded crests and hollows of equal size, but a curve 

 of considerable irregularity, in fact a compound wave 

 would be represented. This compound wave, in 

 accordance with the principle already noted, would be 

 capable of analysis into several simple waves of a 

 harmonic series. In fact, the note of the vibrating 

 string is a compound of a simple note, due to the 

 vibrations of the string as a whole, and of other notes 

 whose vibrations correspond to the movements of the 

 string when divided into two or more segments. It 

 is this mixture of harmonics, partial notes or overtones 

 as they are also called, with the simple fundamental 

 tone that gives the quality to the tone emitted by the 

 string. Indeed, with some attention a trained ear 

 can always detect in the sound of a vibrating string 

 one or more tones higher than the fundamental, i.e. 

 one or more overtones. Each musical instrument 

 produces different harmonics with its fundamental 

 notes. Thus the violin string produces specially the 

 lower harmonics of the series^ hence its mellow sound ; 

 brazen instruments produce specially the higher har- 

 monics, hence their shrill piercing sounds. The tone 

 of a pianoforte, the string of a harp, etc., each pro- 

 duces its own particular mixture of overtones with 

 its fundamental, its own special blend, so to speak, 

 and hence has its own particular quality of sound. 

 The difference in the qualities of human voices singing 

 notes of the same pitch are due to the same causes, 

 namely, the differences in the harmonics that specially 

 predominate in each voice. Dissonance may be 

 produced by overtones even when the fundamental 

 notes are too far removed to produce audible 

 beats. One overtone of one note may be near 

 enough in the number of its vibrations to an overtone 

 of another note to produce beats, and give roughness 

 to the sound. 



