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VIII. §80.] DISSONANT OVERTONES. 167
will therefore be a certain inevitable roughness in its timbre This is the cause of the harsh quality of trumpet or trombone notes, and also of the shrill tremulous sounds sometimes observed in the human voice (p. 136). In fact we may regard the partial-tone series above the seventh tone, when fully represented, as contributing mere noise to the clang. This explains why it is advantageous that only the lower partial-tones of organ reeds should be intensified by resonance [see § 66, p. 132].
80. It has been shown that, when two simple tones are simultaneously sustained, beats can arise directly between them only under one condition, viz. that the tones shall differ in pitch by less than a Minor Third, or thereabouts. When, however, the two co-existing sounds are no longer simple tones, but composite clangs each consisting of a series of well-developed partial-tones, the case becomes altogether different. Let us examine the state of things which then presents itself.
The sounds of most musical instruments practically contain only the first six partial-tones; we will, therefore, assume this to be the case with the clangs before us. No beats can then arise between partial-tones of the same clang for the reason assigned on p. 166. Dissonance due to beats will, however, be produced if a partial-tone belonging