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The Theory Of Sound Which Constitutes The Physical Basis Of The Art Of Music.

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168            DISSONANCE OF TWO CLANGS. [VIII. 81.
to one clang is within the specified distance of a partial-tone belonging to the other clang. Several pairs of tones may be thus situated, and, if so, each will contribute its share of roughness to the general effect. The intensity of the roughness due to any such pair will depend chiefly on the respective orders to which the beating partial-tones belong, and on the interval between them. The lowest partial-tones being the loudest, produce the most powerful beats, and half-Tone beats are, in general, harsher than those of a whole Tone. In determining the general effect of a combination of two clangs, we have to ascertain what pairs of partial-tones come within beating-distance, and to estimate the amount of roughness due to each pair. The joint effect of all these roughnesses, if there are several such pairs* or the roughness of a single pair if there be but one, constitutes the dissonance of the combination. If there be no dissonance, the combination is described as a perfect concord. When dissonance is present, its amount will decide whether the combination shall be called an imperfect concord or a discord. The line separating the two must therefore, of necessity, be somewhat arbitrarily drawn.
81. Let us examine the principal consonant intervals, in the manner above described, beginning with the Octave.
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