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186 COMBINATION-TONES OF OVERTONES. [VIII. § 93.
whatever to Helmholtz's theory of consonance and dissonance, but, so far as it represents actual facts, to be valid against the prevalent views of Musical theorists.
93. A point connected with combination-tones, which might otherwise occur as a difficulty to the reader's mind, shall here be briefly noticed. When two clangs coexist, combination-tones are produced between every pair which can be formed of a tone from one clang with a tone from the other. These intrusive tones will usually be very numerous, and, for aught that appears, may interfere with those originally present to such an extent as to render useless a theory based on the presence of partial-tones only. Helmholtz has removed any such apprehension by showing generally that dissonance due to combina-tion-tones produced between overtones never exists except where it is already present by virtue of direct action among the overtones themselves. Thus the only effect attributable to this source is a somewhat increased roughness in all intervals except absolutely perfect concords. No modifications, therefore, have to be introduced on this score into the conclusions of §§ 81-86.