Acoustics & Sound For Musicians - Online Book

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

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176                PICTURE OF INTERVALS.          [VIII. § 88.
tions, from one given in Helmholtz's work. The in tervals, reckoned from middle-C, are denoted by dis­tances measured along the horizontal straight line. The dissonance for each interval is represented by the vertical distance of the curved line from the corresponding point on the horizontal line. The cal­culations on which the curve is based were made by Helmholtz for two constituent clangs of the quality of the violin.
The figure indicates the sharpness of definition of an interval by the steepness with which the curve ascends in its vicinity. If we regarded the outline as that of a mountain-chain, the discords would be represented by peaks, and the concords by passes. The lowness and narrowness of a particular pass would measure the smoothness and definition of the corresponding musical interval.
88. The theory of musical consonance and dis­sonance, our examination of which is now concluded, shows that the degree of smoothness or roughness
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