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216 TONIC SOL-FA NOTATION. [X. § 116.
sarily follow from this superiority, I desire to express the most confident and uncompromising opinion.l
116. In closing the inquiry which occupies the preceding chapters, it will be advisable to examine very concisely the bearing of our principal result, the theory of consonance and dissonance, on the aesthetics of music. Dissonance was shown to arise from rapid beats, and the concords were classed in order, according to their more or less complete freedom from dissonance; the Octave coming first, followed by the Fifth, Fourth, Major Third and Sixth and Minor Third and Sixth. This classification was strictly physical, depending exclusively on smoothness of effect. On its own ground, therefore, this classification is absolutely unassailable, and whoever says, for instance, that a Major Third is a smoother concord than a Fifth or Octave, asserts what is as demonstrably false as that the moon goes round the earth in an exact circle. Nevertheless, it by no means necessarily follows that the smoothest concords must be the most gratifying to the ear. There may be some other property of an interval which gives us greater satisfaction than mere consonance.
1 These topics will be found handled somewhat more at large in a Lecture delivered by me at Manchester on Jan. 11, 1883. ("The Tonic Sol-fa Movement" London, J. Curwen and Sons, 8 Warwick Lane, E. C.)