On the Sensations of Tone (Dover Books on Music)
by Hermann Helmholtz
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Book Summary Information
Author: Hermann HelmholtzBrand: Alfred Publishing
Edition: Paperback
Audio: English (Unknown); German (Original Language); English (Published)
Published: 1954-06-01
ISBN: 0486607534
Number of pages: 576
Publisher: Dover Publications
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- Helmholtz
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Book Reviews of On the Sensations of Tone (Dover Books on Music)
Book Review: Thorough, leisurely study of the principles of musical harmony and scales
Summary: 5 Stars
Part 1 discusses how tones may be perceived as built up by the base tone and the "harmonic upper partial tones". These upper partial tones are what distinguishes different instruments and they determine the "quality of the tone"; e.g. "if only the unevenly numbered partials are present ... the quality of the tone is hollow, and, when a large number of such upper partials are present, nasal", etc. (p. 119). Helmholtz's model of the ear has it that there is a spectrum of hairs in the ear, each with its own mode of vibration. When we hear a tone it is decomposed into its partials through "sympathetic resonance" of the corresponding hairs, and it is this information--i.e. essentially Fourier coefficients--that is sent to the brain.
Part 2 discusses the theory of consonance. Again, the Fourier analysis point of view is the key. The consonance or dissonance of two tones is determined by the interaction of the partials of the tones, giving mathematical precision to the idea that "two consonant tones flow on quietly side by side in an undisturbed stream; dissonant tones cut one another up into separate pulses of tone" (p. 226). Thus one can claim that "ultimately, then, the reason of the rational numerical relations of Pythagoras is to be found in the theorem of Fourier, and in one sense this theorem may be considered as the prime source of the theory of harmony" and so "the enigma which, about 2500 years ago, Pythagoras proposed to science ... 'Why is consonance determined by the ratios of small whole numbers?' has been solved by the discovery that the ear resolves all complex sounds into pendular oscillations ... and that it regards as harmonious only such excitement of the nerves as continue without disturbance" (p. 229).
Part 3 studies scales; quoting from the conclusion: "the construction of scales ... is a product of artistic invention, and by no means furnished by the natural formation or the natural function of our ear, as it has been hitherto most generally asserted. Of course the laws of the natural function of our ear play a great and influential part in this result; these laws are, as it were, the building stones with which the edifice of our musical system has been erected, and the necessity of accurately understanding the nature of these materials in order to understand the construction of the edifice itself, has been clearly shewn by the course of our investigations upon this very subject. But just as people with differently directed tastes can erect extremely different kinds of buildings with the same stones, so also the history of music shews us that the same properties of the human ear could serve as the foundation of very different musical systems." (p. 366).
Summary of On the Sensations of Tone (Dover Books on Music)
This masterly treatment of classical acoustics embodies the great physicist's lifetime of research and presents his vast knowledge of the field in an easy-to-follow account. Among the topics explored: physical phenomena, the physiology of hearing, the relation of musical phenomena to physics, and historical aspects of musical sound. Includes 68 figures.
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