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

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178
CASE OF SIMPLE TONES
[VIII. § 89.
arrangement reduces to a mini mum the dissonance due to the pairs 4—3 and 5—3. For the interval of a Fourth, the opposite arrangement gives the smoothest effect by minimising the dissonance 3—2. Experiments confirming theoretical conclusions of this kind may be made with great ease on the stops of an organ possessing more than a single manuaL
The above considerations laid down by Helmholtz open a whole field of results which I believe to be entirely in advance of any hitherto obtained by Musical theorists1.
89. It is possible to draw from the general theory of consonance and dissonance an inference which seems, at first sight, fatal to the truth of the theory itself. "If," it may be said, "the difference between a consonant and a dissonant interval depends entirely on the behaviour towards each other of certain pairs of overtones; then, in the case of sounds like those of large stopped flue-pipes, where there are no overtones at all, the distinc­tion between concords and discords ought entirely to disappear, and the interval of a Seventh, for instance, to sound just as smooth as that of an Octave. As this is not the fact, the theory cannot be true."
1 " Musical theory" is as misleading a term as could possibly be invented. "Musical empiricism" would replace it with con­spicuous advantage.
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