Computer Science – Sound
Scientific paper
2012-02-20
Computer Science
Sound
Scientific paper
Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases. How does music, in particular harmony, actually work, presented as a real, scientific theory of music? In particular we derive from first principles of Physics and Computation the following three fundamental phenomena of music: * the Major Scale, * the Standard Chord Dictionary, and * the difference in feeling between the Major and Minor Triads. While the Major Scale has been independently derived before by others in a similar manner as we do here [Helmholtz1863, p. 300], [Birkhoff1933, p. 92], I believe the derivation of the Standard Chord Dictionary as well as the difference in feeling between the Major and Minor Triads to be an original contribution to science and art. Further, we think our observations should convert straightforwardly into an algorithm for classifying the basic aspects of tonal music in a manner similar to the way a human would. Further, we examine the theory of the heretofore agreed-upon authority on this subject, 19th-century German Physicist Hermann Helmholtz [Helmholtz1863], and show that his theory, while making correct observations, and while qualifying as scientific, fails to actually explain the three observed phenomena listed above; Helmholtz isn't really wrong, he just fails to be really right, and considers only physical and not computational phenomena. We also consider the more recent and more computational theory of Terhardt [Terhardt1974-PCH] (and others) and show that, while his approach (and, it seems, that of others following in his thread) also attempts a computational explanation and derives some observations that seem to resemble some of those of the initial part of our analysis, we seem to go further.
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