Harmony Explained: Progress Towards a Scientific Theory of Music (2012)

[Submitted connected 20 Feb 2012 (v1), past revised 9 Jun 2014 (this version, v2)]

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Abstract: Most euphony mentation books are for illustration medieval aesculapian textbooks: they incorporate unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases. How does music, successful peculiar harmony, really work, presented arsenic a real, technological mentation of music?
The halfway to our attack is to see not only the Physical phenomena of quality but besides the Computational phenomena of immoderate instrumentality that must make consciousness of sound, specified arsenic the quality brain. In peculiar we deduce the pursuing 3 basal phenomena of music:
* the Major Scale,
* the Standard Chord Dictionary, and
* the quality successful emotion betwixt the Major and Minor Triads.
While the Major Scale has been independently derived earlier by others successful a akin mode [Helmholtz1863, Birkhoff1933], I judge the derivation of the Standard Chord Dictionary arsenic good arsenic the quality successful emotion betwixt the Major and Minor Triads to beryllium original.
We show to beryllium incomplete the mentation of the heretofore agreed-upon authority connected this subject, 19th-century Physicist Hermann Helmholtz [Helmholtz1863]: he says notes are successful "concord" because the sound playing them together is "less worse" than that of immoderate different notes. But statement that, successful this theory, much notes tin only penalize, immoderate simply little than others, and truthful the astir harmonious sound should beryllium a azygous statement by itself(!) and harmony would not beryllium arsenic a arena of euphony astatine all.
I intend this article to beryllium satisfying to scientists arsenic an original publication to subject and art, yet I besides intend it to beryllium approachable by musicians and different funny members of the wide nationalist who whitethorn person agelong wondered astatine the funny properties of tonal euphony and been disappointment by the deficiency of satisfying, readable exposition connected the subject. Therefore I person written successful a deliberately plain and conversational style, avoiding unnecessarily general language.