If you ever get bored by temperament or other music theory gab on this list because it is too elementary, then click on ............ http://128.111.94.30/mto/contents.html MTO Table of Web Contents Music Theory Online The Online Journal of the Society for Music Theory ---------------------------------------------------------------------------- ---- Volume 4.4 Kenneth P. Scholtz* Algorithms for Mapping Diatonic Keyboard Tunings and Temperaments KEYWORDS: Algorithm, chain of fifths, diatonic scale, equal temperament, enharmonic, just intonation, meantone, Pythagorean tuning, schisma, syntonic comma ABSTRACT: Diatonic keyboard tunings in equal temperament, just intonation, meantone and well tempered scales are derived from Pythagorean tuning using algorithms whose operations involve combinations of pure fifths and syntonic commas. Graphic diagrams of the line of fifths are used to show the harmonic and mathematical relationships between common tunings and temperaments. Four modes of just intonation are derived from Pythagorean tuning by an algorithm that narrows each major third by one syntonic comma. Equal temperament is approximated with imperceptible error by algorithms that narrow Pythagorean and justly tuned enharmonic intervals by one or more syntonic commas. ---------------------------------------------------------------------------- ----
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