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date: 22 November 2019

Pythagorean intonationlocked

  • Mark Lindley

Extract

A tuning of the scale in which all 5ths and 4ths are pure (untempered). Pythagorean tuning provides intonations of several types of scale. A series of five 5ths and 4ths includes the pitch classes of the most familiar kind of pentatonic scale; ascending from F♯ the series would comprise the five chromatic notes of the keyboard. A series of seven 5ths ascending from F yields a diatonic scale comprising the naturals on the keyboard; the 3rds and 6ths in this scale, however, differ from their justly intoned equivalents by a syntonic comma, and therefore do not meet medieval and Renaissance criteria of consonance implied by such terms as ‘perfection’ and ‘unity’. When used as harmonic intervals these Pythagorean 3rds and 6ths are likely to be characterized, on an organ Diapason stop for example, by rather prominent Beats; middle C–E or C–A beat more than 16 times per second at modern concert pitch. A series of 12 Pythagorean 5ths provides a fully chromatic scale that is bound to include, however, one sour ...

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