Equal Temperament and Pythagorean Tuning: a geometrical interpretation in the plane

doi:10.1016/S0165-0114(98)00113-4

Fuzzy Sets and Systems

Volume 114, Issue 2, 1 September 2000, Pages 261-269

https://doi.org/10.1016/S0165-0114(98)00113-4 Get rights and content

Abstract

We show the following: Pythagorean Tuning (17 valued) and Equal Temperament (12 valued) can be canonically represented as discrete sets of the plane and there is a natural parallel projection of Pythagorean Tuning to the points of Equal Temperament. This fact implies particularly that when performing a composition on two instruments simultaneously in both Pythagorean Tuning and Equal Temperament, then the Garbuzov zones (supports of tone fuzzy sets) can be considered as segments on parallel lines in the plane.

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Equal Temperament and Pythagorean Tuning: a geometrical interpretation in the plane

Abstract

Math. Psychol.

Mathematical Theory of Musical Scales

Extracta Mathematicae

On fuzzy coding of information in music

Busefal