User:Zhenlige/Logical tempering

Logical tempering^{[idiosyncratic term]} means using a regular temperament (called the logical temperament^{[idiosyncratic term]}) to get “abstract” notes and intervals, but not directly the actual played notes. Different from “real” tempering, a logical temperament with torsion is allowed.

Examples

Octave equivalence can be thought as logically tempering out 2/1.

The diatonic degrees of 3-limit intervals (seconds, thirds etc.) are the result of logical tempering into 7et. Similarly, all MOS-based degree systems can be thought as a logical temperament based on the equalized scale.

The conventional categorization of 7-limit intervals treats 5/4 as a major third and 7/4 as a minor seventh, which implies dominant as the logical temperament. A piece using adaptive JI with that framework can be thought as a dynamic detempering of a piece in dominant.