User:Zhenlige/Logical tempering: Difference between revisions
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'''Logical tempering'''{{idio}} means using a [[regular temperament]] (called the '''logical temperament''') | '''Logical tempering'''{{idio}} means using a [[regular temperament]] (called the '''logical temperament'''{{idio}}) 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 == | == Examples == | ||
[[Octave equivalence]] can be thought as logically tempering out [[2/1]]. | |||
The [[5L 2s|diatonic]] degrees of [[3-limit]] intervals (seconds, thirds etc.) are the result of logical tempering into [[7edo|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 (temperament)|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. | The conventional categorization of [[7-limit]] intervals treats [[5/4]] as a major third and [[7/4]] as a minor seventh, which implies [[dominant (temperament)|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. | ||
Revision as of 05:59, 15 October 2026
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.