User:Zhenlige/Logical tempering: Difference between revisions

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'''Logical tempering'''{{idio}} means using a [[regular temperament]] (called the '''logical temperament''') ~~as a category system~~. Different from “real” tempering, a temperament with [[torsion]] is allowed~~. For example, diatonic interval degrees are the result of logical tempering [[3-limit]] into [[7edo|7et]], and [[User:Zhenlige/Chromatic notation|chromatic degrees]] are the result of [[12edo|12et]]~~.

'''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 ==

[[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.

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-'''Logical tempering'''{{idio}} means using a [[regular temperament]] (called the '''logical temperament''') as a category system. Different from “real” tempering, a temperament with [[torsion]] is allowed. For example, diatonic interval degrees are the result of logical tempering [[3-limit]] into [[7edo|7et]], and [[User:Zhenlige/Chromatic notation|chromatic degrees]] are the result of [[12edo|12et]].
+'''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 ==
+[[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.