User:Zhenlige/Logical tempering - Revision history

Zhenlige at 07:10, 15 October 2026

2026-10-15T07:10:27Z

← Older revision		Revision as of 07:10, 15 October 2026
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			{{../en2zh}}
	'''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. The commas tempered out in the logical temperament are sometimes called “chromas”, which is a generalization of the concept of MOS [[chroma]]s.		'''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. The commas tempered out in the logical temperament are sometimes called “chromas”, which is a generalization of the concept of MOS [[chroma]]s.

Zhenlige at 06:28, 15 October 2026

2026-10-15T06:28:02Z

← Older revision		Revision as of 06:28, 15 October 2026
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	'''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. The commas tempered out in the logical temperament are sometimes called “chromas”, which is a generalization of the concept of MOS [[chroma]]s.		'''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. The commas tempered out in the logical temperament are sometimes called “chromas”, which is a generalization of the concept of MOS [[chroma]]s.

	Multiple logical temperaments can be used at the same time. For example, one may first categorize intervals as alterations of [[3-limit]] intervals, and then logically temper out [[2187/2048]] to get [[5L 2s\|diatonic]] degrees.		Multiple logical temperaments can be used at the same time. For example, one may first categorize intervals as alterations of [[3-limit]] intervals, and then logically temper out [[2187/2048]] to get [[5L 2s\|diatonic]] degrees. Alternatively, one may use the 5-, 7- and 12-form degree systems in the same piece.

	When the actual notes are already tempered, to get unambiguous results, the logical temperament should be based on the tempered notes i.e. it should [[support]] the actual temperament.		When the actual notes are already tempered, to get unambiguous results, the logical temperament should be based on the tempered notes i.e. it should [[support]] the actual temperament.

Zhenlige at 06:25, 15 October 2026

2026-10-15T06:25:46Z

← Older revision		Revision as of 06:25, 15 October 2026
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	'''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.		'''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. The commas tempered out in the logical temperament are sometimes called “chromas”, which is a generalization of the concept of MOS [[chroma]]s.

			Multiple logical temperaments can be used at the same time. For example, one may first categorize intervals as alterations of [[3-limit]] intervals, and then logically temper out [[2187/2048]] to get [[5L 2s\|diatonic]] degrees.

			When the actual notes are already tempered, to get unambiguous results, the logical temperament should be based on the tempered notes i.e. it should [[support]] the actual temperament.

	== Examples ==		== Examples ==
	[[Octave equivalence]] can be thought as logically tempering out [[2/1]].		[[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 [[5L 2s\|diatonic]] degrees (seconds, thirds etc.) of [[3-limit]] intervals are the result of logical tempering into [[7edo\|7et]], tempering out the diatonic [[chroma]] [[2187/2048]]. Similarly, every [[MOS]]-based degree system 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. Alternatively, 7/4 can be considered as an augmented sixth, giving [[septimal meantone]] logic.

	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 classical triads are made by stacking [[5/4]] and [[6/5]] intervals, meaning their difference [[25/24]] is a chroma, giving a [[dicot]] framework. Merging it with an actual [[5-limit]] [[rank]]-2 temperament gives a unique MOS structure. For example, [[meantone]] gives the famous [[5L 2s]] diatonic scale, and [[diaschismic]] gives [[2L 8s]].

Zhenlige at 05:59, 15 October 2026

2026-10-15T05:59:23Z

← Older revision		Revision as of 05:59, 15 October 2026
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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 ==		== 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.

Zhenlige at 05:00, 15 October 2026

2026-10-15T05:00:50Z

← Older revision		Revision as of 05:00, 15 October 2026
Line 1:		Line 1:
	'''Logical tempering'''{{idio}} means using a [[regular temperament]] (called the '''logical temperament''') as a category system. 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''') 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]].

	== Examples ==		== Examples ==
	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.

Zhenlige at 04:57, 15 October 2026

2026-10-15T04:57:04Z

← Older revision		Revision as of 04:57, 15 October 2026
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	'''Logical tempering'''{{idio}} means using a [[regular temperament]] (~~calles~~ the '''logical temperament''') as a category system. 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''') as a category system. 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]].

	== Examples ==		== Examples ==
	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.

Zhenlige at 04:51, 15 October 2026

2026-10-15T04:51:20Z

← Older revision		Revision as of 04:51, 15 October 2026
Line 1:		Line 1:
	'''Logical tempering''' means using a [[regular temperament]] (calles the '''logical temperament''') as a category system. 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]] (calles the '''logical temperament''') as a category system. 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]].

	== Examples ==		== Examples ==
	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.

Zhenlige at 17:29, 14 October 2026

2026-10-14T17:29:28Z

← Older revision		Revision as of 17:29, 14 October 2026
Line 1:		Line 1:
	'''Logical tempering''' means using a [[regular temperament]] as a category system. 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''' means using a [[regular temperament]] (calles the '''logical temperament''') as a category system. 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]].

			== Examples ==
			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.

Zhenlige: Created page with "'''Logical tempering''' means using a regular temperament as a category system. For example, diatonic interval degrees are the result of logical tempering 3-limit into 7et, and chromatic degrees are the result of 12et."

2026-10-14T17:20:00Z

Created page with "'''Logical tempering''' means using a regular temperament as a category system. For example, diatonic interval degrees are the result of logical tempering 3-limit into 7et, and chromatic degrees are the result of 12et."

New page

'''Logical tempering''' means using a [[regular temperament]] as a category system. 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]].