Fluid just intonation - Revision history

BudjarnLambeth: /* Relationship to other tunings */

2025-03-28T03:59:57Z

Relationship to other tunings

← Older revision		Revision as of 03:59, 28 March 2025
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	'''According to the sheet music's stated cent values:'''		'''According to the sheet music's stated cent values:'''

	Fluid just intonation is a subset of [[13-limit]] just intonation.		Fluid just intonation is a subset of [[17-limit]] just intonation.

	[[32afdo]] is the smallest mode of the harmonic series that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.		[[32afdo]] is the smallest mode of the harmonic series that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.

BudjarnLambeth: /* Relationship to other tunings */

2025-03-28T03:53:00Z

Relationship to other tunings

← Older revision		Revision as of 03:53, 28 March 2025
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	[[30afdo]] is the smallest [[Overtone scale\|mode of the harmonic series]] that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.		[[30afdo]] is the smallest [[Overtone scale\|mode of the harmonic series]] that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.

	[[EDOs]] with progressively better approximations of fluid just intonation's allowed ratios include: {{EDOs\|19, 22, 28, 31, 41, 72, 87, 118...}}		[[EDOs]] with progressively better approximations of fluid just intonation's allowed ratios include: {{EDOs\|'''19''', 22, 28, '''31''', '''41''', 72, '''87''', '''118'''...}}


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	[[32afdo]] is the smallest mode of the harmonic series that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.		[[32afdo]] is the smallest mode of the harmonic series that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.

	[[EDOs]] with progressively better approximations of fluid just intonation's allowed ratios include: {{EDOs\|19, 24, 30, 31, 33, 41, 46, 66, 77, 87, 90, 94, 118...}}		[[EDOs]] with progressively better approximations of fluid just intonation's allowed ratios include: {{EDOs\|'''19''', 24, 30, '''31''', 33, '''41''', 46, 66, 77, '''87''', 90, 94, '''118'''...}}

	== Influences ==		== Influences ==

BudjarnLambeth: /* Relationship to other tunings */

2025-03-28T03:50:33Z

Relationship to other tunings

← Older revision		Revision as of 03:50, 28 March 2025
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	[[30afdo]] is the smallest [[Overtone scale\|mode of the harmonic series]] that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.		[[30afdo]] is the smallest [[Overtone scale\|mode of the harmonic series]] that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.

			[[EDOs]] with progressively better approximations of fluid just intonation's allowed ratios include: {{EDOs\|19, 22, 28, 31, 41, 72, 87, 118...}}


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	[[32afdo]] is the smallest mode of the harmonic series that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.		[[32afdo]] is the smallest mode of the harmonic series that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.

			[[EDOs]] with progressively better approximations of fluid just intonation's allowed ratios include: {{EDOs\|19, 24, 30, 31, 33, 41, 46, 66, 77, 87, 90, 94, 118...}}

	== Influences ==		== Influences ==

BudjarnLambeth: /* Relationship to other tunings */

2025-03-28T03:41:19Z

Relationship to other tunings

← Older revision		Revision as of 03:41, 28 March 2025
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	=== Relationship to other tunings ===		=== Relationship to other tunings ===
	~~Fluid just intonation is a subset of [[13-limit]] just intonation (going by the sheet music's cent values), and possibly also [[11-limit]] just intonation (going by the sheet music's JI ratios).~~

	~~Going by the~~ ''sheet music's ~~cent values~~''~~, [[30afdo]] is the smallest [[Overtone scale\|mode of the harmonic series]] that can approximate all of fluid just intonation~~'~~s allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.~~		'''According to the sheet music's stated JI ratios:'''

	~~Going by~~ the ''sheet music's ~~JI ratios~~'', [[32afdo]] is the smallest mode of the harmonic series that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.		Fluid just intonation is a subset of [[11-limit]] just intonation.

			[[30afdo]] is the smallest [[Overtone scale\|mode of the harmonic series]] that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.


			'''According to the sheet music's stated cent values:'''

			Fluid just intonation is a subset of [[13-limit]] just intonation.

			[[32afdo]] is the smallest mode of the harmonic series that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.

	== Influences ==		== Influences ==

BudjarnLambeth: /* Subsets and supersets */

2025-03-28T03:37:12Z

Subsets and supersets

← Older revision		Revision as of 03:37, 28 March 2025
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	\|}		\|}

	=== ~~Subsets and supersets~~ ===		=== Relationship to other tunings ===
	Fluid just intonation is a subset of [[13-limit]] just intonation (going by the sheet music's cent values), and possibly also [[11-limit]] just intonation (going by the sheet music's JI ratios).		Fluid just intonation is a subset of [[13-limit]] just intonation (going by the sheet music's cent values), and possibly also [[11-limit]] just intonation (going by the sheet music's JI ratios).

			Going by the ''sheet music's cent values'', [[30afdo]] is the smallest [[Overtone scale\|mode of the harmonic series]] that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.

			Going by the ''sheet music's JI ratios'', [[32afdo]] is the smallest mode of the harmonic series that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.

	== Influences ==		== Influences ==

BudjarnLambeth: /* Subsets and supersets */

2025-03-28T03:16:55Z

Subsets and supersets

← Older revision		Revision as of 03:16, 28 March 2025
Line 117:		Line 117:
	\|}		\|}

	== Subsets and supersets ==		=== Subsets and supersets ===
	Fluid just intonation is a subset of [[13-limit]] just intonation (going by the sheet music's cent values), and possibly also [[11-limit]] just intonation (going by the sheet music's JI ratios).		Fluid just intonation is a subset of [[13-limit]] just intonation (going by the sheet music's cent values), and possibly also [[11-limit]] just intonation (going by the sheet music's JI ratios).

BudjarnLambeth: /* Subsets and supersets */

2025-03-28T03:13:51Z

Subsets and supersets

← Older revision		Revision as of 03:13, 28 March 2025
Line 118:		Line 118:

	== Subsets and supersets ==		== Subsets and supersets ==
	Fluid just intonation is a subset of [[13-limit]] just intonation (going by the sheet music's cent values), and possibly also [[11-limit]] just intonation (going by the sheet music's JI ratios).		Fluid just intonation is a subset of [[13-limit]] just intonation (going by the sheet music's cent values), and possibly also [[11-limit]] just intonation (going by the sheet music's JI ratios).

	~~It is also a subset of the [[polymicrotonal]] tuning of ([[15afdo]] and [[16afdo]]~~).

	== Influences ==		== Influences ==

BudjarnLambeth: /* Allowed ratios */ typo

2025-03-28T03:13:09Z

Allowed ratios: typo

← Older revision		Revision as of 03:13, 28 March 2025
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	The sheet music for ''Microtonal Composition in "Fluid Just Intonation"'' includes a table of allowed ratios, and how much they differ from their [[12edo]] tempered version (in [[cents]]).		The sheet music for ''Microtonal Composition in "Fluid Just Intonation"'' includes a table of allowed ratios, and how much they differ from their [[12edo]] tempered version (in [[cents]]).

	However, the JI ratios and the ~~cents~~ values do not all agree with one another.		However, the JI ratios and the cent values do not all agree with one another.

	So, this page will include two tables, one based on the JI ratios provided in the sheet music, and one based on the cent values.		So, this page will include two tables, one based on the JI ratios provided in the sheet music, and one based on the cent values.

BudjarnLambeth: Added links to interval ratios

2025-03-28T03:11:38Z

Added links to interval ratios

← Older revision		Revision as of 03:11, 28 March 2025
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	! Scale degree		! Scale degree
	! Ratio		! Ratio
	! Tuning adjustment in cents		! Tuning adjustment (cents)
	\|-		\|-
	\| 1		\| 1
	\| 1/1		\| [[1/1]]
	\| 0		\| 0
	\|-		\|-
	\| b2		\| b2
	\| 16/15		\| [[16/15]]
	\| +12		\| +12
	\|-		\|-
	\| 2		\| 2
	\| 9/8		\| [[9/8]]
	\| +4		\| +4
	\|-		\|-
	\| b3		\| b3
	\| 6/5		\| [[6/5]]
	\| +16		\| +16
	\|-		\|-
	\| 3		\| 3
	\| 5/4		\| [[5/4]]
	\| -14		\| -14
	\|-		\|-
	\| 4		\| 4
	\| 4/3		\| [[4/3]]
	\| -2		\| -2
	\|-		\|-
	\| #4/b5		\| #4/b5
	\| 11/8		\| [[11/8]]
	\| -49		\| -49
	\|-		\|-
	\| 5		\| 5
	\| 3/2		\| [[3/2]]
	\| +2		\| +2
	\|-		\|-
	\| b6		\| b6
	\| 8/5		\| [[8/5]]
	\| +14		\| +14
	\|-		\|-
	\| 6		\| 6
	\| 5/3		\| [[5/3]]
	\| -16		\| -16
	\|-		\|-
	\| rowspan="2" \|b7		\| rowspan="2" \|b7
	\| 7/4 (dom7)		\| [[7/4]] (''dom7'')
	\| -31 (dom7)		\| -31 (''dom7'')
	\|-		\|-
	\| 9/5 (m7)		\| [[9/5]] (''m7'')
	\| +18 (m7)		\| +18 (''m7'')
	\|-		\|-
	\| 7		\| 7
	\| 15/8		\| [[15/8]]
	\| -12		\| -12
	\|-		\|-
	\| 8ve		\| 8ve
	\| 2/1		\| [[2/1]]
	\| 0		\| 0
	\|}		\|}
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	{\| class="wikitable"		{\| class="wikitable"
	! Scale degree!! Ratio!!Tuning adjustment in cents		! Scale degree!! Ratio!!Tuning adjustment (cents)
	\|-		\|-
	\|1\|\|1/1\|\|0		\|1\|\|[[1/1]]\|\|0
	\|-		\|-
	\|b2\|\|17/16\|\|+5		\|b2\|\|[[17/16]]\|\|+5
	\|-		\|-
	\|2\|\|9/8\|\|+4		\|2\|\|[[9/8]]\|\|+4
	\|-		\|-
	\|b3\|\|6/5\|\|+16		\|b3\|\|[[6/5]]\|\|+16
	\|-		\|-
	\|3\|\|5/4\|\|-14		\|3\|\|[[5/4]]\|\|-14
	\|-		\|-
	\|4\|\|4/3\|\|-2		\|4\|\|[[4/3]]\|\|-2
	\|-		\|-
	\|#4/b5\|\|11/8\|\|-49		\|#4/b5\|\|[[11/8]]\|\|-49
	\|-		\|-
	\|5\|\|3/2\|\|+2		\|5\|\|[[3/2]]\|\|+2
	\|-		\|-
	\|b6\|\|13/8\|\|+41		\|b6\|\|[[13/8]]\|\|+41
	\|-		\|-
	\|6\|\|27/16\|\|+6		\|6\|\|[[27/16]]\|\|+6
	\|-		\|-
	\| rowspan="2" \|b7\|\|7/4 (dom7)\|\|-31 (dom7)		\| rowspan="2" \|b7\|\|[[7/4]] (''dom7'')\|\|-31 (''dom7'')
	\|-		\|-
	\|9/5 (m7)\|\|+18 (m7)		\|[[9/5]] (''m7'')\|\|+18 (''m7'')
	\|-		\|-
	\|7\|\|15/8\|\|-12		\|7\|\|[[15/8]]\|\|-12
	\|-		\|-
	\|8ve\|\|2/1\|\|0		\|8ve\|\|[[2/1]]\|\|0
	\|}		\|}

BudjarnLambeth: Cleaned up messy source formatting

2025-03-28T03:08:10Z

Cleaned up messy source formatting

← Older revision		Revision as of 03:08, 28 March 2025
Line 22:		Line 22:

	{\| class="wikitable"		{\| class="wikitable"
	! Scale degree!! Ratio		! Scale degree
	!Tuning adjustment in [[cents]]		! Ratio
			! Tuning adjustment in cents
	\|-		\|-
	\|1\|\|1/1		\| 1
	\|0		\| 1/1
			\| 0
	\|-		\|-
	\|b2\|\|16/15		\| b2
			\| 16/15
	\| +12		\| +12
	\|-		\|-
	\|2\|\|9/8		\| 2
			\| 9/8
	\| +4		\| +4
	\|-		\|-
	\|b3\|\|6/5		\| b3
			\| 6/5
	\| +16		\| +16
	\|-		\|-
	\|3\|\|5/4		\| 3
			\| 5/4
	\| -14		\| -14
	\|-		\|-
	\|4\|\|4/3		\| 4
			\| 4/3
	\| -2		\| -2
	\|-		\|-
	\|#4/b5\|\|11/8		\| #4/b5
			\| 11/8
	\| -49		\| -49
	\|-		\|-
	\|5\|\|3/2		\| 5
			\| 3/2
	\| +2		\| +2
	\|-		\|-
	\|b6\|\|8/5		\| b6
			\| 8/5
	\| +14		\| +14
	\|-		\|-
	\|6\|\|5/3		\| 6
			\| 5/3
	\| -16		\| -16
	\|-		\|-
	\| rowspan="2" \|b7\|\|7/4 (dom7)		\| rowspan="2" \|b7
			\| 7/4 (dom7)
	\| -31 (dom7)		\| -31 (dom7)
	\|-		\|-
	\|9/5 (m7)		\| 9/5 (m7)
	\| +18 (m7)		\| +18 (m7)
	\|-		\|-
	\|7\|\|15/8		\| 7
			\| 15/8
	\| -12		\| -12
	\|-		\|-
	\|8ve\|\|2/1		\| 8ve
	\|0		\| 2/1
			\| 0
	\|}		\|}

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	{\| class="wikitable"		{\| class="wikitable"
	! Scale degree!! Ratio!!Tuning adjustment in [[cents]]		! Scale degree!! Ratio!!Tuning adjustment in cents
	\|-		\|-
	\|1\|\|1/1\|\|0		\|1\|\|1/1\|\|0