Orwellismic family - Revision history

Lériendil: added guanyintet

2026-01-22T18:05:54Z

added guanyintet

← Older revision		Revision as of 18:05, 22 January 2026
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	== Guanyin ==		== Guanyin ==
			{{See also\|Subgroup temperaments#Guanyintet}}

	Guanyin is the most natural [[11-limit]] extension of orwellismic, where two ~7/6 generators make [[15/11]], tempering out [[540/539]], and two sharpened ~[[5/4]]'s make [[11/7]], tempering out [[176/175]].		Guanyin is the most natural [[11-limit]] extension of orwellismic, where two ~7/6 generators make [[15/11]], tempering out [[540/539]], and two sharpened ~[[5/4]]'s make [[11/7]], tempering out [[176/175]].

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:26:14Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:26, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Orwellismic family\| ]] <!-- main article -->		[[Category:Orwellismic family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]
	[[Category:Guanyin]]		[[Category:Guanyin]]
	[[Category:Listen]]		[[Category:Listen]]

FloraC: + tunings

2025-10-13T11:22:37Z

+ tunings

@@ Line 17: / Line 17: @@
 : 7/6 length = 0.7526, 3/2 length = 1.3931
 : Angle (7/6, 3/2) = 97.5081
 [[Minimax tuning]]:
@@ Line 45: / Line 51: @@
 : 7/6 length = 0.5167, 3/2 length = 1.3055
 : Angle (7/6, 3/2) = 79.0940
 [[Minimax tuning]]:
@@ Line 68: / Line 80: @@
 Mapping: {{mapping| 1 0 0 2 -2 3 | 0 1 0 1 1 -2 | 0 0 3 -1 5 5 }}
 {{Optimal ET sequence|legend=0| 22, 27e, 31, 53, 58, 80, 111, 280cdf }}
@@ Line 83: / Line 99: @@
 Mapping: {{mapping| 1 0 0 2 -2 6 | 0 1 0 1 1 1 | 0 0 3 -1 5 -5 }}
 {{Optimal ET sequence|legend=0| 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff }}
@@ Line 98: / Line 118: @@
 {{Mapping|legend=1| 1 0 0 2 5 | 0 1 0 1 0 | 0 0 3 -1 -2 }}
 {{Optimal ET sequence|legend=1| 4, 5, 9, 17, 22, 31, 53, 84e }}

FloraC: Switch to Sintel's badness, per community consensus

2025-10-13T10:58:55Z

Switch to Sintel's badness, per community consensus

← Older revision		Revision as of 10:58, 13 October 2025
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	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }}

	[[Badness]] (~~Smith~~): 0.~~187 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.826

	[[Projection pair]]: ~5 = 1728/343 to 2.3.7		[[Projection pair]]: ~5 = 1728/343 to 2.3.7
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	{{Optimal ET sequence\|legend=1\| 22, 27e, 31, 53, 58, 80, 111, 280cd }}		{{Optimal ET sequence\|legend=1\| 22, 27e, 31, 53, 58, 80, 111, 280cd }}

	[[Badness]] (~~Smith~~): 0.~~411 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.494

	[[Projection pair]]s: ~5 = 1728/343, ~11 = 186624/16807 to 2.3.7		[[Projection pair]]s: ~5 = 1728/343, ~11 = 186624/16807 to 2.3.7
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	{{Optimal ET sequence\|legend=0\| 22, 27e, 31, 53, 58, 80, 111, 280cdf }}		{{Optimal ET sequence\|legend=0\| 22, 27e, 31, 53, 58, 80, 111, 280cdf }}

	Badness (~~Smith~~): 0.~~758 × 10<sup>-3</sup>~~		Badness (Sintel): 0.708

	Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7		Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7
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	{{Optimal ET sequence\|legend=0\| 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff }}		{{Optimal ET sequence\|legend=0\| 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff }}

	Badness (~~Smith~~): 0.~~904 × 10<sup>-3</sup>~~		Badness (Sintel): 0.845

	Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7		Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7
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	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 22, 31, 53, 84e }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 22, 31, 53, 84e }}

	[[Badness]] (~~Smith~~): 0.~~715 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.859

	Scales: [[orwellian chromatic]]		Scales: [[orwellian chromatic]]

FloraC: Units & misc. cleanup

2025-10-13T10:55:58Z

Units & misc. cleanup

← Older revision		Revision as of 10:55, 13 October 2025
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	{{Technical data page}}		{{Technical data page}}
	The '''orwellismic family''' of rank-3 temperaments tempers out the orwellisma, [[1728/1715]].		The '''orwellismic family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the orwellisma, [[1728/1715]].

	== Orwellismic ==		== Orwellismic ==
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	{{Mapping\|legend=1\| 1 0 0 2 \| 0 1 0 1 \| 0 0 3 -1 }}		{{Mapping\|legend=1\| 1 0 0 2 \| 0 1 0 1 \| 0 0 3 -1 }}

	: mapping generators: ~2, ~3, ~12/7		: mapping generators: ~2, ~3, ~12/7

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	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[7-odd-limit\|7-]] and [[9-odd-limit]]		* [[7-odd-limit\|7-]] and [[9-odd-limit]]
	: {{~~Monzo~~ list\| 1 0 0 0 \| 0 1 0 0 \| 3/2 3/4 3/4 -3/4 \| 3/2 3/4 -1/4 1/4 }}		: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| 3/2 3/4 3/4 -3/4 \| 3/2 3/4 -1/4 1/4 }}
	: [[~~Eigenmonzo~~ basis\|~~Unchanged~~-interval (eigenmonzo) basis]]: 2.3.7/5		: [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }}

	[[Badness]]: 0.187 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.187 × 10<sup>-3</sup>

	[[Projection pair]]: ~5 = 1728/343 to 2.3.7		[[Projection pair]]: ~5 = 1728/343 to 2.3.7
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	== Guanyin ==		== Guanyin ==
	Guanyin is the most natural [[11-limit]] extension of orwellismic, where two ~7/6 generators make [[15/11]] (tempering out [[540/539]]) and two sharpened ~[[5/4]]s make [[11/7]] (tempering out [[176/175]]).		Guanyin is the most natural [[11-limit]] extension of orwellismic, where two ~7/6 generators make [[15/11]], tempering out [[540/539]], and two sharpened ~[[5/4]]'s make [[11/7]], tempering out [[176/175]].

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| -2/9 0 -5/9 5/9 4/9 }}, {{monzo\| 4/3 0 1/3 -1/3 1/3 }}, {{monzo\| 4/3 0 -2/3 2/3 1/3 }}, {{monzo\| 0 0 0 0 1 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| -2/9 0 -5/9 5/9 4/9 }}, {{monzo\| 4/3 0 1/3 -1/3 1/3 }}, {{monzo\| 4/3 0 -2/3 2/3 1/3 }}, {{monzo\| 0 0 0 0 1 }}]
	: [[~~Eigenmonzo~~ basis\|~~Unchanged~~-interval (eigenmonzo) basis]]: 2.11.7/5		: [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.11.7/5

	{{Optimal ET sequence\|legend=1\| 22, 27e, 31, 53, 58, 80, 111, 280cd }}		{{Optimal ET sequence\|legend=1\| 22, 27e, 31, 53, 58, 80, 111, 280cd }}

	[[Badness]]: 0.411 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.411 × 10<sup>-3</sup>

	[[Projection pair]]s: ~5 = 1728/343, ~11 = 186624/16807 to 2.3.7		[[Projection pair]]s: ~5 = 1728/343, ~11 = 186624/16807 to 2.3.7
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	; Music		; Music
	* ''Trio for SoftSaturn, NebulaSing and TromBonehead'' (archived 2010) by [[Gene Ward Smith]] – [https://soundcloud.com/genewardsmith/trio-gorts SoundCloud] \| [https://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297 details] \| [https://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3 play] – ~~guanyin~~[22] in 111edo tuning		* ''Trio for SoftSaturn, NebulaSing and TromBonehead'' (archived 2010) by [[Gene Ward Smith]] – [https://soundcloud.com/genewardsmith/trio-gorts SoundCloud] \| [https://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297 details] \| [https://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3 play] – in Guanyin[22], 111edo tuning

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 0 2 -2 3 \| 0 1 0 1 1 -2 \| 0 0 3 -1 5 5 }}		Mapping: {{mapping\| 1 0 0 2 -2 3 \| 0 1 0 1 1 -2 \| 0 0 3 -1 5 5 }}

	{{Optimal ET sequence\|legend=1\| 22, 27e, 31, 53, 58, 80, 111, 280cdf }}		{{Optimal ET sequence\|legend=0\| 22, 27e, 31, 53, 58, 80, 111, 280cdf }}

	Badness: 0.758 × 10<sup>-3</sup>		Badness (Smith): 0.758 × 10<sup>-3</sup>

	Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7		Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7
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	Mapping: {{mapping\| 1 0 0 2 -2 6 \| 0 1 0 1 1 1 \| 0 0 3 -1 5 -5 }}		Mapping: {{mapping\| 1 0 0 2 -2 6 \| 0 1 0 1 1 1 \| 0 0 3 -1 5 -5 }}

	{{Optimal ET sequence\|legend=1\| 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff }}		{{Optimal ET sequence\|legend=0\| 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff }}

	Badness: 0.904 × 10<sup>-3</sup>		Badness (Smith): 0.904 × 10<sup>-3</sup>

	Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7		Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7
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	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 22, 31, 53, 84e }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 22, 31, 53, 84e }}

	[[Badness]]: 0.715 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.715 × 10<sup>-3</sup>

	Scales: [[orwellian chromatic]]		Scales: [[orwellian chromatic]]

Lériendil at 18:46, 11 October 2025

2025-10-11T18:46:05Z

← Older revision		Revision as of 18:46, 11 October 2025
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	== Orwellismic ==		== Orwellismic ==
			Orwellismic uses three [[~]][[7/6]] generators to reach [[8/5]] while preserving the lattice structure of the [[2.3.7 subgroup]]. Ideally, 7/6 and 5/4 are both tuned slightly sharp.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

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	== Guanyin ==		== Guanyin ==
			Guanyin is the most natural [[11-limit]] extension of orwellismic, where two ~7/6 generators make [[15/11]] (tempering out [[540/539]]) and two sharpened ~[[5/4]]s make [[11/7]] (tempering out [[176/175]]).

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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	== Orwellian ==		== Orwellian ==
			Orwellian is another 11-limit extension of orwellismic that tempers out [[99/98]], which is supported by 11-limit [[orwell]].

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

Lériendil: Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

2025-06-24T00:39:23Z

Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:39, 24 June 2025
Line 101:		Line 101:

	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Orwellismic family\| ]] <!-- main article -->		[[Category:Orwellismic family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]
	[[Category:Guanyin]]		[[Category:Guanyin]]
	[[Category:Listen]]		[[Category:Listen]]

Lériendil: Text replacement - "Eigenmonzo (unchanged-interval)" to "Unchanged-interval (eigenmonzo)"

2025-06-21T06:56:31Z

Text replacement - "Eigenmonzo (unchanged-interval)" to "Unchanged-interval (eigenmonzo)"

← Older revision		Revision as of 06:56, 21 June 2025
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	* [[7-odd-limit\|7-]] and [[9-odd-limit]]		* [[7-odd-limit\|7-]] and [[9-odd-limit]]
	: {{Monzo list\| 1 0 0 0 \| 0 1 0 0 \| 3/2 3/4 3/4 -3/4 \| 3/2 3/4 -1/4 1/4 }}		: {{Monzo list\| 1 0 0 0 \| 0 1 0 0 \| 3/2 3/4 3/4 -3/4 \| 3/2 3/4 -1/4 1/4 }}
	: [[Eigenmonzo basis\|~~Eigenmonzo (unchanged~~-interval) basis]]: 2.3.7/5		: [[Eigenmonzo basis\|Unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }}
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| -2/9 0 -5/9 5/9 4/9 }}, {{monzo\| 4/3 0 1/3 -1/3 1/3 }}, {{monzo\| 4/3 0 -2/3 2/3 1/3 }}, {{monzo\| 0 0 0 0 1 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| -2/9 0 -5/9 5/9 4/9 }}, {{monzo\| 4/3 0 1/3 -1/3 1/3 }}, {{monzo\| 4/3 0 -2/3 2/3 1/3 }}, {{monzo\| 0 0 0 0 1 }}]
	: [[Eigenmonzo basis\|~~Eigenmonzo (unchanged~~-interval) basis]]: 2.11.7/5		: [[Eigenmonzo basis\|Unchanged-interval (eigenmonzo) basis]]: 2.11.7/5

	{{Optimal ET sequence\|legend=1\| 22, 27e, 31, 53, 58, 80, 111, 280cd }}		{{Optimal ET sequence\|legend=1\| 22, 27e, 31, 53, 58, 80, 111, 280cd }}

FloraC: /* Guanyin */ +historical note

2025-05-11T11:32:01Z

Guanyin: +historical note

← Older revision		Revision as of 11:32, 11 May 2025
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	=== Avalokita ===		=== Avalokita ===
			This extension used to be known as ''georgian''.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

CompactStar at 20:30, 10 May 2025

2025-05-10T20:30:51Z

← Older revision		Revision as of 20:30, 10 May 2025
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	Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7		Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7

	=== ~~Georgian~~ ===		=== Avalokita ===
	~~This temperament is also known as '''avalokita'''.~~

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

← Older revision		Revision as of 06:56, 21 June 2025
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	* [[7-odd-limit\|7-]] and [[9-odd-limit]]		* [[7-odd-limit\|7-]] and [[9-odd-limit]]
	: {{Monzo list\| 1 0 0 0 \| 0 1 0 0 \| 3/2 3/4 3/4 -3/4 \| 3/2 3/4 -1/4 1/4 }}		: {{Monzo list\| 1 0 0 0 \| 0 1 0 0 \| 3/2 3/4 3/4 -3/4 \| 3/2 3/4 -1/4 1/4 }}
	: [[Eigenmonzo basis\|~~Eigenmonzo (unchanged~~-interval) basis]]: 2.3.7/5		: [[Eigenmonzo basis\|Unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }}
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| -2/9 0 -5/9 5/9 4/9 }}, {{monzo\| 4/3 0 1/3 -1/3 1/3 }}, {{monzo\| 4/3 0 -2/3 2/3 1/3 }}, {{monzo\| 0 0 0 0 1 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| -2/9 0 -5/9 5/9 4/9 }}, {{monzo\| 4/3 0 1/3 -1/3 1/3 }}, {{monzo\| 4/3 0 -2/3 2/3 1/3 }}, {{monzo\| 0 0 0 0 1 }}]
	: [[Eigenmonzo basis\|~~Eigenmonzo (unchanged~~-interval) basis]]: 2.11.7/5		: [[Eigenmonzo basis\|Unchanged-interval (eigenmonzo) basis]]: 2.11.7/5

	{{Optimal ET sequence\|legend=1\| 22, 27e, 31, 53, 58, 80, 111, 280cd }}		{{Optimal ET sequence\|legend=1\| 22, 27e, 31, 53, 58, 80, 111, 280cd }}