Landscape family - Revision history

FloraC: /* House */ + very obvious 13-limit extension

2026-04-21T14:13:50Z

House: + very obvious 13-limit extension

@@ Line 138: / Line 138: @@
 [[Badness]] (Sintel): 2.31
 [[Category:Temperament families]]
 [[Category:Landscape family| ]] <!-- main article -->
 [[Category:Rank 3]]

FloraC at 13:54, 21 April 2026

2026-04-21T13:54:47Z

← Older revision		Revision as of 13:54, 21 April 2026
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	The '''landscape family''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the [[landscape comma]], 250047/250000.		The '''landscape family''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the [[landscape comma]], 250047/250000.

	~~Considered below are landy and house, besides the 7-limit temperament.~~

	== Landscape ==		== Landscape ==
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	[[Badness]] (Sintel): 0.0940		[[Badness]] (Sintel): 0.0940

			=== Overview to extensions ===
			Extensions of landscape include landy, odin, tyr and house, all considered below.

	== Landy ==		== Landy ==

FloraC: Move odin and tyr here

2026-04-20T13:25:17Z

Move odin and tyr here

@@ Line 2: / Line 2: @@
 The '''landscape family''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[landscape comma]], 250047/250000.
 Considered below are landy and house, besides the 7-limit temperament.
@@ Line 68: / Line 64: @@
 Badness (Sintel): 0.923
 == House ==

FloraC at 13:48, 19 April 2026

2026-04-19T13:48:16Z

← Older revision		Revision as of 13:48, 19 April 2026
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	== Landy ==		== Landy ==
	~~Landy~~ tempers out the [[441/440\|werckisma]] and [[4375/4356\|fantaresma]], alongside the landscape comma.		Named by [[Xenllium]] in 2026, landy tempers out the [[441/440\|werckisma]] and [[4375/4356\|fantaresma]], alongside the landscape comma.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	== House ==		== House ==
	~~House~~ tempers out the [[quartisma]] alongside the landscape comma.		Named by [[Eliora]] in 2024, house tempers out the [[quartisma]] alongside the landscape comma.

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

FloraC: Switch to Sintel's badness, WE & CWE tunings

2026-04-19T13:37:53Z

Switch to Sintel's badness, WE & CWE tunings

← Older revision		Revision as of 13:37, 19 April 2026
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	{{Technical data page}}		{{Technical data page}}

	The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000.		The '''landscape family''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the [[landscape comma]], 250047/250000.

	Discussed elsewhere are:		Discussed elsewhere are:
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	{{Mapping\|legend=1\| 3 0 0 4 \| 0 1 0 -2 \| 0 0 1 2 }}		{{Mapping\|legend=1\| 3 0 0 4 \| 0 1 0 -2 \| 0 0 1 2 }}

	: mapping generators: ~63/50, ~3, ~5		: mapping generators: ~63/50, ~3, ~5

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~63/50 = 400.~~001~~{{c}}, ~3/2 = 701.~~938~~{{c}}, ~5/4 = 386.~~335~~{{c}}		* [[WE]]: ~63/50 = 400.0012{{c}}, ~3/2 = 701.9383{{c}}, ~5/4 = 386.3350{{c}}
	* [[CWE]]: ~63/50 = 400.~~000~~{{c}}, ~3/2 = 701.~~939~~{{c}}, ~5/4 = 386.~~339~~{{c}}		: [[error map]]: {{val\| +0.004 -0.013 +0.028 -0.021 }}
			* [[CWE]]: ~63/50 = 400.0000{{c}}, ~3/2 = 701.9387{{c}}, ~5/4 = 386.3385{{c}}
			: error map: {{val\| 0.000 -0.016 +0.025 -0.026 }}

	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[7-odd-limit]]		* [[7-odd-limit]]
	: {{monzo list\| 9 0 0 0 \| 4 3 6 -3 \| 0 0 9 0 \| 4 -6 6 6 }}/9		: {{monzo list\| 9 0 0 0 \| 4 3 6 -3 \| 0 0 9 0 \| 4 -6 6 6 }}/9
	: [[~~Eigenmonzo~~ basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3		: [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3
	* [[9-odd-limit]]		* [[9-odd-limit]]
	: {{monzo list\| 12 0 0 0 \| 4 6 6 -3 \| 0 0 12 0 \| 8 -12 12 6 }}/12		: {{monzo list\| 12 0 0 0 \| 4 6 6 -3 \| 0 0 12 0 \| 8 -12 12 6 }}/12
	: ~~[[Eigenmonzo basis\|~~unchanged-interval (eigenmonzo) basis]]: 2.5.9/7		: unchanged-interval (eigenmonzo) basis: 2.5.9/7

	{{Optimal ET sequence\|legend=1\| 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555 }}		{{Optimal ET sequence\|legend=1\| 12, 27, 39d, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555, 22920d }}

	[[Badness]] (Sintel): 0.~~094<!-- 0.02130 × 10<sup>-3</sup> by Smith's -->~~		[[Badness]] (Sintel): 0.0940

	== Landy ==		== Landy ==
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	{{Mapping\|legend=1\| 3 0 0 4 -1 \| 0 1 0 -2 -2 \| 0 0 1 2 3 }}		{{Mapping\|legend=1\| 3 0 0 4 -1 \| 0 1 0 -2 -2 \| 0 0 1 2 3 }}

	~~: mapping generators: ~63/50, ~3, ~5~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~63/50 = 400.078{{c}}, ~3/2 = 701.696{{c}}, ~5/4 = 385.162{{c}}		* [[WE]]: ~63/50 = 400.078{{c}}, ~3/2 = 701.696{{c}}, ~5/4 = 385.162{{c}}
			: [[error map]]: {{val\| +0.234 -0.025 -0.684 -1.116 +1.632 }}
	* [[CWE]]: ~63/50 = 400.000{{c}}, ~3/2 = 701.709{{c}}, ~5/4 = 385.341{{c}}		* [[CWE]]: ~63/50 = 400.000{{c}}, ~3/2 = 701.709{{c}}, ~5/4 = 385.341{{c}}
			: error map: {{val\| 0.000 -0.246 -0.972 -1.562 +1.287 }}

	{{Optimal ET sequence\|legend=1\| 12, 15, 27e, 45e, 57, 60e, 72, 159 }}		{{Optimal ET sequence\|legend=1\| 12, 15, 27e, 45e, 57, 60e, 72, 159, 231, 330, 402d }}

	[[Badness]] (Sintel): 0.792		[[Badness]] (Sintel): 0.792
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	Comma list: 364/363, 441/440, 625/624		Comma list: 364/363, 441/440, 625/624

	Mapping: {{~~Mapping~~\| 3 0 0 4 -1 -12 \| 0 1 0 -2 -2 -1 \| 0 0 1 2 3 4 }}		Mapping: {{mapping\| 3 0 0 4 -1 -12 \| 0 1 0 -2 -2 -1 \| 0 0 1 2 3 4 }}

	Optimal tunings:		Optimal tunings:
	* WE: ~63/50 = 400.~~055~~{{c}}, ~3/2 = 701.~~814~~{{c}}, ~5/4 = 385.~~398~~{{c}}		* WE: ~63/50 = 400.0548{{c}}, ~3/2 = 701.8141{{c}}, ~5/4 = 385.3981{{c}}
	* CWE: ~63/50 = 400.~~000~~{{c}}, ~3/2 = 701.~~772~~{{c}}, ~5/4 = 385.~~442~~{{c}}		* CWE: ~63/50 = 400.0000{{c}}, ~3/2 = 701.7720{{c}}, ~5/4 = 385.4420{{c}}

	{{Optimal ET sequence\|legend=0\| 12f, 15, 27eff, 57f, 60eff, 72~~, 84~~, 87, ~~99ef~~, ~~159~~, ~~171~~ }}		{{Optimal ET sequence\|legend=0\| 12f, 15, 27eff, 45efff, 57f, 60eff, 72, 87, 159, 243, 330 }}

	Badness (Sintel): 0.923		Badness (Sintel): 0.923
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	[[Comma list]]: 250047/250000, 117440512/117406179		[[Comma list]]: 250047/250000, 117440512/117406179

	{{Mapping\|legend=1\| 3 0 ~~2 8 16~~ \| 0 1 4 6 0 \| 0 0 -5 -10 2 }}		{{Mapping\|legend=1\| 3 0 -13 -22 10 \| 0 1 4 6 0 \| 0 0 5 10 -2 }}
			: mapping generators: ~63/50, ~3, ~10240/9801
	: mapping generators: ~63/50, ~3, ~9801~~/5120~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~63/50 = 399.~~996~~{{c}}, ~3/2 = 701.~~960~~{{c}}, ~9801~~/5120~~ = ~~1124~~.~~286~~{{c}}		* [[WE]]: ~63/50 = 399.9958{{c}}, ~3/2 = 701.9604{{c}}, ~10240/9801 = 75.7013{{c}}
	* [[CWE]]: ~63/50 = 400.~~000~~{{c}}, ~3/2 = 701.~~965~~{{c}}, ~9801~~/5120~~ = ~~1124~~.~~298~~{{c}}		: [[error map]]: {{val\| -0.012 -0.007 +0.039 -0.034 +0.043 }}
			* [[CWE]]: ~63/50 = 400.0000{{c}}, ~3/2 = 701.9652{{c}}, ~10240/9801 = 75.7024{{c}}
			: error map: {{val\| 0.000 +0.010 +0.059 -0.011 +0.087 }}

	{{Optimal ET sequence\|legend=1\| 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee }}		{{Optimal ET sequence\|legend=1\| 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee }}

	[[Badness]] (Sintel): 2.~~305~~		[[Badness]] (Sintel): 2.31

	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Landscape family\| ]] <!-- main article -->		[[Category:Landscape family\| ]] <!-- main article -->
	~~[[Category:Landscape\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

Xenllium at 05:34, 21 February 2026

2026-02-21T05:34:59Z

← Older revision		Revision as of 05:34, 21 February 2026
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	[[Badness]] (Sintel): 0.792		[[Badness]] (Sintel): 0.792

			=== 13-limit ===
			Subgroup: 2.3.5.7.11.13

			Comma list: 364/363, 441/440, 625/624

			Mapping: {{Mapping\| 3 0 0 4 -1 -12 \| 0 1 0 -2 -2 -1 \| 0 0 1 2 3 4 }}

			Optimal tunings:
			* WE: ~63/50 = 400.055{{c}}, ~3/2 = 701.814{{c}}, ~5/4 = 385.398{{c}}
			* CWE: ~63/50 = 400.000{{c}}, ~3/2 = 701.772{{c}}, ~5/4 = 385.442{{c}}

			{{Optimal ET sequence\|legend=0\| 12f, 15, 27eff, 57f, 60eff, 72, 84, 87, 99ef, 159, 171 }}

			Badness (Sintel): 0.923

	== House ==		== House ==

Xenllium at 04:49, 21 February 2026

2026-02-21T04:49:00Z

@@ Line 3: / Line 3: @@
 The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000.
-Considered below is house, besides the 7-limit temperament. Discussed elsewhere are [[Kalismic temperaments #Odin|odin]] and [[Lehmerismic temperaments #Tyr|tyr]].
+Discussed elsewhere are:
-== Landscape  ==
+Considered below are landy and house, besides the 7-limit temperament.
 [[Subgroup]]: 2.3.5.7
@@ Line 29: / Line 33: @@
 [[Badness]] (Sintel): 0.094<!-- 0.02130 × 10<sup>-3</sup> by Smith's -->
 == House ==

Xenllium at 04:27, 21 February 2026

2026-02-21T04:27:09Z

← Older revision		Revision as of 04:27, 21 February 2026
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	{{Technical data page}}		{{Technical data page}}
	~~__FORCETOC__~~
	The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000.		The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000.

			Considered below is house, besides the 7-limit temperament. Discussed elsewhere are [[Kalismic temperaments #Odin\|odin]] and [[Lehmerismic temperaments #Tyr\|tyr]].

	== Landscape ==		== Landscape ==

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

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	: mapping generators: ~63/50, ~3, ~5		: mapping generators: ~63/50, ~3, ~5

			[[Optimal tuning]]s:
			* [[WE]]: ~63/50 = 400.001{{c}}, ~3/2 = 701.938{{c}}, ~5/4 = 386.335{{c}}
			* [[CWE]]: ~63/50 = 400.000{{c}}, ~3/2 = 701.939{{c}}, ~5/4 = 386.339{{c}}

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	{{Optimal ET sequence\|legend=1\| 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555 }}		{{Optimal ET sequence\|legend=1\| 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555 }}

	[[Badness]]: 0.02130 × 10<sup>-3</sup>		[[Badness]] (Sintel): 0.094<!-- 0.02130 × 10<sup>-3</sup> by Smith's -->

	== House ==		== House ==
	House tempers out the [[quartisma]] alongside the landscape comma.		House tempers out the [[quartisma]] alongside the landscape comma.
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	: mapping generators: ~63/50, ~3, ~9801/5120		: mapping generators: ~63/50, ~3, ~9801/5120

	[[Optimal tuning]] ([[~~CTE~~]]) ~63/50 = 1\3, ~3/2 = 701.~~9592~~, ~9801/5120 = 1124.~~2969~~		[[Optimal tuning]]s:
			* [[WE]]: ~63/50 = 399.996{{c}}, ~3/2 = 701.960{{c}}, ~9801/5120 = 1124.286{{c}}
			* [[CWE]]: ~63/50 = 400.000{{c}}, ~3/2 = 701.965{{c}}, ~9801/5120 = 1124.298{{c}}

	{{Optimal ET sequence\|legend=1\| 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee }}		{{Optimal ET sequence\|legend=1\| 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee }}

	[[Badness]]: 1.~~92 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 2.305

	~~== Odin ==~~
	~~{{See also\| Kalismic temperaments #Odin }}~~

	~~== Tyr ==~~
	~~{{See also\| Lehmerismic temperaments #Tyr }}~~

	[[Category:Temperament families]]		[[Category:Temperament families]]

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

2025-11-27T12:25:17Z

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

← Older revision		Revision as of 12:25, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Landscape family\| ]] <!-- main article -->		[[Category:Landscape family\| ]] <!-- main article -->
	[[Category:Landscape\| ]] <!-- key article -->		[[Category:Landscape\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-06-24T00:37:58Z

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

← Older revision		Revision as of 00:37, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Landscape family\| ]] <!-- main article -->		[[Category:Landscape family\| ]] <!-- main article -->
	[[Category:Landscape\| ]] <!-- key article -->		[[Category:Landscape\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]