11th-octave temperaments - Revision history

Xenllium at 02:34, 11 February 2026

2026-02-11T02:34:04Z

← Older revision		Revision as of 02:34, 11 February 2026
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	: Mapping generators: ~16/15, ~3		: Mapping generators: ~16/15, ~3

	[[Optimal tuning]] ([[~~POTE~~]]): ~16/15 = 109.~~091~~, ~3/2 = 702.~~947~~		[[Optimal tuning]]s:
			* [[CTE]]: ~16/15 = 109.091¢, ~3/2 = 702.794¢
			* [[CWE]]: ~16/15 = 109.091¢, ~3/2 = 702.908¢

	{{Optimal ET sequence\|legend=1\| 22, 55, 77, 99 }}		{{Optimal ET sequence\|legend=1\| 22, 55, 77, 99 }}
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	: Mapping generators: ~648/625, ~3		: Mapping generators: ~648/625, ~3

	[[Optimal tuning]] ([[~~POTE~~]]): ~648/625 = 109.~~091~~, ~3/2 = ~~703~~.~~829~~		[[Optimal tuning]]s:
			* [[CTE]]: ~648/625 = 109.091¢, ~3/2 = 705.652¢
			* [[CWE]]: ~648/625 = 109.091¢, ~3/2 = 704.698¢

	{{Optimal ET sequence\|legend=1\| 22, 77c, 99c, 121c }}		{{Optimal ET sequence\|legend=1\| 22, 77c, 99c, 121c }}
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	: Mapping generators: ~3125/2916, ~{{monzo\| 10 29 -24 }}		: Mapping generators: ~3125/2916, ~{{monzo\| 10 29 -24 }}

	[[Optimal tuning]] ([[~~POTE~~]]): ~~~648~~/~~625~~ = 109.~~091~~, ~6/5 = ~~317~~.~~681~~		[[Optimal tuning]]s:
			* [[CTE]]: ~3125/2916 = 109.091¢, ~5/3 = 882.353¢
			* [[CWE]]: ~3125/2916 = 109.091¢, ~5/3 = 882.336¢

	{{Optimal ET sequence\|legend=1\| 121, 253, 374 }}		{{Optimal ET sequence\|legend=1\| 121, 253, 374 }}

Xenllium at 02:22, 11 February 2026

2026-02-11T02:22:51Z

← Older revision		Revision as of 02:22, 11 February 2026
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	{{Optimal ET sequence\|legend=1\| 22, 55, 77, 99 }}		{{Optimal ET sequence\|legend=1\| 22, 55, 77, 99 }}

	[[Badness]]: 0.~~454083~~		[[Badness]] (Sintel): 10.652

	=== Undekapent ===		=== Undekapent ===
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	{{Optimal ET sequence\|legend=1\| 22, 77c, 99c, 121c }}		{{Optimal ET sequence\|legend=1\| 22, 77c, 99c, 121c }}

	[[Badness]]: 0.~~727539~~		[[Badness]] (Sintel): 17.067

			=== Elven ===
			{{see also\| Sensibeta temperaments #Elven }}
			This temperament has a period of 1/11 octave, which represents [[3125/2916]] in the 5-limit.

			[[Subgroup]]: 2.3.5

			[[Comma list]]: {{monzo\|-23 -66 55}}

			{{Mapping\|legend=1\| 11 2 7 \| 0 5 6 }}

			: Mapping generators: ~3125/2916, ~{{monzo\| 10 29 -24 }}

			[[Optimal tuning]] ([[POTE]]): ~648/625 = 109.091, ~6/5 = 317.681

			{{Optimal ET sequence\|legend=1\| 121, 253, 374 }}

			[[Badness]] (Sintel): 429.4

	== Hendeca ==		== Hendeca ==
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	{{Optimal ET sequence\|legend=1\| 11, 22, 55d, 77d, 99dd }}		{{Optimal ET sequence\|legend=1\| 11, 22, 55d, 77d, 99dd }}

	[[Badness]]: 0.~~172714~~		[[Badness]] (Sintel): 4.371

	=== 11-limit ===		=== 11-limit ===
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	{{Optimal ET sequence\|legend=0\| 11, 22, 55d, 77d, 99dd }}		{{Optimal ET sequence\|legend=0\| 11, 22, 55d, 77d, 99dd }}

	Badness: 0.~~074543~~		Badness (Sintel): 2.464

	== Undeka ==		== Undeka ==
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	{{Optimal ET sequence\|legend=1\| 11c, 22 }}		{{Optimal ET sequence\|legend=1\| 11c, 22 }}

	[[Badness]]: 0.~~141782~~		[[Badness]] (Sintel): 3.588

	=== 11-limit ===		=== 11-limit ===
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	{{Optimal ET sequence\|legend=0\| 11c, 22 }}		{{Optimal ET sequence\|legend=0\| 11c, 22 }}

	Badness: 0.~~068672~~		Badness (Sintel): 2.270

	=== 13-limit ===		=== 13-limit ===
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	{{Optimal ET sequence\|legend=0\| 11cf, 22 }}		{{Optimal ET sequence\|legend=0\| 11cf, 22 }}

	Badness: 0.~~056528~~		Badness (Sintel): 2.336

	{{Navbox fractional-octave}}		{{Navbox fractional-octave}}

VectorGraphics at 04:40, 12 June 2025

2025-06-12T04:40:32Z

← Older revision		Revision as of 04:40, 12 June 2025
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	: Mapping generators: ~16/15, ~3		: Mapping generators: ~16/15, ~3

	~~{{Multival\|legend=1\| 11 -11 0 -43 -31 31 }}~~

	[[Optimal tuning]] ([[POTE]]): ~16/15 = 109.091, ~3/2 = 703.313		[[Optimal tuning]] ([[POTE]]): ~16/15 = 109.091, ~3/2 = 703.313
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	: Mapping generators: ~21/20, ~3		: Mapping generators: ~21/20, ~3

	~~{{Multival\|legend=1\| 11 11 0 -8 -31 -31 }}~~

	[[Optimal tuning]] ([[POTE]]): ~21/20 = 109.091, ~3/2 = 708.792		[[Optimal tuning]] ([[POTE]]): ~21/20 = 109.091, ~3/2 = 708.792

FloraC: -hendecatonic (duplicate). No more weird backslashes

2025-04-24T11:55:13Z

-hendecatonic (duplicate). No more weird backslashes

← Older revision		Revision as of 11:55, 24 April 2025
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	== 5-limit temperaments ==		== 5-limit temperaments ==
	=== Hendecapent ===		=== Hendecapent ===
	This temperament has a period of 1/11 octave, which represents [[16/15]] in the 5-limit. There are some 7-limit extensions include [[#Hendecatonic\|hendecatonic]] (22 &~~amp;~~ 77) and [[#Hendeca\|hendeca]] (22 &~~amp;~~ 33).		This temperament has a period of 1/11 octave, which represents [[16/15]] in the 5-limit. There are some 7-limit extensions include [[Porwell temperaments #Hendecatonic\|hendecatonic]] ({{nowrap\| 22 & 77 }}) and [[#Hendeca\|hendeca]] ({{nowrap\| 22 & 33 }}).

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	: Mapping generators: ~16/15, ~3		: Mapping generators: ~16/15, ~3

	[[Optimal tuning]] ([[POTE]]): ~16/15 = ~~1＼11~~, ~3/2 = 702.947		[[Optimal tuning]] ([[POTE]]): ~16/15 = 109.091, ~3/2 = 702.947

	{{Optimal ET sequence\|legend=1\| 22, 55, 77, 99 }}		{{Optimal ET sequence\|legend=1\| 22, 55, 77, 99 }}
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	: Mapping generators: ~648/625, ~3		: Mapping generators: ~648/625, ~3

	[[Optimal tuning]] ([[POTE]]): ~648/625 = ~~1＼11~~, ~3/2 = 703.829		[[Optimal tuning]] ([[POTE]]): ~648/625 = 109.091, ~3/2 = 703.829

	{{Optimal ET sequence\|legend=1\| 22, 77c, 99c, 121c }}		{{Optimal ET sequence\|legend=1\| 22, 77c, 99c, 121c }}
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	[[Badness]]: 0.727539		[[Badness]]: 0.727539

	== ~~Hendecatonic~~ ==		== Hendeca ==
	~~: <Small>''For 11-limit extensions, see [[Porwell temperaments #Hendecatonic]].''</small>~~		{{Distinguish\|Hendec}}

	~~This temperament has a period of 1/11 octave, four of them represent [[9/7]] in the 7-limit.~~

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 6144/6125, 10976/10935~~

	~~{{Mapping\|legend=1\| 11 0 43 -4 \| 0 1 -1 2 }}~~

	~~: Mapping generators: ~16/15, ~3~~

	{{~~Multival~~\|~~legend=1\| 11 -11 22 -43 4 82~~ }}

	~~[[Optimal tuning]] ([[POTE]]): ~16/15 = 1＼11, ~3/2 = 703.054~~

	~~{{Optimal ET sequence\|legend=1\| 22, 55, 77, 99 }}~~

	~~[[Badness]]: 0.041081~~

	~~== Hendeca ==~~
	~~{{distinguish\|Hendec}}~~
	This temperament has a period of 1/11 octave, nine of them represent [[7/4]] in the 7-limit, as well as [[#undeka\|undeka]].		This temperament has a period of 1/11 octave, nine of them represent [[7/4]] in the 7-limit, as well as [[#undeka\|undeka]].

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	{{Multival\|legend=1\| 11 -11 0 -43 -31 31 }}		{{Multival\|legend=1\| 11 -11 0 -43 -31 31 }}

	[[Optimal tuning]] ([[POTE]]): ~16/15 = ~~1＼11~~, ~3/2 = 703.313		[[Optimal tuning]] ([[POTE]]): ~16/15 = 109.091, ~3/2 = 703.313

	{{Optimal ET sequence\|legend=1\| 11, 22, 55d, 77d, 99dd }}		{{Optimal ET sequence\|legend=1\| 11, 22, 55d, 77d, 99dd }}
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	Mapping: {{mapping\| 11 0 43 31 38 \| 0 1 -1 0 0 }}		Mapping: {{mapping\| 11 0 43 31 38 \| 0 1 -1 0 0 }}

	Optimal tuning (POTE): ~16/15 = ~~1＼11~~, ~3/2 = 703.090		Optimal tuning (POTE): ~16/15 = 109.091, ~3/2 = 703.090

	{{Optimal ET sequence\|legend=0\| 11, 22, 55d, 77d, 99dd }}		{{Optimal ET sequence\|legend=0\| 11, 22, 55d, 77d, 99dd }}
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	{{Multival\|legend=1\| 11 11 0 -8 -31 -31 }}		{{Multival\|legend=1\| 11 11 0 -8 -31 -31 }}

	[[Optimal tuning]] ([[POTE]]): ~21/20 = ~~1＼11~~, ~3/2 = 708.792		[[Optimal tuning]] ([[POTE]]): ~21/20 = 109.091, ~3/2 = 708.792

	{{Optimal ET sequence\|legend=1\| 11c, 22 }}		{{Optimal ET sequence\|legend=1\| 11c, 22 }}
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	Mapping: {{mapping\| 11 0 8 31 38 \| 0 1 1 0 0 }}		Mapping: {{mapping\| 11 0 8 31 38 \| 0 1 1 0 0 }}

	Optimal tuning (POTE): ~21/20 = ~~1＼11~~, ~3/2 = 706.768		Optimal tuning (POTE): ~21/20 = 109.091, ~3/2 = 706.768

	{{Optimal ET sequence\|legend=0\| 11c, 22 }}		{{Optimal ET sequence\|legend=0\| 11c, 22 }}
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	Mapping: {{mapping\| 11 0 8 31 38 23 \| 0 1 1 0 0 1 }}		Mapping: {{mapping\| 11 0 8 31 38 23 \| 0 1 1 0 0 1 }}

	Optimal tuning (POTE): ~13/12 = ~~1＼11~~, ~3/2 = 707.764		Optimal tuning (POTE): ~13/12 = 109.091, ~3/2 = 707.764

	{{Optimal ET sequence\|legend=0\| 11cf, 22 }}		{{Optimal ET sequence\|legend=0\| 11cf, 22 }}

Xenllium at 13:35, 13 April 2025

2025-04-13T13:35:28Z

← Older revision		Revision as of 13:35, 13 April 2025
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			{{Technical data page}}
	{{Infobox fractional-octave\|11}}		{{Infobox fractional-octave\|11}}
	Although [[11edo]] itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 11 are.		An 11th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 11. Although [[11edo]] itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 11 are.

	== 5-limit temperaments ==		== 5-limit temperaments ==

Xenllium: Hendeca temperament: Not to be confused with hendec.

2025-04-13T12:16:15Z

Hendeca temperament: Not to be confused with hendec.

← Older revision		Revision as of 12:16, 13 April 2025
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	== Hendeca ==		== Hendeca ==
			{{distinguish\|Hendec}}
	This temperament has a period of 1/11 octave, nine of them represent [[7/4]] in the 7-limit, as well as [[#undeka\|undeka]].		This temperament has a period of 1/11 octave, nine of them represent [[7/4]] in the 7-limit, as well as [[#undeka\|undeka]].

Xenllium: Created page with "{{Infobox fractional-octave|11}} Although 11edo itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 11 are. == 5-limit temperaments == === Hendecapent === This temperament has a period of 1/11 octave, which represents 16/15 in the 5-limit. There are some 7-limit extensions include hendecatonic (22 & 77) and hendeca (22 & 33). Subgroup: 2.3.5 Comma list: 879609..."

2025-04-13T12:00:41Z

Created page with "{{Infobox fractional-octave|11}} Although 11edo itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 11 are. == 5-limit temperaments == === Hendecapent === This temperament has a period of 1/11 octave, which represents 16/15 in the 5-limit. There are some 7-limit extensions include hendecatonic (22 & 77) and hendeca (22 & 33). Subgroup: 2.3.5 Comma list: 879609..."

New page

{{Infobox fractional-octave|11}}
Although [[11edo]] itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 11 are.

== 5-limit temperaments ==
=== Hendecapent ===
This temperament has a period of 1/11 octave, which represents [[16/15]] in the 5-limit. There are some 7-limit extensions include [[#Hendecatonic|hendecatonic]] (22 & 77) and [[#Hendeca|hendeca]] (22 & 33).

[[Subgroup]]: 2.3.5

[[Comma list]]: 8796093022208/8649755859375

{{Mapping|legend=1| 11 0 43 | 0 1 -1 }}

: Mapping generators: ~16/15, ~3

[[Optimal tuning]] ([[POTE]]): ~16/15 = 1＼11, ~3/2 = 702.947

{{Optimal ET sequence|legend=1| 22, 55, 77, 99 }}

[[Badness]]: 0.454083

=== Undekapent ===
This temperament has a period of 1/11 octave, three of them represent [[6/5]] in the 5-limit.

[[Subgroup]]: 2.3.5

[[Comma list]]: 48828125/45349632

{{Mapping|legend=1| 11 0 8 | 0 1 1 }}

: Mapping generators: ~648/625, ~3

[[Optimal tuning]] ([[POTE]]): ~648/625 = 1＼11, ~3/2 = 703.829

{{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }}

[[Badness]]: 0.727539

== Hendecatonic ==
: <Small>''For 11-limit extensions, see [[Porwell temperaments #Hendecatonic]].''</small>

This temperament has a period of 1/11 octave, four of them represent [[9/7]] in the 7-limit.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 6144/6125, 10976/10935

{{Mapping|legend=1| 11 0 43 -4 | 0 1 -1 2 }}

: Mapping generators: ~16/15, ~3

{{Multival|legend=1| 11 -11 22 -43 4 82 }}

[[Optimal tuning]] ([[POTE]]): ~16/15 = 1＼11, ~3/2 = 703.054

{{Optimal ET sequence|legend=1| 22, 55, 77, 99 }}

[[Badness]]: 0.041081

== Hendeca ==
This temperament has a period of 1/11 octave, nine of them represent [[7/4]] in the 7-limit, as well as [[#undeka|undeka]].

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 225/224, 122880/117649

{{Mapping|legend=1| 11 0 43 31 | 0 1 -1 0 }}

: Mapping generators: ~16/15, ~3

{{Multival|legend=1| 11 -11 0 -43 -31 31 }}

[[Optimal tuning]] ([[POTE]]): ~16/15 = 1＼11, ~3/2 = 703.313

{{Optimal ET sequence|legend=1| 11, 22, 55d, 77d, 99dd }}

[[Badness]]: 0.172714

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 352/343

Mapping: {{mapping| 11 0 43 31 38 | 0 1 -1 0 0 }}

Optimal tuning (POTE): ~16/15 = 1＼11, ~3/2 = 703.090

{{Optimal ET sequence|legend=0| 11, 22, 55d, 77d, 99dd }}

Badness: 0.074543

== Undeka ==
[[Subgroup]]: 2.3.5.7

[[Comma list]]: 875/864, 3200/3087

{{Mapping|legend=1| 11 0 8 31 | 0 1 1 0 }}

: Mapping generators: ~21/20, ~3

{{Multival|legend=1| 11 11 0 -8 -31 -31 }}

[[Optimal tuning]] ([[POTE]]): ~21/20 = 1＼11, ~3/2 = 708.792

{{Optimal ET sequence|legend=1| 11c, 22 }}

[[Badness]]: 0.141782

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 100/99, 352/343, 385/384

Mapping: {{mapping| 11 0 8 31 38 | 0 1 1 0 0 }}

Optimal tuning (POTE): ~21/20 = 1＼11, ~3/2 = 706.768

{{Optimal ET sequence|legend=0| 11c, 22 }}

Badness: 0.068672

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

Comma list: 65/63, 100/99, 169/165, 352/343

Mapping: {{mapping| 11 0 8 31 38 23 | 0 1 1 0 0 1 }}

Optimal tuning (POTE): ~13/12 = 1＼11, ~3/2 = 707.764

{{Optimal ET sequence|legend=0| 11cf, 22 }}

Badness: 0.056528

{{Navbox fractional-octave}}