11edt - Revision history

Lucius Chiaraviglio: /* 21st century */ Add ''Microtonal Ambient Music - 11EDT (stretched 7EDO)'' (2020) by The Rasa

2026-05-05T00:10:17Z

21st century: Add ''Microtonal Ambient Music - 11EDT (stretched 7EDO)'' (2020) by The Rasa

← Older revision		Revision as of 00:10, 5 May 2026
Line 105:		Line 105:

	=== 21st century ===		=== 21st century ===
			; [[The Rasa]]
			* [https://www.youtube.com/watch?v=cY1tgPbf5Ig ''Microtonal Ambient Music - 11EDT (stretched 7EDO)''] (2020)

	; [[Chris Vaisvil]]		; [[Chris Vaisvil]]
	* ''Frozen Time Occupies Wall Street'' (2011) – [https://www.chrisvaisvil.com/frozen-time-occupies-wall-street/ blog] \| [https://web.archive.org/web/20220911143825/http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 play]		* ''Frozen Time Occupies Wall Street'' (2011) – [https://www.chrisvaisvil.com/frozen-time-occupies-wall-street/ blog] \| [https://web.archive.org/web/20220911143825/http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 play]

FloraC: +see also

2025-05-26T12:48:24Z

+see also

← Older revision		Revision as of 12:48, 26 May 2025
Line 108:		Line 108:
	* ''Frozen Time Occupies Wall Street'' (2011) – [https://www.chrisvaisvil.com/frozen-time-occupies-wall-street/ blog] \| [https://web.archive.org/web/20220911143825/http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 play]		* ''Frozen Time Occupies Wall Street'' (2011) – [https://www.chrisvaisvil.com/frozen-time-occupies-wall-street/ blog] \| [https://web.archive.org/web/20220911143825/http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 play]
	* ''Molly's Playground'' (2011) – [https://www.chrisvaisvil.com/mollys-playground/ blog] \| [https://web.archive.org/web/20201127013949/http://micro.soonlabel.com/11edt/daily20111118-3-11of-edt-mollys-playground.mp3 play]		* ''Molly's Playground'' (2011) – [https://www.chrisvaisvil.com/mollys-playground/ blog] \| [https://web.archive.org/web/20201127013949/http://micro.soonlabel.com/11edt/daily20111118-3-11of-edt-mollys-playground.mp3 play]

			== See also ==
			* [[7edo]] – relative edo
			* [[18ed6]] – relative ed6

FloraC: /* Theory */ +subsets and supersets

2025-05-26T12:46:24Z

Theory: +subsets and supersets

← Older revision		Revision as of 12:46, 26 May 2025
Line 12:		Line 12:
	{{Harmonics in equal\|11\|3\|1\|intervals=integer\|columns=11}}		{{Harmonics in equal\|11\|3\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|11\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 11edt (continued)}}		{{Harmonics in equal\|11\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 11edt (continued)}}

			=== Subsets and supersets ===
			11edt is the fifth [[prime equal division\|prime edt]], following [[7edt]] and before [[13edt]], so it does not contain any nontrivial subset edts.

	== Intervals ==		== Intervals ==

FloraC: /* Intervals */ +/-

2025-05-26T12:45:05Z

Intervals: +/-

← Older revision		Revision as of 12:45, 26 May 2025
Line 19:		Line 19:
	! [[Cent]]s		! [[Cent]]s
	! [[Hekt]]s		! [[Hekt]]s
	! Approximate ratios		! Approximate ratios*
	! [[Arcturus]] ~~nonatonic~~ notation (J = 1/1)		! [[Arcturus]]<br>enneatonic notation (J = 1/1)
	\|-		\|-
	\| 0		\| 0
Line 31:		Line 31:
	\| 172.9		\| 172.9
	\| 118.1		\| 118.1
	\| [[11/10]], [[10/9]]		\| [[10/9]], [[11/10]]
	\| J#, Kb		\| J#, Kb
	\|-		\|-
Line 37:		Line 37:
	\| 345.8		\| 345.8
	\| 236.2		\| 236.2
	\| [[11/9]]		\| [[5/4]], [[6/5]], [[11/9]], [[27/22]]
	\| K		\| K
	\|-		\|-
Line 43:		Line 43:
	\| 518.7		\| 518.7
	\| 354.3		\| 354.3
	\| [[4/3]], [[27/20]]		\| [[4/3]], [[15/11]]
	\| L		\| L
	\|-		\|-
Line 49:		Line 49:
	\| 691.6		\| 691.6
	\| 472.4		\| 472.4
	\| [[3/2~~]], [[40/27~~]]		\| [[3/2]]
	\| M		\| M
	\|-		\|-
Line 55:		Line 55:
	\| 864.5		\| 864.5
	\| 590.5		\| 590.5
	\| [[5/3]], [[28/17]], [[~~105~~/64]]		\| [[5/3]], [[18/11]], [[33/20]]
	\| N		\| N
	\|-		\|-
Line 61:		Line 61:
	\| 1037.4		\| 1037.4
	\| 708.6		\| 708.6
	\| [[29/16]], [[20/11]], [[64/35]]		\| [[9/5]], [[11/6]], [[20/11]]
	\| N#, Ob		\| N#, Ob
	\|-		\|-
Line 73:		Line 73:
	\| 1383.2		\| 1383.2
	\| 944.8		\| 944.8
	\|		\| [[9/4]], [[11/5]]
	\| P		\| P
	\|-		\|-
Line 79:		Line 79:
	\| 1556.1		\| 1556.1
	\| 1062.9		\| 1062.9
	\|		\| [[5/2]], [[12/5]], [[22/9]], [[27/11]]
	\| Q		\| Q
	\|-		\|-
Line 85:		Line 85:
	\| 1729.0		\| 1729.0
	\| 1181.0		\| 1181.0
	\|		\| [[8/3]], [[11/4]]
	\| R		\| R
	\|-		\|-
Line 91:		Line 91:
	\| 1902.0		\| 1902.0
	\| 1300.0		\| 1300.0
	\|		\| [[3/1]]
	\| J		\| J
	\|}		\|}
			<nowiki/>* As a 2.3.5.11-subgroup temperament

	== Music ==		== Music ==

FloraC: Cleanup

2025-05-26T12:29:47Z

Cleanup

← Older revision		Revision as of 12:29, 26 May 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	From a no-~~two~~ point of view, 11edt has a [[5/3]] major sixth that is 19.8 cents flat. However, 11edt has an extremely inaccurate seventh harmonic [[7/1]], which is off by almost half a step (or about a semitone), which causes it to temper out [[49/45]] in the 7-limit. 11edt is at the extreme end of [[arcturus]] temperament, defined by tempering out [[15625/15309]] in the 3.5.7 subgroup. It gives an equalized interpretation for the [[9L 2s (3/1-equivalent)\|sub-arcturus]] [[~~MOS~~]] ~~scale~~.		11edt can be seen as a very [[stretched and compressed tuning\|stretched]] version of [[7edo]], with octaves sharpened by 10.3 cents. The octave stretching makes the [[3/2]] perfect fifth in better tune, while preserving a just [[3/1]] tritave.

			From a no-2 point of view, 11edt has a [[5/3]] major sixth that is 19.8 cents flat. However, 11edt has an extremely inaccurate seventh harmonic [[7/1]], which is off by almost half a step (or about a semitone), which causes it to temper out [[49/45]] in the 7-limit. 11edt is at the extreme end of [[arcturus]] temperament, defined by tempering out [[15625/15309]] in the 3.5.7 subgroup. It gives an equalized interpretation for the [[9L 2s (3/1-equivalent)\|sub-arcturus]] [[mos scale]].

	The 11th harmonic, [[11/1]], only 1.6 cents flat, is very close to just. By exploiting the badly tuned seventh harmonic, 11edt tempers out [[35/33]] and [[77/75]] in the 11-limit. In the 3.5.11 subgroup, it tempers out [[125/121]].		The 11th harmonic, [[11/1]], only 1.6 cents flat, is very close to just. By exploiting the badly tuned seventh harmonic, 11edt tempers out [[35/33]] and [[77/75]] in the 11-limit. In the 3.5.11 subgroup, it tempers out [[125/121]].

	=== ~~Relation to edos~~ ===		=== Harmonics ===
	~~11edt can be seen as a very stretched version of [[7edo]], with octaves sharpened by 10.~~3 ~~cents. The octave stretching makes the [[3/2]] perfect fifth~~ in ~~better tune, while preserving a just [[~~3/1~~]] tritave.~~		{{Harmonics in equal\|11\|3\|1\|intervals=integer\|columns=11}}
			{{Harmonics in equal\|11\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 11edt (continued)}}

	==~~= Prime harmonics ===~~		== Intervals ==
	~~{{Harmonics in equal\|11\|3\|1}}~~		{\| class="wikitable center-1 right-2 right-3"
	~~{{Harmonics in equal\|11\|3\|1\|intervals=prime}}~~

	~~=== Interval table =~~==
	{\| class="wikitable center-~~all~~"
	\|-		\|-
	! #		! #
Line 23:		Line 22:
	! [[Arcturus]] nonatonic notation (J = 1/1)		! [[Arcturus]] nonatonic notation (J = 1/1)
	\|-		\|-
	\| ~~colspan = "3"~~ \| 0		\| 0
			\| 0.0
			\| 0.0
	\| [[1/1]]		\| [[1/1]]
	\| J		\| J
Line 82:		Line 83:
	\|-		\|-
	\| 10		\| 10
	\| 1729		\| 1729.0
	\| 1181		\| 1181.0
	\|		\|
	\| R		\| R
	\|-		\|-
	\| 11		\| 11
	\| 1902		\| 1902.0
	\| 1300		\| 1300.0
	\|		\|
	\| J		\| J
	\|}		\|}

	== ~~Pieces~~ ==		== Music ==
	Mozart's [http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 ~~sonata #~~11 in A ~~Major K331 in 11 EDT~~] (using a 11 ~~=>~~ 12 key mapping so octaves become tritaves)		=== Modern renderings ===
			; {{W\|Wolfgang Amadeus Mozart}}
	[http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 Frozen Time Occupies Wall Street] by [http://www.chrisvaisvil.com Chris Vaisvil] =>[http://chrisvaisvil.com/?p=1392 information about the piece]		* [https://web.archive.org/web/20201127012444/http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 ''Piano Sonata No. 11'' in A major, K. 331] – using a 11 → 12 key mapping so octaves become tritaves

	[http://micro.soonlabel.com/~~11edt~~/~~daily20111118-3-11of-edt-mollys-playground~~.mp3 Molly's Playground~~] by~~ [~~http~~://www.chrisvaisvil.com ~~Chris Vaisvil~~] ~~=>~~ [http://~~chrisvaisvil~~.com/~~?p=1716 information about the piece]~~		=== 21st century ===
	~~[[category:macrotonal]~~]		; [[Chris Vaisvil]]
			* ''Frozen Time Occupies Wall Street'' (2011) – [https://www.chrisvaisvil.com/frozen-time-occupies-wall-street/ blog] \| [https://web.archive.org/web/20220911143825/http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 play]
			* ''Molly's Playground'' (2011) – [https://www.chrisvaisvil.com/mollys-playground/ blog] \| [https://web.archive.org/web/20201127013949/http://micro.soonlabel.com/11edt/daily20111118-3-11of-edt-mollys-playground.mp3 play]

ArrowHead294 at 16:55, 18 February 2025

2025-02-18T16:55:02Z

← Older revision		Revision as of 16:55, 18 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

	From a no-two point of view, 11edt has a [[5/3]] major sixth that is 19.8 cents flat. However, 11edt has an extremely inaccurate seventh harmonic [[7/1]], which is off by almost half a step (or about a semitone), which causes it to temper out [[49/45]] in the 7-limit. 11edt is at the extreme end of [[arcturus]] temperament, defined by tempering out [[15625/15309]] in the 3.5.7 subgroup. It gives an equalized interpretation for the [[9L 2s (3/1-equivalent)\|sub-arcturus]] [[MOS]] scale.		From a no-two point of view, 11edt has a [[5/3]] major sixth that is 19.8 cents flat. However, 11edt has an extremely inaccurate seventh harmonic [[7/1]], which is off by almost half a step (or about a semitone), which causes it to temper out [[49/45]] in the 7-limit. 11edt is at the extreme end of [[arcturus]] temperament, defined by tempering out [[15625/15309]] in the 3.5.7 subgroup. It gives an equalized interpretation for the [[9L 2s (3/1-equivalent)\|sub-arcturus]] [[MOS]] scale.

Line 9:		Line 8:

	=== Relation to edos ===		=== Relation to edos ===
	11edt can be seen as a very stretched version of [[7edo]], with octaves sharpened by 10.3 cents. The octave stretching makes the [[3/2]] perfect fifth in better tune, while preserving a just [[3/1]] tritave.		11edt can be seen as a very stretched version of [[7edo]], with octaves sharpened by 10.3 cents. The octave stretching makes the [[3/2]] perfect fifth in better tune, while preserving a just [[3/1]] tritave.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|11\|3\|1}}		{{Harmonics in equal\|11\|3\|1}}
Line 15:		Line 15:

	=== Interval table ===		=== Interval table ===

	{\| class="wikitable center-all"		{\| class="wikitable center-all"
			\|-
	! #		! #
	! [[Cent]]s		! [[Cent]]s
Line 95:		Line 95:

	== Pieces ==		== Pieces ==

	Mozart's [http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 sonata #11 in A Major K331 in 11 EDT] (using a 11 => 12 key mapping so octaves become tritaves)		Mozart's [http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 sonata #11 in A Major K331 in 11 EDT] (using a 11 => 12 key mapping so octaves become tritaves)

Akselai: clean up

2024-05-20T10:32:03Z

clean up

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-edt means the division of 3, the tritave, into 11 equal parts of 175.905 cents each, corresponding to 6.940 edo. It can therefore be seen as a very stretched version of [[7edo|7edo]], with octaves sharpened by ten and a third cents. The octave stretching makes the fifth in better tune, and of course the twelfth is the pure 3/1 tritave.
+{{EDO intro}}
-From a no-two point of view, it tempers out 49/45 and 15625/15309 in the 7-limit and 35/33 and 77/75 in the 11-limit.
+== Theory ==
-== Intervals ==
+From a no-two point of view, 11edt has a [[5/3]] major sixth that is 19.8 cents flat. However, 11edt has an extremely inaccurate seventh harmonic [[7/1]], which is off by almost half a step (or about a semitone), which causes it to temper out [[49/45]] in the 7-limit. 11edt is at the extreme end of [[arcturus]] temperament, defined by tempering out [[15625/15309]] in the 3.5.7 subgroup. It gives an equalized interpretation for the [[9L 2s (3/1-equivalent)|sub-arcturus]] [[MOS]] scale.
 {| class="wikitable center-all"
 ! #
-! Cents
+! [[Cent]]s
-! Hekts
+! [[Hekt]]s
 ! Approximate ratios
 ! [[Arcturus]] nonatonic notation (J = 1/1)
@@ Line 83: / Line 93: @@
 | J
 |}
 == Pieces ==

Akselai: /* Prime harmonics */

2024-01-17T09:39:22Z

Prime harmonics

← Older revision		Revision as of 09:39, 17 January 2024
Line 85:		Line 85:

	== Prime harmonics ==		== Prime harmonics ==
	{{Harmonics in equal\|11\|3\|1}}		{{Harmonics in equal\|11\|3\|1\|intervals=prime}}

	== Scala file ==		== Scala file ==

Akselai: add harmonics in equal

2024-01-17T09:30:03Z

add harmonics in equal

← Older revision		Revision as of 09:30, 17 January 2024
Line 83:		Line 83:
	\| J		\| J
	\|}		\|}

			== Prime harmonics ==
			{{Harmonics in equal\|11\|3\|1}}

	== Scala file ==		== Scala file ==

CompactStar: Changing H = 1/1 to J = 1/1 as it seems to be more common

2023-03-01T03:47:25Z

Changing H = 1/1 to J = 1/1 as it seems to be more common

← Older revision		Revision as of 03:47, 1 March 2023
Line 11:		Line 11:
	! Hekts		! Hekts
	! Approximate ratios		! Approximate ratios
	! [[Arcturus]] nonatonic notation		! [[Arcturus]] nonatonic notation (J = 1/1)
	\|-		\|-
	\| colspan = "3" \| 0		\| colspan = "3" \| 0
	\| [[1/1]]		\| [[1/1]]
	\| H		\| J
	\|-		\|-
	\| 1		\| 1
Line 21:		Line 21:
	\| 118.1		\| 118.1
	\| [[11/10]], [[10/9]]		\| [[11/10]], [[10/9]]
	\| H#, Ib		\| J#, Kb
	\|-		\|-
	\| 2		\| 2
Line 27:		Line 27:
	\| 236.2		\| 236.2
	\| [[11/9]]		\| [[11/9]]
	\| I		\| K
	\|-		\|-
	\| 3		\| 3
Line 33:		Line 33:
	\| 354.3		\| 354.3
	\| [[4/3]], [[27/20]]		\| [[4/3]], [[27/20]]
	\| J		\| L
	\|-		\|-
	\| 4		\| 4
Line 39:		Line 39:
	\| 472.4		\| 472.4
	\| [[3/2]], [[40/27]]		\| [[3/2]], [[40/27]]
	\| K		\| M
	\|-		\|-
	\| 5		\| 5
Line 45:		Line 45:
	\| 590.5		\| 590.5
	\| [[5/3]], [[28/17]], [[105/64]]		\| [[5/3]], [[28/17]], [[105/64]]
	\| L		\| N
	\|-		\|-
	\| 6		\| 6
Line 51:		Line 51:
	\| 708.6		\| 708.6
	\| [[29/16]], [[20/11]], [[64/35]]		\| [[29/16]], [[20/11]], [[64/35]]
	\| L#, Mb		\| N#, Ob
	\|-		\|-
	\| 7		\| 7
Line 57:		Line 57:
	\| 826.7		\| 826.7
	\| [[2/1]]		\| [[2/1]]
	\| M		\| O
	\|-		\|-
	\| 8		\| 8
Line 63:		Line 63:
	\| 944.8		\| 944.8
	\|		\|
	\| N		\| P
	\|-		\|-
	\| 9		\| 9
Line 69:		Line 69:
	\| 1062.9		\| 1062.9
	\|		\|
	\| O		\| Q
	\|-		\|-
	\| 10		\| 10
Line 75:		Line 75:
	\| 1181		\| 1181
	\|		\|
	\| P		\| R
	\|-		\|-
	\| 11		\| 11
Line 81:		Line 81:
	\| 1300		\| 1300
	\|		\|
	\| H		\| J
	\|}		\|}