11edo - Revision history

Lucius Chiaraviglio: /* 21st century */ Add Joseph Monzo's ''Monzo, 2026-0608: 11edo, 11/8 time, piano, musescore3'' (2026)

2026-06-10T19:19:02Z

21st century: Add Joseph Monzo's ''Monzo, 2026-0608: 11edo, 11/8 time, piano, musescore3'' (2026)

← Older revision		Revision as of 19:19, 10 June 2026
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	* [https://www.youtube.com/watch?v=fwyM3quEzu4 ''Prelude & Fugue in 11edo, in Four Parts, for Recorder, Organ, Cello''] (2022)		* [https://www.youtube.com/watch?v=fwyM3quEzu4 ''Prelude & Fugue in 11edo, in Four Parts, for Recorder, Organ, Cello''] (2022)
	* [https://www.youtube.com/watch?v=qNqDuAq6O5k ''George Secor · 11EDO improvisation (1971)''] (2022)		* [https://www.youtube.com/watch?v=qNqDuAq6O5k ''George Secor · 11EDO improvisation (1971)''] (2022)

			; [[Joseph Monzo]]
			* [https://www.youtube.com/shorts/JMrFUKfqfeY ''Monzo, 2026-0608: 11edo, 11/8 time, piano, musescore3''] (2026)

	; [[Mundoworld]]		; [[Mundoworld]]

Lucius Chiaraviglio: /* Instruments */ Another Lumatone mapping for 11edo is coming real soon

2026-05-08T03:19:19Z

Instruments: Another Lumatone mapping for 11edo is coming real soon

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	[[File:11-edo-ukulele.JPG\|alt=11-edo-ukulele.JPG\|404x304px\|11-edo-ukulele.JPG]]		[[File:11-edo-ukulele.JPG\|alt=11-edo-ukulele.JPG\|404x304px\|11-edo-ukulele.JPG]]


	'''Ensembles'''		'''Ensembles'''

	In February 2011, [http://oddmusicuc.wordpress.com/ Oddmusic U-C], as part of its Microtonal Design Seminar, generated a 7-piece ensemble for playing music in 11edo. Instrumentation: autotuner, cümbüş, electronic keyboard, kalimba, retrofretted guitar, tuned bottles, udderbot. Recordings forthcoming.		In February 2011, [http://oddmusicuc.wordpress.com/ Oddmusic U-C], as part of its Microtonal Design Seminar, generated a 7-piece ensemble for playing music in 11edo. Instrumentation: autotuner, cümbüş, electronic keyboard, kalimba, retrofretted guitar, tuned bottles, udderbot. Recordings forthcoming.


	'''Lumatone'''		'''Lumatone'''

	~~There is a~~ [[Lumatone mapping for 11edo]].		[[Lumatone mapping for 11edo\|Lumatone mappings for 11edo]] are available.

	== Introductory Materials ==		== Introductory Materials ==

Lucius Chiaraviglio: /* Unequal Derivatives of 11edo */ Full version has tuning specification

2026-05-08T03:13:00Z

Unequal Derivatives of 11edo: Full version has tuning specification

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	* ''11 Tone March'' (2023/2024)		* ''11 Tone March'' (2023/2024)
	** [https://www.youtube.com/shorts/K2QVvaRUXIQ <nowiki>[short clip]</nowiki>] (2023, with Lumatone view)		** [https://www.youtube.com/shorts/K2QVvaRUXIQ <nowiki>[short clip]</nowiki>] (2023, with Lumatone view)
	** [https://www.youtube.com/watch?v=z0lWcguNsNs <nowiki>[full version]</nowiki>] (2024)		** [https://www.youtube.com/watch?v=z0lWcguNsNs <nowiki>[full version]</nowiki>] (2024, with tuning specification in video description)

	== Videos ==		== Videos ==

Lucius Chiaraviglio: /* Notation */ --> Intervals and Notation

2026-05-06T16:12:28Z

Notation: --> Intervals and Notation

← Older revision		Revision as of 16:12, 6 May 2026
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	[[File:0-8-16-20 chord.wav\|thumb\|A 0–8–16–20 chord in 11edo illustrating harmony generated from stacking 9/7 intervals.]]		[[File:0-8-16-20 chord.wav\|thumb\|A 0–8–16–20 chord in 11edo illustrating harmony generated from stacking 9/7 intervals.]]

	== Notation ==		== Intervals and Notation ==
	=== Ups and downs notation ===		=== Ups and downs notation ===
	11edo can be notated using ups and downs. Conventional notation, including the staff, note names, relative notation, etc. can be used in two ways. The first preserves the ''melodic'' meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.		11edo can be notated using ups and downs. Conventional notation, including the staff, note names, relative notation, etc. can be used in two ways. The first preserves the ''melodic'' meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.

Lucius Chiaraviglio: /* Unequal Derivatives of 11edo */ Bryan Deister's ''11 Tone March'' (2023/2024): Add short clip, with Lumatone view

2026-05-06T07:07:03Z

Unequal Derivatives of 11edo: Bryan Deister's ''11 Tone March'' (2023/2024): Add short clip, with Lumatone view

← Older revision		Revision as of 07:07, 6 May 2026
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	=== Unequal Derivatives of 11edo ===		=== Unequal Derivatives of 11edo ===
	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/watch?v=z0lWcguNsNs ~~''11 Tone March''~~] (2024)		* ''11 Tone March'' (2023/2024)
			** [https://www.youtube.com/shorts/K2QVvaRUXIQ <nowiki>[short clip]</nowiki>] (2023, with Lumatone view)
			** [https://www.youtube.com/watch?v=z0lWcguNsNs <nowiki>[full version]</nowiki>] (2024)

	== Videos ==		== Videos ==

Overthink: /* Commas */ shows its inaccuracy

2026-03-23T04:12:04Z

Commas: shows its inaccuracy

← Older revision		Revision as of 04:12, 23 March 2026
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	\| Layobi		\| Layobi
	\| Major chroma		\| Major chroma
			\|-
			\| 5
			\| [[144/125]]
			\| {{Monzo\| 4 2 -3 }}
			\| 244.97
			\| Trigu
			\| University comma
	\|-		\|-
	\| 5		\| 5

Videogamer1002: /* Videos */

2026-01-29T03:54:49Z

Videos

← Older revision		Revision as of 03:54, 29 January 2026
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	* [https://www.youtube.com/watch?v=AhPjsCoMy-Q 11-equal Improvisation]'', [[Mike Battaglia FAQ\|Mike Battaglia]] - youtube		* [https://www.youtube.com/watch?v=AhPjsCoMy-Q 11-equal Improvisation]'', [[Mike Battaglia FAQ\|Mike Battaglia]] - youtube
			* [https://www.youtube.com/watch?v=4WlTPfRDPCY untitled1], computer

	== See also ==		== See also ==

Lucius Chiaraviglio: /* Strict 11edo */ Make heading consistent with the corresponding section in 5edo/Music

2025-12-16T11:13:06Z

Strict 11edo: Make heading consistent with the corresponding section in 5edo/Music

← Older revision		Revision as of 11:13, 16 December 2025
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	== Music ==		== Music ==
	{{Catrel\|11edo tracks}}		{{Catrel\|11edo tracks}}
	=== ~~Strict~~ 11edo ===		=== 11 equal divisions of the octave (11edo proper) ===
	==== Modern renderings ====		==== Modern renderings ====
	; {{W\|Arthur Schutt}}		; {{W\|Arthur Schutt}}

Overthink: move harmonics table later

2025-12-14T04:46:49Z

move harmonics table later

← Older revision		Revision as of 04:46, 14 December 2025
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	{{ED intro}}		{{ED intro}}
	== Theory ==		== Theory ==
	~~{{Harmonics in equal\|11\|intervals=odd}}~~

	Compared to 12edo, the intervals of 11edo are stretched:		Compared to 12edo, the intervals of 11edo are stretched:

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	* The "major third" at 436.36 cents, is quite sharp, and closer to the [[supermajor]] third of frequency ratio [[9/7]] than the simpler third of 5/4.		* The "major third" at 436.36 cents, is quite sharp, and closer to the [[supermajor]] third of frequency ratio [[9/7]] than the simpler third of 5/4.
	* The "perfect fourth" at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the [[11/8]] superfourth than the simpler perfect fourth of 4/3.		* The "perfect fourth" at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the [[11/8]] superfourth than the simpler perfect fourth of 4/3.
			{{Harmonics in equal\|11}}

	11edo does not approximate many small prime harmonics well, only providing good approximations to 7/4 and 11/8. However, 11edo can be treated as a subset of 22edo, and take 22edo's [[6/5]], [[9/7]], and [[16/15]] via direct approximation.		11edo does not approximate many small prime harmonics well, only providing good approximations to 7/4 and 11/8. However, 11edo can be treated as a subset of 22edo, and take 22edo's [[6/5]], [[9/7]], and [[16/15]] via direct approximation.

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	Being less than twelve, 11edo maps easily to the standard keyboard. The suggested mapping disregards the Ab/G# key, leaving [[Orgone]][7] on the whites. The superfluous Ab can be made a note of [[22edo]], a tuning known as "[[elevenplus]]".		Being less than twelve, 11edo maps easily to the standard keyboard. The suggested mapping disregards the Ab/G# key, leaving [[Orgone]][7] on the whites. The superfluous Ab can be made a note of [[22edo]], a tuning known as "[[elevenplus]]".

	[[File:0-8-16-20 chord.wav\|thumb\|A 0–8–16–20 chord in 11edo illustrating harmony generated from stacking 9/7 intervals.]]		[[File:0-8-16-20 chord.wav\|thumb\|A 0–8–16–20 chord in 11edo illustrating harmony generated from stacking 9/7 intervals.]]

BudjarnLambeth: /* Octave stretch or compression */

2025-09-19T08:46:01Z

Octave stretch or compression

← Older revision		Revision as of 08:46, 19 September 2025
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	11edo has about equally bad sharp and flat mappings of [[prime]]s 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight [[octave shrinking]] is advisable. Examples of slightly compressed versions of 11edo include (least to most compressed) [[ed6\|28ed6]], [[ed12\|39ed12]], [[zpi\|30zpi]], [[equal tuning\|35ed9]] and [[ed7\|31ed7]].		11edo has about equally bad sharp and flat mappings of [[prime]]s 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight [[octave shrinking]] is advisable. Examples of slightly compressed versions of 11edo include (least to most compressed) [[ed6\|28ed6]], [[ed12\|39ed12]], [[zpi\|30zpi]], [[equal tuning\|35ed9]] and [[ed7\|31ed7]].

	To use its primes 3 or 5, extreme octave shrinking can be used, at the cost of making the octaves sound significantly weaker. [[~~ed10~~\|37ed10]] is a very compressed version of 11edo.		To use its primes 3 or 5, extreme octave shrinking can be used, at the cost of making the octaves sound significantly weaker. [[equal tuning\|37ed10]] is a very compressed version of 11edo.

	== Scales ==		== Scales ==