36edo - Revision history

CompactStar: /* Relation to 12edo and other tunings */

2026-11-06T09:09:14Z

Relation to 12edo and other tunings

← Older revision		Revision as of 09:09, 6 November 2026
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	For people accustomed to 12edo, 36edo is one of the easiest (if not ''the'' easiest) higher edo to become accustomed to. This is because one way to envision it is as an extended 12edo to which [https://en.wikipedia.org/wiki/Blue_note blue notes] (which are a sixth-tone lower than normal) and "red notes" (a sixth-tone higher) have been added.		For people accustomed to 12edo, 36edo is one of the easiest (if not ''the'' easiest) higher edo to become accustomed to. This is because one way to envision it is as an extended 12edo to which [https://en.wikipedia.org/wiki/Blue_note blue notes] (which are a sixth-tone lower than normal) and "red notes" (a sixth-tone higher) have been added.

	The intervals in 36edo are all either the familiar 12edo intervals, or else "red" and "blue" versions of them. In [[24edo]], intervals such as 250{{c}} (halfway between a tone and a third) and 450{{c}} (halfway between a fourth and a third) tend to sound genuinely foreign, whereas the new intervals in 36edo are all variations on existing ones. Unlike 24edo, 36edo is also relatively free of what Easley Blackwood called "discordant" intervals. The 5th and 11th harmonics fall almost halfway in between scale degrees of 36edo, and thus intervals containing them can be approximated two different ways, one of which is significantly sharp and the other significantly flat. The 33{{frac\|1\|3}}{{c}} interval (the "red minor third" or "supraminor third") sharply approximates 6/5 and flatly approximates 11/9, for instance, whereas the sharp 11/9 is 366{{frac\|2\|3}}{{c}} and the flat 6/5 is 300{{c}}. However, 11/10, 20/11, 15/11, and 22/15 all have accurate and consistent approximations since the errors on the 5th and 11th harmonics cancel out with both tending sharp.		The intervals in 36edo are all either the familiar 12edo intervals, or else "red" and "blue" versions of them. In [[24edo]], intervals such as 250{{c}} (halfway between a tone and a third) and 450{{c}} (halfway between a fourth and a third) tend to sound genuinely foreign, whereas the new intervals in 36edo are all variations on existing ones. Unlike 24edo, 36edo is also relatively free of what Easley Blackwood called "discordant" intervals. The 5th and 11th harmonics fall almost halfway in between scale degrees of 36edo, and thus intervals containing them can be approximated two different ways, one of which is significantly sharp and the other significantly flat. The 333{{frac\|1\|3}}{{c}} interval (the "red minor third" or "supraminor third") sharply approximates 6/5 and flatly approximates 11/9, for instance, whereas the sharp 11/9 is 366{{frac\|2\|3}}{{c}} and the flat 6/5 is 300{{c}}. However, 11/10, 20/11, 15/11, and 22/15 all have accurate and consistent approximations since the errors on the 5th and 11th harmonics cancel out with both tending sharp.

	36edo is fairly cosmopolitan because many genres of world music can be played in it. Because of the presence of blue notes, and the closeness with which the 7th harmonic and its intervals are matched, 36edo is an ideal scale to use for African-American genres of music such as blues and jazz, in which septimal intervals are frequently encountered. Indonesian gamelan music using pelog easily adapts to it as well, since 9edo is a subset and can be notated as every fourth note, and Slendro can be approximated in several different ways as well, most notably as a very soft [[1L 4s]] scale. 36edo can therefore function as a "bridge" between these genres and Western music. Arabic and Persian music do not adapt as well, however, since their microtonal intervals consist of mostly quarter tones.		36edo is fairly cosmopolitan because many genres of world music can be played in it. Because of the presence of blue notes, and the closeness with which the 7th harmonic and its intervals are matched, 36edo is an ideal scale to use for African-American genres of music such as blues and jazz, in which septimal intervals are frequently encountered. Indonesian gamelan music using pelog easily adapts to it as well, since 9edo is a subset and can be notated as every fourth note, and Slendro can be approximated in several different ways as well, most notably as a very soft [[1L 4s]] scale. 36edo can therefore function as a "bridge" between these genres and Western music. Arabic and Persian music do not adapt as well, however, since their microtonal intervals consist of mostly quarter tones.

Lucius Chiaraviglio: /* 21st century */ Fix vertical spacing

2026-11-02T15:20:33Z

21st century: Fix vertical spacing

← Older revision		Revision as of 15:20, 2 November 2026
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	; [[Wusuinianmai Wanjunqushou]] (吾虽年迈万军取shou)		; [[Wusuinianmai Wanjunqushou]] (吾虽年迈万军取shou)

	* ''[https://www.bilibili.com/video/BV1874P6hEmn G is the seventh letter]'' (2026)		* ''[https://www.bilibili.com/video/BV1874P6hEmn G is the seventh letter]'' (2026)



	[[Category:Listen]]		[[Category:Listen]]

Haidilao at 13:48, 2 November 2026

2026-11-02T13:48:01Z

← Older revision		Revision as of 13:48, 2 November 2026
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	; [[Stephen Weigel]]		; [[Stephen Weigel]]
	* [https://soundcloud.com/overtoneshock/exponentially-more-lost-and-forgetful-36-edo ''Exponentially More Lost and Forgetful''] (2017) played by flautists Orlando Cela and Wei Zhao		* [https://soundcloud.com/overtoneshock/exponentially-more-lost-and-forgetful-36-edo ''Exponentially More Lost and Forgetful''] (2017) played by flautists Orlando Cela and Wei Zhao

			; [[Wusuinianmai Wanjunqushou]] (吾虽年迈万军取shou)

			* ''[https://www.bilibili.com/video/BV1874P6hEmn G is the seventh letter]'' (2026)



	[[Category:Listen]]		[[Category:Listen]]

Lucius Chiaraviglio: /* 21st century */ Add Norokusi's ''Septet in a 36-EDO Subset'' (2026) and its orchestral arrangement

2026-11-01T10:16:31Z

21st century: Add Norokusi's ''Septet in a 36-EDO Subset'' (2026) and its orchestral arrangement

← Older revision		Revision as of 10:16, 1 November 2026
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	** [https://www.youtube.com/watch?v=l5SQOI1kTHc ''Arranged for orchestra''] (2026)		** [https://www.youtube.com/watch?v=l5SQOI1kTHc ''Arranged for orchestra''] (2026)
	* [https://www.youtube.com/watch?v=_DQKj0afWwE ''Hiroki Naito - Symphony: Moratorium for Large Orchestra in a 36EDO Subset''] (2025 - 2026) (also has a [[24edo]] vibraphone part)		* [https://www.youtube.com/watch?v=_DQKj0afWwE ''Hiroki Naito - Symphony: Moratorium for Large Orchestra in a 36EDO Subset''] (2025 - 2026) (also has a [[24edo]] vibraphone part)
			* [https://www.youtube.com/watch?v=Sno4HVCegF8 ''Septet in a 36-EDO Subset''] (2026)
			** [https://www.youtube.com/watch?v=dZgwqWYzGNc ''Pieces for Orchestra nr.103b in a 36-EDO Subset''] (this is the orchestral arrangement of the Septet)

	; [[NullPointerException Music]]		; [[NullPointerException Music]]

Lucius Chiaraviglio: /* 21st century */ Add Norokusi's ''Hiroki Naito - Symphony: Moratorium for Large Orchestra in a 36EDO Subset'' (2025 - 2026)

2026-09-21T07:06:36Z

21st century: Add Norokusi's ''Hiroki Naito - Symphony: Moratorium for Large Orchestra in a 36EDO Subset'' (2025 - 2026)

← Older revision		Revision as of 07:06, 21 September 2026
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	* [https://www.youtube.com/watch?v=JPpjYzddGSg&t=495s ''Symphony for String Orchestra''] (2024)		* [https://www.youtube.com/watch?v=JPpjYzddGSg&t=495s ''Symphony for String Orchestra''] (2024)
	** [https://www.youtube.com/watch?v=l5SQOI1kTHc ''Arranged for orchestra''] (2026)		** [https://www.youtube.com/watch?v=l5SQOI1kTHc ''Arranged for orchestra''] (2026)
			* [https://www.youtube.com/watch?v=_DQKj0afWwE ''Hiroki Naito - Symphony: Moratorium for Large Orchestra in a 36EDO Subset''] (2025 - 2026) (also has a [[24edo]] vibraphone part)

	; [[NullPointerException Music]]		; [[NullPointerException Music]]

Yourmusic Productions: /* Music */ This one also belongs in the 20th century section.

2026-09-20T14:26:05Z

Music: This one also belongs in the 20th century section.

← Older revision		Revision as of 14:26, 20 September 2026
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	** [https://www.youtube.com/watch?v=UJwLdLMvdu8 String quartet version] — performed by Stamitz Quartet (unknown recording date) (currently the video title erroneously says this is for sixteenth-tone harmonium)		** [https://www.youtube.com/watch?v=UJwLdLMvdu8 String quartet version] — performed by Stamitz Quartet (unknown recording date) (currently the video title erroneously says this is for sixteenth-tone harmonium)
	** [https://www.youtube.com/watch?v=-Ktbo7EfhEA Sixth-tone harmonium version] — performed by Miroslav Beinhauer ([https://miroslavbeinhauer.com/?page_id=139&lang=en site]) (2019, with much of the video showing keyboard views of the sixth-tone harmonium being played)		** [https://www.youtube.com/watch?v=-Ktbo7EfhEA Sixth-tone harmonium version] — performed by Miroslav Beinhauer ([https://miroslavbeinhauer.com/?page_id=139&lang=en site]) (2019, with much of the video showing keyboard views of the sixth-tone harmonium being played)

			; {{W\|Henri Pousseur}}
			* [https://www.youtube.com/watch?v=tiWbbbU6ZPw ''Prospection''] (1952-1953) – for three pianos detuned by a sixth-tone from each other

	=== 21st century ===		=== 21st century ===
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	; [[Chris Orphal]]		; [[Chris Orphal]]
	* [https://www.youtube.com/watch?v=qbOOzC4360M ''Vademecum - Vadetecum (36-EDO) - Perf. New Music New Mexico''] (2023) (Saxophone: Edwin Anthony; Horn: Samuel Lutz; Trumpet: Doug Falk; Guitar: Carlos Arellano; Guitar tuned -31¢: Chris Orphal; Piano: Axel Retif)		* [https://www.youtube.com/watch?v=qbOOzC4360M ''Vademecum - Vadetecum (36-EDO) - Perf. New Music New Mexico''] (2023) (Saxophone: Edwin Anthony; Horn: Samuel Lutz; Trumpet: Doug Falk; Guitar: Carlos Arellano; Guitar tuned -31¢: Chris Orphal; Piano: Axel Retif)

	~~; {{W\|Henri Pousseur}}~~
	* [https://www.youtube.com/watch?v=tiWbbbU6ZPw ''Prospection''] (1952-1953) – for three pianos detuned by a sixth-tone from each other

	; [[Chris Vaisvil]]		; [[Chris Vaisvil]]

Lucius Chiaraviglio: /* Instruments */ Fix missing parenthesis

2026-09-20T09:04:08Z

Instruments: Fix missing parenthesis

← Older revision		Revision as of 09:04, 20 September 2026
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	36edo can also be played using three instruments tuned to 12edo with different root notes (that is, a sixth-tone apart).		36edo can also be played using three instruments tuned to 12edo with different root notes (that is, a sixth-tone apart).

	At least one 36edo harmonium has been built (the "sixth-tone harmonium" used by 20th century Czech microtonal composer {{W\|Alois Habá}}), having effectively two quasi-Halberstadt keyboards (but with the bottom one duplicated at the top, each having 18 notes per octave organized in 6 groups of 2 natural-position notes and 1 flat/sharp-position note — see the Music section below for a video demonstration.		At least one 36edo harmonium has been built (the "sixth-tone harmonium" used by 20th century Czech microtonal composer {{W\|Alois Habá}}), having effectively two quasi-Halberstadt keyboards (but with the bottom one duplicated at the top), each having 18 notes per octave organized in 6 groups of 2 natural-position notes and 1 flat/sharp-position note — see the Music section below for a video demonstration.

	== Music ==		== Music ==

Lucius Chiaraviglio: /* 20th century */ Fix wording

2026-09-20T08:59:57Z

20th century: Fix wording

← Older revision		Revision as of 08:59, 20 September 2026
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	* ''Six compositions for sixth-tone harmonium, op. 37'' (1928)		* ''Six compositions for sixth-tone harmonium, op. 37'' (1928)
	** [https://www.youtube.com/watch?v=UJwLdLMvdu8 String quartet version] — performed by Stamitz Quartet (unknown recording date) (currently the video title erroneously says this is for sixteenth-tone harmonium)		** [https://www.youtube.com/watch?v=UJwLdLMvdu8 String quartet version] — performed by Stamitz Quartet (unknown recording date) (currently the video title erroneously says this is for sixteenth-tone harmonium)
	** [https://www.youtube.com/watch?v=-Ktbo7EfhEA Sixth-tone harmonium version] — performed by Miroslav Beinhauer ([https://miroslavbeinhauer.com/?page_id=139&lang=en site]) (2019, with much of the video showing keyboard ~~view~~ of sixth-tone harmonium being played)		** [https://www.youtube.com/watch?v=-Ktbo7EfhEA Sixth-tone harmonium version] — performed by Miroslav Beinhauer ([https://miroslavbeinhauer.com/?page_id=139&lang=en site]) (2019, with much of the video showing keyboard views of the sixth-tone harmonium being played)

	=== 21st century ===		=== 21st century ===

Lucius Chiaraviglio: /* Instruments */ Add 36edo harmonium has been built (the "sixth-tone harmonium" used by 20th century Czech microtonal composer Alois Habá)

2026-09-20T08:58:51Z

Instruments: Add 36edo harmonium has been built (the "sixth-tone harmonium" used by 20th century Czech microtonal composer Alois Habá)

← Older revision		Revision as of 08:58, 20 September 2026
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	36edo can also be played using three instruments tuned to 12edo with different root notes (that is, a sixth-tone apart).		36edo can also be played using three instruments tuned to 12edo with different root notes (that is, a sixth-tone apart).

			At least one 36edo harmonium has been built (the "sixth-tone harmonium" used by 20th century Czech microtonal composer {{W\|Alois Habá}}), having effectively two quasi-Halberstadt keyboards (but with the bottom one duplicated at the top, each having 18 notes per octave organized in 6 groups of 2 natural-position notes and 1 flat/sharp-position note — see the Music section below for a video demonstration.

	== Music ==		== Music ==

Lucius Chiaraviglio: /* Music */ Add 20th century sub-section, starting with Alois Hába's ''Six compositions for sixth-tone harmonium, op. 37'' (1928)

2026-09-20T08:51:53Z

Music: Add 20th century sub-section, starting with Alois Hába's ''Six compositions for sixth-tone harmonium, op. 37'' (1928)

← Older revision		Revision as of 08:51, 20 September 2026
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	== Music ==		== Music ==
			=== 20th century ===
			; [[Alois Hába]]
			* ''Six compositions for sixth-tone harmonium, op. 37'' (1928)
			** [https://www.youtube.com/watch?v=UJwLdLMvdu8 String quartet version] — performed by Stamitz Quartet (unknown recording date) (currently the video title erroneously says this is for sixteenth-tone harmonium)
			** [https://www.youtube.com/watch?v=-Ktbo7EfhEA Sixth-tone harmonium version] — performed by Miroslav Beinhauer ([https://miroslavbeinhauer.com/?page_id=139&lang=en site]) (2019, with much of the video showing keyboard view of sixth-tone harmonium being played)

			=== 21st century ===
	; [[Ambient Esoterica]]		; [[Ambient Esoterica]]
	* [https://www.youtube.com/watch?v=nadDPD1m-1Y ''A Trip to PRS with a Circle of Augmented 5ths''] (2024)		* [https://www.youtube.com/watch?v=nadDPD1m-1Y ''A Trip to PRS with a Circle of Augmented 5ths''] (2024)