65edo - Revision history

Lucius Chiaraviglio: /* Subsets and supersets */ Fix typo

2026-09-16T06:09:45Z

Subsets and supersets: Fix typo

← Older revision		Revision as of 06:09, 16 September 2026
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	65edo contains [[5edo]] and [[13edo]] as subsets. The offset between a just perfect fifth at 702 cents and the 13edo superfifth at 738.5 cents, is approximately 2 degrees of 65edo. Therefore, an instrument fretted to 13edo, with open strings tuned to 3-limit intervals such as 4/3, 3/2, 9/8, 16/9 etc, will approximate a subset of 65edo. For an example of this, see [[Andrew Heathwaite]]'s composition [https://soundcloud.com/andrew_heathwaite/rubble-a-xenuke-unfolded ''Rubble: a Xenuke Unfolded''].		65edo contains [[5edo]] and [[13edo]] as subsets. The offset between a just perfect fifth at 702 cents and the 13edo superfifth at 738.5 cents, is approximately 2 degrees of 65edo. Therefore, an instrument fretted to 13edo, with open strings tuned to 3-limit intervals such as 4/3, 3/2, 9/8, 16/9 etc, will approximate a subset of 65edo. For an example of this, see [[Andrew Heathwaite]]'s composition [https://soundcloud.com/andrew_heathwaite/rubble-a-xenuke-unfolded ''Rubble: a Xenuke Unfolded''].

	[[130edo]], which doubles ~~its~~, corrects its approximation to harmonics 7 and 13.		[[130edo]], which doubles it, corrects its approximation to harmonics 7 and 13.

	== Intervals ==		== Intervals ==

Lucius Chiaraviglio: /* Intervals */ sed -E "s#([0-9]+)/([0-9]+)#\[\[\1/\2\]\]#g" 65EDOintervals.txt > 65EDOintervals.new.txt

2026-09-16T06:08:45Z

Intervals: sed -E "s#([0-9]+)/([0-9]+)#\[\[\1/\2\]\]#g" 65EDOintervals.txt > 65EDOintervals.new.txt

Show changes

Lucius Chiaraviglio: /* 21st century */ Add Bryan Deister's ''65edo improv'' (2026)

2026-09-16T05:03:11Z

21st century: Add Bryan Deister's ''65edo improv'' (2026)

← Older revision		Revision as of 05:03, 16 September 2026
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	* [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026)		* [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026)
	* [https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026)		* [https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026)
			* [https://www.youtube.com/shorts/pSIT-4VaGD0 ''65edo improv''] (2026)

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

Lucius Chiaraviglio: /* Music */ Add Modern Renderings section, starting with Sunkissed Lola's ''Pasilyo'' (2022) — microtonal cover in 65edo by Bryan Deister (2026); convert 2 other microtonal covers by Bryan Deister to Modern Modern Renderings format

2026-08-15T06:35:01Z

Music: Add Modern Renderings section, starting with Sunkissed Lola's ''Pasilyo'' (2022) — microtonal cover in 65edo by Bryan Deister (2026); convert 2 other microtonal covers by Bryan Deister to Modern Modern Renderings format

← Older revision		Revision as of 06:35, 15 August 2026
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	== Music ==		== Music ==
			=== Modern renderings ===
			; {{W\|Soundgarden}}
			* [https://www.youtube.com/shorts/c0eWd7UvNQU ''Black Hole Sun''] (1994) — microtonal cover in 65edo by [[Bryan Deister]] (2026)

			; {{W\|SunKissed Lola}}
			* [https://www.youtube.com/shorts/_qcJ7Q9MkLE ''Pasilyo''] (2022) — microtonal cover in 65edo by [[Bryan Deister]] (2026)

			; {{W\|Nobuo Uematsu}}
			* [https://www.youtube.com/shorts/UJZw9NQuGnY ''Zanarkand''] via ''{{W\|Final Fantasy X}}'' (2001) — microtonal cover in 65edo by [[Bryan Deister]] (2026)

			=== 21st century ===
	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/W5PXWFduPco ''microtonal improvisation in 65edo''] (2025)		* [https://www.youtube.com/shorts/W5PXWFduPco ''microtonal improvisation in 65edo''] (2025)
	* [https://www.youtube.com/shorts/UJZw9NQuGnY ''Zanarkand - Nobuo Uematsu (microtonal cover in 65edo)''] (2026)
	* [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026)		* [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026)
	* [https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026)		* [https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026)
	* [https://www.youtube.com/shorts/c0eWd7UvNQU ''Black Hole Sun - Soundgarden (microtonal cover in 65edo)''] (2026)

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

Fitzgerald Lee: /* Notation */added interval mappings for 65 and 65d

2026-05-16T11:37:45Z

Notation: added interval mappings for 65 and 65d

← Older revision		Revision as of 11:37, 16 May 2026
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	default [[File:65-EDO_Evo-SZ_Sagittal.svg]]		default [[File:65-EDO_Evo-SZ_Sagittal.svg]]
	</imagemap>		</imagemap>
			== Approximation to JI ==
			=== 15-odd-limit interval mappings ===
			{{Q-odd-limit intervals\|65}}
			{{Q-odd-limit intervals\|65.1\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 65d val mapping}}

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: /* Notation */ SZG notation

2026-05-12T14:01:01Z

Notation: SZG notation

← Older revision		Revision as of 14:01, 12 May 2026
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	== Notation ==		== Notation ==
	=== ~~Ups~~ and downs notation ===		=== Stein–Zimmermann–Gould notation ===
	65edo can be notated with ups and downs, spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.		[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
			{{Sharpness-sharp6-szg}}

			If double arrows are not desirable, arrows can be attached to quartertone accidentals:
			{{Sharpness-sharp6-qt-szg}}

			=== Kite's ups and downs notation ===
			65edo can also be notated with [[Kite's ups and downs notation\|Kite's ups and downs]], spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.
	{{Sharpness-sharp6a}}		{{Sharpness-sharp6a}}

	Half-sharps and half-flats can be used to avoid triple arrows:		Half-sharps and half-flats can be used to avoid triple arrows:
	{{Sharpness-sharp6b}}		{{Sharpness-sharp6b}}

	~~[[Alternative symbols for ups and downs notation#Sharp-6\| Alternative ups and downs]] have arrows borrowed from extended [[Helmholtz–Ellis notation]]:~~
	~~{{Sharpness-sharp6}}~~

	~~If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:~~
	~~{{Sharpness-sharp6-qt}}~~

	=== Ivan Wyschnegradsky's notation ===		=== Ivan Wyschnegradsky's notation ===
	Since a sharp raises by six steps, Wyschnegradsky accidentals borrowed from [[72edo]] can also be used:		Since a sharp raises by six steps, Wyschnegradsky accidentals borrowed from [[72edo]] can also be used:
			{{Sharpness-sharp6-iw}}
	{{~~sharpness~~-sharp6-iw}}

	=== Sagittal notation ===		=== Sagittal notation ===
	This notation uses the same sagittal sequence as ~~EDOs~~ [[72edo#Sagittal notation\|72]] and [[79edo#Sagittal notation\|79]].		This notation uses the same sagittal sequence as edos [[72edo #Sagittal notation\|72]] and [[79edo #Sagittal notation\|79]].

	==== Evo flavor ====		==== Evo flavor ====

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Black Hole Sun - Soundgarden (microtonal cover in 65edo)'' (2026)

2026-05-07T02:19:46Z

Music: Add Bryan Deister's ''Black Hole Sun - Soundgarden (microtonal cover in 65edo)'' (2026)

← Older revision		Revision as of 02:19, 7 May 2026
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	* [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026)		* [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026)
	* [https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026)		* [https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026)
			* [https://www.youtube.com/shorts/c0eWd7UvNQU ''Black Hole Sun - Soundgarden (microtonal cover in 65edo)''] (2026)

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

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''65edo prelude'' (2026)

2026-03-17T09:32:03Z

Music: Add Bryan Deister's ''65edo prelude'' (2026)

← Older revision		Revision as of 09:32, 17 March 2026
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	* [https://www.youtube.com/shorts/UJZw9NQuGnY ''Zanarkand - Nobuo Uematsu (microtonal cover in 65edo)''] (2026)		* [https://www.youtube.com/shorts/UJZw9NQuGnY ''Zanarkand - Nobuo Uematsu (microtonal cover in 65edo)''] (2026)
	* [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026)		* [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026)
			* [https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026)

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

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Waltz in 65edo'' (2026)

2026-03-14T11:16:37Z

Music: Add Bryan Deister's ''Waltz in 65edo'' (2026)

← Older revision		Revision as of 11:16, 14 March 2026
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	* [https://www.youtube.com/shorts/W5PXWFduPco ''microtonal improvisation in 65edo''] (2025)		* [https://www.youtube.com/shorts/W5PXWFduPco ''microtonal improvisation in 65edo''] (2025)
	* [https://www.youtube.com/shorts/UJZw9NQuGnY ''Zanarkand - Nobuo Uematsu (microtonal cover in 65edo)''] (2026)		* [https://www.youtube.com/shorts/UJZw9NQuGnY ''Zanarkand - Nobuo Uematsu (microtonal cover in 65edo)''] (2026)
			* [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026)

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

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:32:50Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:32, 13 March 2026
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	\| [[Countdown]]		\| [[Countdown]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Octave stretch or compression ==		== Octave stretch or compression ==