65edo - Revision history

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 ==

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Zanarkand - Nobuo Uematsu (microtonal cover in 65edo)'' (2026)

2026-02-06T06:58:48Z

Music: Add Bryan Deister's ''Zanarkand - Nobuo Uematsu (microtonal cover in 65edo)'' (2026)

← Older revision		Revision as of 06:58, 6 February 2026
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	== Music ==		== Music ==
	; [[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)

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

BudjarnLambeth: /* Octave stretch or compression */ add stretched examples

2025-09-19T11:36:45Z

Octave stretch or compression: add stretched examples

← Older revision		Revision as of 11:36, 19 September 2025
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	65edo tunes [[primes]] 2, 3, 5 and 11 very well, but its 7 and 13 have two about equally-bad mappings. [[Stretched and compressed tuning\|Stretching or shrinking the octave]] of 65edo for improvements in its approximations of [[JI]] therefore depends on which mapping is used: the sharp tending 65d val wants octave shrinking, whereas the flat tending 65f val wants octave stretching; both can be achieved at the cost of relatively little damage to other primes.		65edo tunes [[primes]] 2, 3, 5 and 11 very well, but its 7 and 13 have two about equally-bad mappings. [[Stretched and compressed tuning\|Stretching or shrinking the octave]] of 65edo for improvements in its approximations of [[JI]] therefore depends on which mapping is used: the sharp tending 65d val wants octave shrinking, whereas the flat tending 65f val wants octave stretching; both can be achieved at the cost of relatively little damage to other primes.

	Compressed tunings of 65edo ~~which are suited for 65d~~ include [[zpi\|334zpi]], [[ed5\|151ed5]] and [[equal tuning\|225ed11]].		Compressed tunings of 65edo that well approximate JI include [[zpi\|334zpi]], [[ed5\|151ed5]] and [[equal tuning\|225ed11]].

			Stretched tunings of 65edo that well approximate JI include [[WE\|13-lim WE-tuned 65f]] (18.473cET) and [[TE\|13-lim TE-tuned 65f]] (18.474cET).

	== Scales ==		== Scales ==

BudjarnLambeth: /* Octave stretch or compression */ Change the last line to reflect the recent changes to this section

2025-09-19T11:14:30Z

Octave stretch or compression: Change the last line to reflect the recent changes to this section

← Older revision		Revision as of 11:14, 19 September 2025
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	65edo tunes [[primes]] 2, 3, 5 and 11 very well, but its 7 and 13 have two about equally-bad mappings. [[Stretched and compressed tuning\|Stretching or shrinking the octave]] of 65edo for improvements in its approximations of [[JI]] therefore depends on which mapping is used: the sharp tending 65d val wants octave shrinking, whereas the flat tending 65f val wants octave stretching; both can be achieved at the cost of relatively little damage to other primes.		65edo tunes [[primes]] 2, 3, 5 and 11 very well, but its 7 and 13 have two about equally-bad mappings. [[Stretched and compressed tuning\|Stretching or shrinking the octave]] of 65edo for improvements in its approximations of [[JI]] therefore depends on which mapping is used: the sharp tending 65d val wants octave shrinking, whereas the flat tending 65f val wants octave stretching; both can be achieved at the cost of relatively little damage to other primes.

	~~Some~~ tunings of 65edo which ~~do this~~ include [[zpi\|334zpi]], [[ed5\|151ed5]] and [[equal tuning\|225ed11]].		Compressed tunings of 65edo which are suited for 65d include [[zpi\|334zpi]], [[ed5\|151ed5]] and [[equal tuning\|225ed11]].

	== Scales ==		== Scales ==

FloraC: Corrections based on the fact that 65edo's 7 and 13 err on the opposite sides in the patent val

2025-09-19T11:11:49Z

Corrections based on the fact that 65edo's 7 and 13 err on the opposite sides in the patent val

← Older revision		Revision as of 11:11, 19 September 2025
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	== Octave stretch or compression ==		== Octave stretch or compression ==
	65edo tunes [[primes]] 2, 3, 5 and 11 very well, but its 7 and 13 have two about equally-bad mappings. [[~~Octave~~ shrinking~~\|Shrinking~~]] ~~the octave~~ of 65edo ~~by the right amount improves~~ its approximations of [[JI]] ~~by flipping 7 and 13 to their opposite [[~~mapping]], at the cost of relatively little damage to other primes. ~~(Stretching would do unacceptably much damage.)~~		65edo tunes [[primes]] 2, 3, 5 and 11 very well, but its 7 and 13 have two about equally-bad mappings. [[Stretched and compressed tuning\|Stretching or shrinking the octave]] of 65edo for improvements in its approximations of [[JI]] therefore depends on which mapping is used: the sharp tending 65d val wants octave shrinking, whereas the flat tending 65f val wants octave stretching; both can be achieved at the cost of relatively little damage to other primes.

	Some tunings of 65edo which do this include [[zpi\|334zpi]], [[ed5\|151ed5]] and [[equal tuning\|225ed11]].		Some tunings of 65edo which do this include [[zpi\|334zpi]], [[ed5\|151ed5]] and [[equal tuning\|225ed11]].