64edo - Revision history

FloraC: /* Notation */ SZG notation

2026-05-12T13:56:46Z

Notation: SZG notation

← Older revision		Revision as of 13:56, 12 May 2026
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	== Notation ==		== Notation ==
	=== ~~Ups~~ and downs notation ===		=== Stein–Zimmermann–Gould notation ===
			64edo can be notated with [[Stein–Zimmermann–Gould notation]]:
			{{Sharpness-sharp3-szg}}

			Here, a sharp raises by three steps, and a flat lowers by three steps, so arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, some notes may be best spelled with double arrows.

			=== Kite's ups and downs notation ===
	Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud.		Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud.
	{{sharpness-sharp3a}}		{{sharpness-sharp3a}}

	~~Using [[Helmholtz–Ellis]] accidentals, 64edo can also be notated using [[Alternative symbols for ups and downs notation#Sharp-3\|alternative ups and downs]]:~~
	~~{{Sharpness-sharp3}}~~
	Here, a sharp raises by three steps, and a flat lowers by three steps, so arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, some notes may be best spelled with double arrows.

	=== Sagittal notation ===		=== Sagittal notation ===
	==== Best fifth notation ====		==== Best fifth notation ====
	This notation uses the same sagittal sequence as ~~EDOs~~ [[50edo#Sagittal notation\|50]], [[57edo#Sagittal notation\|57]], and [[71edo#Second-best fifth notation\|71b]].		This notation uses the same sagittal sequence as edos [[50edo #Sagittal notation\|50]], [[57edo #Sagittal notation\|57]], and [[71edo #Second-best fifth notation\|71b]].

	===== Evo flavor =====		===== Evo flavor =====
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	</imagemap>		</imagemap>

	In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this ~~EDO~~.		In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation #Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo.

	==== Second-best fifth notation ====		==== Second-best fifth notation ====
	This notation is a superset of the notation for [[32edo#Sagittal notation\|~~32-EDO~~]].		This notation is a superset of the notation for [[32edo #Sagittal notation\|32edo]].

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

Overthink: Undo revision 228771 by Pizzabagel shef (talk) a power of an edo doesn't make sense, it's (power of two) edo

2026-04-28T19:14:15Z

Undo revision 228771 by Pizzabagel shef (talk) a power of an edo doesn't make sense, it's (power of two) edo

← Older revision		Revision as of 19:14, 28 April 2026
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	64edo is the 6th power of ~~[[2edo]]~~, and it has subset edos {{EDOs\| 2, 4, 8, 16, 32 }}. [[128edo]], which doubles it, corrects its approximation to many of the lower harmonics.		64edo is the 6th power of two edo, and it has subset edos {{EDOs\| 2, 4, 8, 16, 32 }}. [[128edo]], which doubles it, corrects its approximation to many of the lower harmonics.

	== Intervals ==		== Intervals ==

Pizzabagel shef: /* Subsets and supersets */

2026-04-28T06:14:14Z

Subsets and supersets

← Older revision		Revision as of 06:14, 28 April 2026
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	64edo is the 6th power of ~~two edo~~, and it has subset edos {{EDOs\| 2, 4, 8, 16, 32 }}. [[128edo]], which doubles it, corrects its approximation to many of the lower harmonics.		64edo is the 6th power of [[2edo]], and it has subset edos {{EDOs\| 2, 4, 8, 16, 32 }}. [[128edo]], which doubles it, corrects its approximation to many of the lower harmonics.

	== Intervals ==		== Intervals ==

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Servant of Evil - Mothy (microtonal cover in 64edo)'' (2026)

2026-02-02T09:18:38Z

Music: Add Bryan Deister's ''Servant of Evil - Mothy (microtonal cover in 64edo)'' (2026)

← Older revision		Revision as of 09:18, 2 February 2026
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025)		* [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025)
			* [https://www.youtube.com/shorts/cwEY-eXjMFw ''Servant of Evil - Mothy (microtonal cover in 64edo)''] (2026)

Overthink: /* Theory */ note 72edo represents these in the right order

2026-01-27T00:41:39Z

Theory: note 72edo represents these in the right order

← Older revision		Revision as of 00:41, 27 January 2026
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	64be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]].		64be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]].

	The patent val of 64edo is the first patent val to represent the intervals 5/4, 81/64, 14/11, 9/7, 13/10, 21/16, and 4/3 distinctly, although in 64edo they are not in the correct order.		The patent val of 64edo is the first patent val to represent the intervals 5/4, 81/64, 14/11, 9/7, 13/10, 21/16, and 4/3 distinctly, although in 64edo they are not in the correct order. [[72edo]] represents all of these intervals distinctly and in the correct order.

	=== Odd harmonics ===		=== Odd harmonics ===

Hotcrystal0: Probably somewhat notable since the intervals are close to one another. Undo revision 221102 by Overthink (talk)

2026-01-08T02:05:41Z

Probably somewhat notable since the intervals are close to one another. Undo revision 221102 by Overthink (talk)

← Older revision		Revision as of 02:05, 8 January 2026
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	64be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]].		64be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]].

			The patent val of 64edo is the first patent val to represent the intervals 5/4, 81/64, 14/11, 9/7, 13/10, 21/16, and 4/3 distinctly, although in 64edo they are not in the correct order.

	=== Odd harmonics ===		=== Odd harmonics ===

Overthink: /* Theory */ If they're in the wrong order, is it even notable?

2026-01-07T23:03:24Z

Theory: If they're in the wrong order, is it even notable?

← Older revision		Revision as of 23:03, 7 January 2026
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	64be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]].		64be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]].

	~~The patent val of 64edo is the first patent val to represent the intervals 5/4, 81/64, 14/11, 9/7, 13/10, 21/16, and 4/3 distinctly, although in 64edo they are not in the correct order.~~

	=== Odd harmonics ===		=== Odd harmonics ===

Overthink: /* Theory */ idiosyncratic term

2026-01-07T22:56:07Z

Theory: idiosyncratic term

← Older revision		Revision as of 22:56, 7 January 2026
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	== Theory ==		== Theory ==
	64edo is a [[The Riemann zeta function and tuning #Valley_edos\|zeta valley edo]] and is very bad at approximating [[JI]] for its size. It has two options of [[3/2\|fifth]] almost equally far from [[just]]. The sharp fifth from the 64b [[val]] is inherited from [[32edo]] and produces a hard [[superpythagorean]] scale, while the slightly more accurate flat fifth from the [[patent val]] is within the [[meantone]]/[[flattone]] range. However bizarrely, the flat fifth does not [[support]] meantone or flattone in its [[patent val]], and instead supports the obscure {{nowrap\|7c & 12c}} (or {{nowrap\|19 & 64}}) temperament (named [[User:Jerdle/The_Ocean\|meso]] by [[User:Jerdle\|Jerdle]]) which reaches [[5/4]] as a double-diminished fourth. In order to interpret it as flattone, the 64cd val must be used.		64edo is a [[The Riemann zeta function and tuning #Valley_edos\|zeta valley edo]] and is very bad at approximating [[JI]] for its size. It has two options of [[3/2\|fifth]] almost equally far from [[just]]. The sharp fifth from the 64b [[val]] is inherited from [[32edo]] and produces a hard [[superpythagorean]] scale, while the slightly more accurate flat fifth from the [[patent val]] is within the [[meantone]]/[[flattone]] range. However bizarrely, the flat fifth does not [[support]] meantone or flattone in its [[patent val]], and instead supports the obscure {{nowrap\|7c & 12c}} (or {{nowrap\|19 & 64}}) temperament (named [[User:Jerdle/The_Ocean\|meso]]{{idio}} by [[User:Jerdle\|Jerdle]]) which reaches [[5/4]] as a double-diminished fourth. In order to interpret it as flattone, the 64cd val must be used.

	Still, the patent val [[tempering out\|tempers out]] [[648/625]] in the 5-limit and [[225/224]] in the 7-limit, plus [[66/65]], [[121/120]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit. It provides the optimal patent val in the 7-, 11- and 13-limits for the 16&64 temperament.		Still, the patent val [[tempering out\|tempers out]] [[648/625]] in the 5-limit and [[225/224]] in the 7-limit, plus [[66/65]], [[121/120]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit. It provides the optimal patent val in the 7-, 11- and 13-limits for the 16&64 temperament.

Jerdle: /* Theory */Added name for 19&64.

2026-01-07T13:14:13Z

Theory: Added name for 19&64.

← Older revision		Revision as of 13:14, 7 January 2026
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	== Theory ==		== Theory ==
	64edo is a [[The Riemann zeta function and tuning #Valley_edos\|zeta valley edo]] and is very bad at approximating [[JI]] for its size. It has two options of [[3/2\|fifth]] almost equally far from [[just]]. The sharp fifth from the 64b [[val]] is inherited from [[32edo]] and produces a hard [[superpythagorean]] scale, while the slightly more accurate flat fifth from the [[patent val]] is within the [[meantone]]/[[flattone]] range. However bizarrely, the flat fifth does not [[support]] meantone or flattone in its [[patent val]], and instead supports the obscure ~~unnamed~~ {{nowrap\|7c & 12c}} (or {{nowrap\|19 & 64}}) temperament which reaches [[5/4]] as a double-diminished fourth. In order to interpret it as flattone, the 64cd val must be used.		64edo is a [[The Riemann zeta function and tuning #Valley_edos\|zeta valley edo]] and is very bad at approximating [[JI]] for its size. It has two options of [[3/2\|fifth]] almost equally far from [[just]]. The sharp fifth from the 64b [[val]] is inherited from [[32edo]] and produces a hard [[superpythagorean]] scale, while the slightly more accurate flat fifth from the [[patent val]] is within the [[meantone]]/[[flattone]] range. However bizarrely, the flat fifth does not [[support]] meantone or flattone in its [[patent val]], and instead supports the obscure {{nowrap\|7c & 12c}} (or {{nowrap\|19 & 64}}) temperament (named [[User:Jerdle/The_Ocean\|meso]] by [[User:Jerdle\|Jerdle]]) which reaches [[5/4]] as a double-diminished fourth. In order to interpret it as flattone, the 64cd val must be used.

	Still, the patent val [[tempering out\|tempers out]] [[648/625]] in the 5-limit and [[225/224]] in the 7-limit, plus [[66/65]], [[121/120]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit. It provides the optimal patent val in the 7-, 11- and 13-limits for the 16&64 temperament.		Still, the patent val [[tempering out\|tempers out]] [[648/625]] in the 5-limit and [[225/224]] in the 7-limit, plus [[66/65]], [[121/120]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit. It provides the optimal patent val in the 7-, 11- and 13-limits for the 16&64 temperament.

BudjarnLambeth: /* Scales */

2025-09-28T01:20:29Z

Scales

← Older revision		Revision as of 01:20, 28 September 2025
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	== Scales ==		== Scales ==
	* [[Maeve Gutierrez\|Gutierrez Moonglade scale]]		* [[Maeve Gutierrez\|Gutierrez Moonglade scale]]: 1 4 5 1 4 2 4 6 1 3 5 1 1 4 4 1 5 1 1 3 1 1 4 1

	== Instruments ==		== Instruments ==