58edo - Revision history

BudjarnLambeth: /* Scales */

2026-09-09T06:10:40Z

Scales

← Older revision		Revision as of 06:10, 9 September 2026
Line 652:		Line 652:

	== Scales ==		== Scales ==
			* Baobab{{idio}}: 15 9 10 9 8 7 (approximated from [[30afdo]])
	* [[Compdye]]		* [[Compdye]]
	* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic\|Gutierrez-Lambeth quasi-subharmonic pentatonic]]		* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic\|Gutierrez-Lambeth quasi-subharmonic pentatonic]]{{idio}}
	* [[Hemif7]]		* [[Hemif7]]
	* [[Hemif10]]		* [[Hemif10]]

FloraC: /* Regular temperament properties */ move emmthird out (not practical in this edo)

2026-08-28T12:45:48Z

Regular temperament properties: move emmthird out (not practical in this edo)

← Older revision		Revision as of 12:45, 28 August 2026
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	\| 49/40		\| 49/40
	\| [[Hemififths]]		\| [[Hemififths]]
	\|-
	~~\| 1~~
	~~\| 19\58~~
	~~\| 393.1~~
	~~\| 64/51~~
	~~\| [[Emmthird]]~~
	\|-		\|-
	\| 1		\| 1
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	<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]		<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]

	58et can also be detempered to [[semihemi]] ({{nowrap\| 58 & 140 }}), [[condor]] ({{nowrap\| 58 & 159 }}), and [[eagle]] ({{nowrap\| 58 & 212 }}).		58et can also be detempered to [[emmthird]] ({{nowrap\| 58 & 113 }}), [[semihemi]] ({{nowrap\| 58 & 140 }}), [[condor]] ({{nowrap\| 58 & 159 }}), and [[eagle]] ({{nowrap\| 58 & 212 }}).

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

FloraC: /* Regular temperament properties */ + mintone, + bisemidim; also move supers to the table as this edo is a practical tuning for it

2026-08-28T12:32:39Z

Regular temperament properties: + mintone, + bisemidim; also move supers to the table as this edo is a practical tuning for it

← Older revision		Revision as of 12:32, 28 August 2026
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	\| 28/27		\| 28/27
	\| [[Unicorn]] / alicorn / qilin		\| [[Unicorn]] / alicorn / qilin
			\|-
			\| 1
			\| 9\58
			\| 186.2
			\| 10/9
			\| [[Mintone]]
	\|-		\|-
	\| 1		\| 1
Line 613:		Line 619:
	\| 17/16		\| 17/16
	\| [[Diaschismic]]		\| [[Diaschismic]]
			\|-
			\| 2
			\| 7\58
			\| 144.8
			\| 13/12
			\| [[Bisemidim]]
	\|-		\|-
	\| 2		\| 2
Line 618:		Line 630:
	\| 165.5		\| 165.5
	\| 11/10		\| 11/10
	\| [[Echidna]]		\| [[Echidna]] / [[supers]]
	\|-		\|-
	\| 2		\| 2
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	<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]		<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]

	58et can also be detempered to [[semihemi]] ({{nowrap\| 58 & 140 ~~}}), [[supers]] ({{nowrap\| 58 & 152~~ }}), [[condor]] ({{nowrap\| 58 & 159 }}), and [[eagle]] ({{nowrap\| 58 & 212 }}).		58et can also be detempered to [[semihemi]] ({{nowrap\| 58 & 140 }}), [[condor]] ({{nowrap\| 58 & 159 }}), and [[eagle]] ({{nowrap\| 58 & 212 }}).

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

FloraC: /* Regular temperament properties */ rework to minimal-genreator form

2026-08-28T12:25:40Z

Regular temperament properties: rework to minimal-genreator form

← Older revision		Revision as of 12:25, 28 August 2026
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	\| 11/8		\| 11/8
	\| [[Thuja]]		\| [[Thuja]]
			\|-
			\| 2
			\| 1\58
			\| 20.7
			\| 81/80
			\| [[Bicommatic]]
	\|-		\|-
	\| 2		\| 2
Line 597:		Line 603:
	\|-		\|-
	\| 2		\| 2
	\| 1\58		\| 4\58
	\| 20.7		\| 82.8
	\| 81/80		\| 21/20
	\| [[~~Bicommatic~~]]		\| [[Harry]]
			\|-
			\| 2
			\| 5\58
			\| 103.4
			\| 17/16
			\| [[Diaschismic]]
			\|-
			\| 2
			\| 8\58
			\| 165.5
			\| 11/10
			\| [[Echidna]]
	\|-		\|-
	\| 2		\| 2
Line 609:		Line 627:
	\|-		\|-
	\| 2		\| 2
	\| ~~17\58<br>(~~12\58)		\| 12\58
	\| ~~351.7<br>(~~248.3)		\| 248.3
	\| ~~11/9<br>(~~15/13)		\| 15/13
	\| [[Sruti]]		\| [[Sruti]]
	\|-
	~~\| 2~~
	~~\| 21\58<br>(8\58)~~
	~~\| 434.5<br>(165.5)~~
	~~\| 9/7<br>(11/10)~~
	~~\| [[Echidna]]~~
	\|-
	~~\| 2~~
	~~\| 24\58<br>(5\58)~~
	~~\| 496.6<br>(103.4)~~
	~~\| 4/3<br>(17/16)~~
	~~\| [[Diaschismic]]~~
	\|-
	~~\| 2~~
	~~\| 25\58<br>(4\58)~~
	~~\| 517.2<br>(82.8)~~
	~~\| 27/20<br>(21/20)~~
	~~\| [[Harry]]~~
	\|-		\|-
	\| 29		\| 29
	\| ~~19\58<br>(~~1\58)		\| 1\58
	\| ~~393.1<br>(~~20.7)		\| 20.7
	\| ~~5/4<br>(~~91/90)		\| 91/90
	\| [[Mystery]]		\| [[Mystery]]
	\|}		\|}
	<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~~		<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]

	58et can also be detempered to [[semihemi]] ({{nowrap\| 58 & 140 }}), [[supers]] ({{nowrap\| 58 & 152 }}), [[condor]] ({{nowrap\| 58 & 159 }}), and [[eagle]] ({{nowrap\| 58 & 212 }}).		58et can also be detempered to [[semihemi]] ({{nowrap\| 58 & 140 }}), [[supers]] ({{nowrap\| 58 & 152 }}), [[condor]] ({{nowrap\| 58 & 159 }}), and [[eagle]] ({{nowrap\| 58 & 212 }}).

FloraC: Note unicorn comma in the theory section

2026-08-28T12:10:19Z

Note unicorn comma in the theory section

← Older revision		Revision as of 12:10, 28 August 2026
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	=== As a tuning of other temperaments ===		=== As a tuning of other temperaments ===
	As an equal temperament, 58et [[tempering out\|tempers out]] [[~~2048~~/~~2025~~]] in the [[5-limit]]; [[126/125]], [[1728/1715]], and [[5120/5103]] in the [[7-limit]]; [[176/175]], [[243/242]], [[441/440]], [[540/539]], and [[896/891]] in the 11-limit; [[144/143]], [[351/350]], [[364/363]] in the 13-limit. It [[support]]s [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[mystery]], [[buzzard]], [[thuja]] [[regular temperament\|temperament]]s plus a number of [[gravity family]] [[extension]]s, and supplies the [[optimal patent val]] for the 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank-3 temperaments [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].		As an equal temperament, 58et [[tempering out\|tempers out]] 2048/2025 ([[diaschisma]]) and 1594323/1562500 ([[unicorn comma]]) in the [[5-limit]]; [[126/125]], [[1728/1715]], and [[5120/5103]] in the [[7-limit]]; [[176/175]], [[243/242]], [[441/440]], [[540/539]], and [[896/891]] in the 11-limit; [[144/143]], [[351/350]], [[364/363]] in the 13-limit. It [[support]]s [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[mystery]], [[buzzard]], [[thuja]] [[regular temperament\|temperament]]s plus a number of [[gravity family]] [[extension]]s, and supplies the [[optimal patent val]] for the 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank-3 temperaments [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].

	Of all edos which map the syntonic comma ([[81/80]]) to 1 step by patent val, 58edo is the one with the step size closest to 81/80, with one step of 58edo being less than 1{{cent}} narrower than the just interval.		Of all edos which map the syntonic comma ([[81/80]]) to 1 step by patent val, 58edo is the one with the step size closest to 81/80, with one step of 58edo being less than 1{{cent}} narrower than the just interval.
Line 490:		Line 490:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| 2048/2025, [[1594323/1562500]]		\| 2048/2025, 1594323/1562500
	\| {{Mapping\| 58 92 135 }}		\| {{Mapping\| 58 92 135 }}
	\| −1.29		\| −1.29

FloraC: /* Theory */ + second harmonics table

2026-08-25T15:18:54Z

Theory: + second harmonics table

← Older revision		Revision as of 15:18, 25 August 2026
Line 11:		Line 11:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|58}}		{{Harmonics in equal\|58\|columns=11}}
			{{Harmonics in equal\|58\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 58edo (continued)}}

	=== As a tuning of other temperaments ===		=== As a tuning of other temperaments ===

FloraC: /* Regular temperament properties */ + gravity & extensions

2026-05-26T07:42:36Z

Regular temperament properties: + gravity & extensions

← Older revision		Revision as of 07:42, 26 May 2026
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	\| 21/16		\| 21/16
	\| [[Buzzard]] / [[subfourth]]		\| [[Buzzard]] / [[subfourth]]
			\|-
			\| 1
			\| 25\58
			\| 517.2
			\| 27/20
			\| [[Gravity]] / [[abergravity]] / [[gravid]]
	\|-		\|-
	\| 1		\| 1

FloraC: /* Notation */ SZG notation

2026-05-12T14:23:08Z

Notation: SZG notation

← Older revision		Revision as of 14:23, 12 May 2026
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	== Notation ==		== Notation ==
	=== ~~Ups~~ and downs notation ===		=== Stein–Zimmermann–Gould notation ===
	58edo 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]] for 58edo uses sharps and flats combined with quartertone accidentals and arrows:
			{{Sharpness-sharp6-szg}}

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

			=== Kite's ups and downs notation ===
			58edo 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.
	{{Ups and downs sharpness}}		{{Ups and downs sharpness}}

	Half-sharps and half-flats can be used to avoid triple arrows:		Half-sharps and half-flats can be used to avoid triple arrows:
	{{Ups and downs sharpness\|58\|true}}		{{Ups and downs sharpness\|58\|true}}

	~~Alternatively, a combination of quarter tone accidentals and arrow accidentals from [[Helmholtz–Ellis notation]] can be used.~~
	~~{{Sharpness-sharp6}}~~

	~~If double arrows are not desirable, then 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}}

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	\|+ style="font-size: 105%; white-space: nowrap;" \| Hemipyth notation for 58edo (SW3-style)		\|+ style="font-size: 105%; white-space: nowrap;" \| Hemipyth notation for 58edo (SW3-style)
	\|-		\|-
	! &#~~35;~~		! #
	! Cents		! Cents
	! Note names<br />on D		! Note names<br>on D
	\|-		\|-
	\| 0		\| 0

Lucius Chiaraviglio: /* Music */ Xotla's "Wormhole Shmurmhole": Fix copy/paste error in description

2026-05-09T10:47:48Z

Music: Xotla's "Wormhole Shmurmhole": Fix copy/paste error in description

← Older revision		Revision as of 10:47, 9 May 2026
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	; [[Xotla]]		; [[Xotla]]
	* [https://www.youtube.com/watch?v=yTkPhjTEQMw "Wormhole Shmurmhole"], from [https://www.youtube.com/playlist?list=PL4HmfPDldHXueRjmTV-iJN3fsLn_O9jvT ''Just Another Microtonal Music Album''] (2025–2026) – in part, the rest being in ~~58edo~~		* [https://www.youtube.com/watch?v=yTkPhjTEQMw "Wormhole Shmurmhole"], from [https://www.youtube.com/playlist?list=PL4HmfPDldHXueRjmTV-iJN3fsLn_O9jvT ''Just Another Microtonal Music Album''] (2025–2026) – in part, the rest being in 31edo

	[[Category:Buzzard]]		[[Category:Buzzard]]

FloraC: /* Music */ +1

2026-05-09T10:20:13Z

Music: +1

← Older revision		Revision as of 10:20, 9 May 2026
Line 665:		Line 665:
	; [[Cam Taylor]]		; [[Cam Taylor]]
	* [https://www.youtube.com/watch?v=Keclakcqie8 ''58EDO, Mystery temperament and 2 rings of Pythagorean on the Lumatone''] (2021)		* [https://www.youtube.com/watch?v=Keclakcqie8 ''58EDO, Mystery temperament and 2 rings of Pythagorean on the Lumatone''] (2021)

			; [[Xotla]]
			* [https://www.youtube.com/watch?v=yTkPhjTEQMw "Wormhole Shmurmhole"], from [https://www.youtube.com/playlist?list=PL4HmfPDldHXueRjmTV-iJN3fsLn_O9jvT ''Just Another Microtonal Music Album''] (2025–2026) – in part, the rest being in 58edo

	[[Category:Buzzard]]		[[Category:Buzzard]]