51edo - Revision history

Lucius Chiaraviglio: /* Odd harmonics */ Section heading says odd harmonics, but table was displaying only prime harmonics — fixing this and adding another row

2026-05-28T03:35:11Z

Odd harmonics: Section heading says odd harmonics, but table was displaying only prime harmonics — fixing this and adding another row

← Older revision		Revision as of 03:35, 28 May 2026
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|51}}		{{Harmonics in equal\|51\|intervals=odd\|prec=2\|columns=14}}
			{{Harmonics in equal\|51\|intervals=odd\|columns=14\|prec=2\|start=15\|collapsed=true\|title=Approximation of odd harmonics in 51edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

Lucius Chiaraviglio: /* Theory */ Fix link to aerodino

2026-05-28T03:20:37Z

Theory: Fix link to aerodino

← Older revision		Revision as of 03:20, 28 May 2026
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	Using the [[patent val]], 51et [[tempering out\|tempers out]] [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[porky]] temperament, which is sonic plus 225/224. It contains an archeotonic ([[6L 1s]]) scale based on repetitions of 8\51, creating a scale with a whole-tone-like drive towards the tonic through the 17edo semitone at the top.		Using the [[patent val]], 51et [[tempering out\|tempers out]] [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[porky]] temperament, which is sonic plus 225/224. It contains an archeotonic ([[6L 1s]]) scale based on repetitions of 8\51, creating a scale with a whole-tone-like drive towards the tonic through the 17edo semitone at the top.

	Using the 51c val {{val\| 51 81 '''119''' 143 }}, the [[5/4]] is mapped to 1\3 (400 cents), [[support]]ing [[augmented (temperament)\|augmented]]. In the 7-limit it tempers out [[245/243]] and supports [[hemiaug]] and [[rodan]]. Alternatively, the 51cd val {{val\| 51 81 '''119''' '''144''' }} takes the same [[7/4]] from 17edo, and supports [[augene]]. The 51ce val {{val\| 51 81 '''119''' 143 '''177''' 189 }} supports a variant of rodan called [[aerodino]].		Using the 51c val {{val\| 51 81 '''119''' 143 }}, the [[5/4]] is mapped to 1\3 (400 cents), [[support]]ing [[augmented (temperament)\|augmented]]. In the 7-limit it tempers out [[245/243]] and supports [[hemiaug]] and [[rodan]]. Alternatively, the 51cd val {{val\| 51 81 '''119''' '''144''' }} takes the same [[7/4]] from 17edo, and supports [[augene]]. The 51ce val {{val\| 51 81 '''119''' 143 '''177''' 189 }} supports a variant of rodan called [[Gamelismic_clan#Aerodino\|aerodino]].

	51edo's step is the closest direct approximation to the [[Pythagorean comma]] by edosteps, though that comma itself is mapped to a different interval.		51edo's step is the closest direct approximation to the [[Pythagorean comma]] by edosteps, though that comma itself is mapped to a different interval.

Lucius Chiaraviglio: /* Music */ Add Bryan ''Preludio Sentimentale (microtonal improvisation in 28edo)'' and Deister's ''28edo blues'' (both 2023)

2026-05-28T02:48:27Z

Music: Add Bryan ''Preludio Sentimentale (microtonal improvisation in 28edo)'' and Deister's ''28edo blues'' (both 2023)

← Older revision		Revision as of 02:48, 28 May 2026
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	== Music ==		== Music ==
	; [[Bryan Deister]]		; [[Bryan Deister]]
			* [https://www.youtube.com/watch?v=sySLQUXnQ70 ''Preludio Sentimentale (microtonal improvisation in 28edo)''] (2023)
			* [https://www.youtube.com/watch?v=sCE0MjUyRUk ''28edo blues''] (2023)
	* [https://www.youtube.com/shorts/sTPJtuHUwkg ''51edo improv''] (2025-02-03)		* [https://www.youtube.com/shorts/sTPJtuHUwkg ''51edo improv''] (2025-02-03)
	* [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02)		* [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02)

FloraC: /* Regular temperament properties */ + abergravity

2026-05-26T07:45:49Z

Regular temperament properties: + abergravity

← Older revision		Revision as of 07:45, 26 May 2026
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	\| 235.3		\| 235.3
	\| 8/7		\| 8/7
	\| [[Rodan]] (~~51cf…~~, out of tune) / aerodino (51ce)		\| [[Rodan]] (51cf, out of tune) / aerodino (51ce)
	\|-		\|-
	\| 1		\| 1
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	\| 517.6		\| 517.6
	\| 27/20		\| 27/20
	\| [[Gravity]] (51ce)		\| [[Gravity]] (51ce) / [[abergravity]] (51ce)
	\|-		\|-
	\| 1		\| 1

Hotcrystal0: edosteps has no space

2026-05-12T14:59:03Z

edosteps has no space

← Older revision		Revision as of 14:59, 12 May 2026
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	Using the 51c val {{val\| 51 81 '''119''' 143 }}, the [[5/4]] is mapped to 1\3 (400 cents), [[support]]ing [[augmented (temperament)\|augmented]]. In the 7-limit it tempers out [[245/243]] and supports [[hemiaug]] and [[rodan]]. Alternatively, the 51cd val {{val\| 51 81 '''119''' '''144''' }} takes the same [[7/4]] from 17edo, and supports [[augene]]. The 51ce val {{val\| 51 81 '''119''' 143 '''177''' 189 }} supports a variant of rodan called [[aerodino]].		Using the 51c val {{val\| 51 81 '''119''' 143 }}, the [[5/4]] is mapped to 1\3 (400 cents), [[support]]ing [[augmented (temperament)\|augmented]]. In the 7-limit it tempers out [[245/243]] and supports [[hemiaug]] and [[rodan]]. Alternatively, the 51cd val {{val\| 51 81 '''119''' '''144''' }} takes the same [[7/4]] from 17edo, and supports [[augene]]. The 51ce val {{val\| 51 81 '''119''' 143 '''177''' 189 }} supports a variant of rodan called [[aerodino]].

	51edo's step is the closest direct approximation to the [[Pythagorean comma]] by ~~edo steps~~, though that comma itself is mapped to a different interval.		51edo's step is the closest direct approximation to the [[Pythagorean comma]] by edosteps, though that comma itself is mapped to a different interval.

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

FloraC: /* Notation */

2026-05-12T14:22:32Z

Notation

← Older revision		Revision as of 14:22, 12 May 2026
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	If double arrows are not desirable, then arrows can be attached to quartertone accidentals:		If double arrows are not desirable, then arrows can be attached to quartertone accidentals:
	{{Sharpness-sharp6-qt}}		{{Sharpness-sharp6-qt-szg}}

	=== Kite's ups and downs notation ===		=== Kite's ups and downs notation ===

FloraC: /* Notation */ SZG notation

2026-05-12T14:21:12Z

Notation: SZG notation

← Older revision		Revision as of 14:21, 12 May 2026
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	== Notation ==		== Notation ==
	=== ~~Ups~~ and downs notation ===		=== Stein–Zimmermann–Gould notation ===
	51edo 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 51edo 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}}

			=== Kite's ups and downs notation ===
			51edo 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}}

	~~In 51edo, 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}}

	=== Sagittal notation ===		=== Sagittal notation ===
	In the following diagrams, 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 following diagrams, 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.

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

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''51edo improv'' (2026-04-22)

2026-04-23T20:37:21Z

Music: Add Bryan Deister's ''51edo improv'' (2026-04-22)

← Older revision		Revision as of 20:37, 23 April 2026
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	* [https://www.youtube.com/shorts/Fymg9vYO6iQ ''Northernlight - Deltarune (microtonal cover in 51edo)''] (2025)		* [https://www.youtube.com/shorts/Fymg9vYO6iQ ''Northernlight - Deltarune (microtonal cover in 51edo)''] (2025)
	* [https://www.youtube.com/shorts/SJW-JTHyeIA ''51edo prelude''] (2026)		* [https://www.youtube.com/shorts/SJW-JTHyeIA ''51edo prelude''] (2026)
			* [https://www.youtube.com/watch?v=k3NOBYbiqpo ''51edo improv''] (2026-04-22)

	; [[Frédéric Gagné]]		; [[Frédéric Gagné]]

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"

2026-03-13T13:30:09Z

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 13:30, 13 March 2026
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	\| style="text-align: left;" \| [[Fog]] (51)		\| style="text-align: left;" \| [[Fog]] (51)
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|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

	== Scales ==		== Scales ==

FloraC: /* Regular temperament properties */

2026-02-19T15:52:52Z

Regular temperament properties

← Older revision		Revision as of 15:52, 19 February 2026
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	\| rowspan="2" \| 494.1<br>(94.1)		\| rowspan="2" \| 494.1<br>(94.1)
	\| 4/3<br>(16/15)		\| 4/3<br>(16/15)
	\| [[Augmented (temperament)\|Augmented]] (~~51c~~)		\| [[Augmented (temperament)\|Augmented]] (7-limit, 51cd)
	\|-		\|-
	\| style="text-align: center;" \| 4/3<br>(21/20)		\| style="text-align: center;" \| 4/3<br>(21/20)