57edo - Revision history

FloraC: /* Notation */ SZG notation

2026-05-12T13:49:36Z

Notation: SZG notation

← Older revision		Revision as of 13:49, 12 May 2026
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	== Notation ==		== Notation ==
	=== ~~Ups~~ and downs notation ===		=== Stein–Zimmermann–Gould notation ===
			57edo can be notated using [[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.
	{{Ups and downs sharpness}}		{{Ups and downs sharpness}}

	~~Using [[Helmholtz–Ellis]] accidentals, 57edo 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 ===
	This notation uses the same sagittal sequence as ~~EDOs~~ [[50edo#Sagittal notation\|50]], [[64edo#Sagittal notation\|64]], and [[71edo#Sagittal notation\|71b]], and is a superset of the notation for [[19edo#Sagittal notation\|~~19-EDO~~]].		This notation uses the same sagittal sequence as edos [[50edo #Sagittal notation\|50]], [[64edo #Sagittal notation\|64]], and [[71edo #Sagittal notation\|71b]], and is a superset of the notation for [[19edo #Sagittal notation\|19edo]].

	==== 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.

	== Scales ==		== Scales ==

Lucius Chiaraviglio: /* Intervals */ Found that 31/21 was a ratio legitimately added by the automated interval table generator -- restored this to its proper place (assuming we want to keep primes that high); added its octave complement; fixed a typo

2026-01-04T11:24:54Z

Intervals: Found that 31/21 was a ratio legitimately added by the automated interval table generator -- restored this to its proper place (assuming we want to keep primes that high); added its octave complement; fixed a typo

← Older revision		Revision as of 11:24, 4 January 2026
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	\| 25		\| 25
	\| 526.32		\| 526.32
	\|[[19/14]], [[23/17]]		\|[[19/14]], [[42/31]], [[23/17]]
	\| {{UDnote\|step=25}}		\| {{UDnote\|step=25}}
	\| {{UDnote\|fifth=34\|step=25}}		\| {{UDnote\|fifth=34\|step=25}}
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	\| 32		\| 32
	\| 673.68		\| 673.68
	\|[[28/19]], [[34/23]]		\|[[28/19]], [[31/21]], [[34/23]]
	\| {{UDnote\|step=32}}		\| {{UDnote\|step=32}}
	\| {{UDnote\|fifth=34\|step=32}}		\| {{UDnote\|fifth=34\|step=32}}
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	\| 35		\| 35
	\| 736.84		\| 736.84
	\|[[26/17]], [[32/21]] [[29/19]]		\|[[26/17]], [[32/21]], [[29/19]]
	\| {{UDnote\|step=35}}		\| {{UDnote\|step=35}}
	\| {{UDnote\|fifth=34\|step=35}}		\| {{UDnote\|fifth=34\|step=35}}

Lucius Chiaraviglio: /* Theory */ Add more odd harmonics

2026-01-04T11:16:57Z

Theory: Add more odd harmonics

← Older revision		Revision as of 11:16, 4 January 2026
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|57}}		{{Harmonics in equal\|57}}
			{{Harmonics in equal\|57\|intervals=odd\|columns=11\|prec=2\|start=12\|collapsed=true\|title=Approximation of odd harmonics in 57edo (continued)}}

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

Lucius Chiaraviglio: /* Intervals */ Fix subgroup — supposed to be full 31-limit after filling in the incomplete results of the automatic interval table generator, but needs checking

2026-01-02T13:31:52Z

Intervals: Fix subgroup — supposed to be full 31-limit after filling in the incomplete results of the automatic interval table generator, but needs checking

← Older revision		Revision as of 13:31, 2 January 2026
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	\| {{UDnote\|fifth=34\|step=57}}		\| {{UDnote\|fifth=34\|step=57}}
	\|}		\|}
	<nowiki>*</nowiki> As a 2.5/3.7.11.13.17.19.23.29.31/3-subgroup temperament, in ''italics'' if inconsistent		<nowiki>*</nowiki> As a 2.3.5.7.11.13.17.19.23.29.31-subgroup temperament, in ''italics'' if inconsistent

	== Notation ==		== Notation ==

Lucius Chiaraviglio: /* Intervals */ Remove 31/21 (accidentally created by edit botch or typo?)

2026-01-02T13:27:49Z

Intervals: Remove 31/21 (accidentally created by edit botch or typo?)

← Older revision		Revision as of 13:27, 2 January 2026
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	\| 32		\| 32
	\| 673.68		\| 673.68
	\|[[28/19~~]], [[31/21~~]], [[34/23]]		\|[[28/19]], [[34/23]]
	\| {{UDnote\|step=32}}		\| {{UDnote\|step=32}}
	\| {{UDnote\|fifth=34\|step=32}}		\| {{UDnote\|fifth=34\|step=32}}

Lucius Chiaraviglio: /* Intervals */ Move inconsistent ratios to last in their table cells as recommended by edit partially lost due to edit clash

2026-01-02T13:21:47Z

Intervals: Move inconsistent ratios to last in their table cells as recommended by edit partially lost due to edit clash

← Older revision		Revision as of 13:21, 2 January 2026
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	\| 9		\| 9
	\| 189.47		\| 189.47
	\|''[[9/8]]'', [[10/9]],<br>[[19/17]], [[29/26]]		\|[[19/17]], [[29/26]],<br>[[10/9]], ''[[9/8]]''
	\| {{UDnote\|step=9}}		\| {{UDnote\|step=9}}
	\| {{UDnote\|fifth=34\|step=9}}		\| {{UDnote\|fifth=34\|step=9}}
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	\| 20		\| 20
	\| 421.05		\| 421.05
	\|''[[9/7]]'', [[14/11]]		\|[[14/11]], ''[[9/7]]''
	\| {{UDnote\|step=20}}		\| {{UDnote\|step=20}}
	\| {{UDnote\|fifth=34\|step=20}}		\| {{UDnote\|fifth=34\|step=20}}
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	\| 37		\| 37
	\| 778.95		\| 778.95
	\|''[[14/9]]'', [[11/7]]		\|[[11/7]], ''[[14/9]]''
	\| {{UDnote\|step=37}}		\| {{UDnote\|step=37}}
	\| {{UDnote\|fifth=34\|step=37}}		\| {{UDnote\|fifth=34\|step=37}}
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	\| 48		\| 48
	\| 1010.53		\| 1010.53
	\|''[[16/9]]'', [[9/5]],<br>[[34/19]], [[52/29]]		\|[[34/19]], [[52/29]],<br>[[9/5]], ''[[16/9]]''
	\| {{UDnote\|step=48}}		\| {{UDnote\|step=48}}
	\| {{UDnote\|fifth=34\|step=48}}		\| {{UDnote\|fifth=34\|step=48}}

Lucius Chiaraviglio: /* Intervals */ Fill in some more intervals that the automated interval table generator missed, including 3/2 and 4/3; also fix typo in one of the intervals filled in previously; attempt to recover from edit clash

2026-01-02T13:14:44Z

Intervals: Fill in some more intervals that the automated interval table generator missed, including 3/2 and 4/3; also fix typo in one of the intervals filled in previously; attempt to recover from edit clash

Show changes

FloraC: /* Intervals */ don't add the 19edo interpretation of 9 if you don't intend to add the corresponding 3

2026-01-02T13:03:08Z

Intervals: don't add the 19edo interpretation of 9 if you don't intend to add the corresponding 3

Show changes

Lucius Chiaraviglio: /* Intervals */ Fix a couple of places where the visual edit botched the formatting

2026-01-02T12:52:46Z

Intervals: Fix a couple of places where the visual edit botched the formatting

← Older revision		Revision as of 12:52, 2 January 2026
Line 78:		Line 78:
	\| 9		\| 9
	\| 189.47		\| 189.47
	\|''[[9/8]]'', [[10/9]],		\|''[[9/8]]'', [[10/9]],<br>[[19/17]], [[29/26]]
	[[19/17]], [[29/26]]
	\| {{UDnote\|step=9}}		\| {{UDnote\|step=9}}
	\| {{UDnote\|fifth=34\|step=9}}		\| {{UDnote\|fifth=34\|step=9}}
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	\| 48		\| 48
	\| 1010.53		\| 1010.53
	\|''[[16/9]]'', [[9/5]],		\|''[[16/9]]'', [[9/5]],<br>[[34/19]], [[52/29]]
	[[34/19]], [[52/29]]
	\| {{UDnote\|step=48}}		\| {{UDnote\|step=48}}
	\| {{UDnote\|fifth=34\|step=48}}		\| {{UDnote\|fifth=34\|step=48}}

Lucius Chiaraviglio: /* Intervals */ Add some more common intervals and intervals specified by Orwell, including some for which only the octave complement was present in the automatically generated output

2026-01-02T12:51:16Z

Intervals: Add some more common intervals and intervals specified by Orwell, including some for which only the octave complement was present in the automatically generated output

← Older revision		Revision as of 12:51, 2 January 2026
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	\| 6		\| 6
	\| 126.32		\| 126.32
	\|[[14/13]]		\|[[14/13]], ''[[16/15]]''
	\| {{UDnote\|step=6}}		\| {{UDnote\|step=6}}
	\| {{UDnote\|fifth=34\|step=6}}		\| {{UDnote\|fifth=34\|step=6}}
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	\| 9		\| 9
	\| 189.47		\| 189.47
	\|[[19/17]], [[29/26]]		\|''[[9/8]]'', [[10/9]],
			[[19/17]], [[29/26]]
	\| {{UDnote\|step=9}}		\| {{UDnote\|step=9}}
	\| {{UDnote\|fifth=34\|step=9}}		\| {{UDnote\|fifth=34\|step=9}}
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	\| 22		\| 22
	\| 463.16		\| 463.16
	\|[[17/13]]		\|[[17/13]], [[21/16]], [[38/29]]
	\| {{UDnote\|step=22}}		\| {{UDnote\|step=22}}
	\| {{UDnote\|fifth=34\|step=22}}		\| {{UDnote\|fifth=34\|step=22}}
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	\| 35		\| 35
	\| 736.84		\| 736.84
	\|[[26/17]], [[29/19]]		\|[[26/17]], [[32/21]] [[29/19]]
	\| {{UDnote\|step=35}}		\| {{UDnote\|step=35}}
	\| {{UDnote\|fifth=34\|step=35}}		\| {{UDnote\|fifth=34\|step=35}}
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	\| 48		\| 48
	\| 1010.53		\| 1010.53
	\|[[34/19]]		\|''[[16/9]]'', [[9/5]],
			[[34/19]], [[52/29]]
	\| {{UDnote\|step=48}}		\| {{UDnote\|step=48}}
	\| {{UDnote\|fifth=34\|step=48}}		\| {{UDnote\|fifth=34\|step=48}}
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	\| 51		\| 51
	\| 1073.68		\| 1073.68
	\|[[13/7]]		\|[[13/7]], ''[[15/8]]''
	\| {{UDnote\|step=51}}		\| {{UDnote\|step=51}}
	\| {{UDnote\|fifth=34\|step=51}}		\| {{UDnote\|fifth=34\|step=51}}