557edo - Revision history

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"

2026-03-13T13:32:04Z

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
Line 54:		Line 54:
	\| [[Fifthplus]]		\| [[Fifthplus]]
	\|}		\|}
	<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

	== Scales ==		== Scales ==

Francium: changed EDO intro to ED intro

2025-02-21T05:59:39Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:59, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|557~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:04, 15 January 2025

2025-01-15T17:04:08Z

← Older revision		Revision as of 17:04, 15 January 2025
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	\| {{monzo\| 883 -557 }}		\| {{monzo\| 883 -557 }}
	\| {{mapping\| 557 883 }}		\| {{mapping\| 557 883 }}
	\| ~~−0~~.1195		\| −0.1195
	\| 0.1195		\| 0.1195
	\| 5.55		\| 5.55
Line 54:		Line 54:
	\| [[Fifthplus]]		\| [[Fifthplus]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

ArrowHead294: Partial undo

2024-11-16T13:21:10Z

Partial undo

← Older revision		Revision as of 13:21, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\| 883 -557 }}		\| {{monzo\| 883 -557 }}
	\| {{mapping\| 557 883 }}		\| {{mapping\| 557 883 }}
	\| -0.1195		\| −0.1195
	\| 0.1195		\| 0.1195
	\| 5.55		\| 5.55
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	\| 0.2169		\| 0.2169
	\| 10.07		\| 10.07
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
Line 37:		Line 53:
	\| 3645/2744		\| 3645/2744
	\| [[Fifthplus]]		\| [[Fifthplus]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==

ArrowHead294 at 01:31, 16 November 2024

2024-11-16T01:31:53Z

← Older revision		Revision as of 01:31, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
Line 35:		Line 27:
	\| 0.2169		\| 0.2169
	\| 10.07		\| 10.07
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\| 3645/2744		\| 3645/2744
	\| [[Fifthplus]]		\| [[Fifthplus]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Scales ==		== Scales ==

Francium: +music

2024-08-03T12:20:47Z

+music

← Older revision		Revision as of 12:20, 3 August 2024
Line 57:		Line 57:
	* [[Laz5]]		* [[Laz5]]
	* [[Laz9]]		* [[Laz9]]

			== Music ==
			; [[Francium]]
			* "Are You A Youth Medium?" from ''Questions'' (2024) – [https://open.spotify.com/track/4S3oY6c2VRNHBrYD16owoF Spotify] \| [https://francium223.bandcamp.com/track/are-you-a-youth-medium Bandcamp] \| [https://www.youtube.com/watch?v=OAxdvEZJ-8M YouTube] – sidi in 557edo tuning

FloraC: Rework; cleanup; clarify the title row of the rank-2 temp table

2023-10-29T11:02:14Z

Rework; cleanup; clarify the title row of the rank-2 temp table

← Older revision		Revision as of 11:02, 29 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|557}}		{{EDO intro\|557}}
	==Theory==
	~~557et tempers out~~ [[~~645700815/645657712~~]], ~~2460375/2458624~~, [[65625/65536]] ~~and~~ 420175/419904 in the 7-limit; ~~820125~~/~~819896, 2097152/2096325~~, [[4000/3993]]~~, 78675968/78594219, [[536870912/535869675]], 180224/180075, 1375/1372, 184549376/184528125~~, [[19712/19683]], 43923/43904, ~~20614528~~/~~20588575~~ and 322102/321489 in the 11-limit.		== Theory ==
	===Prime harmonics===		557edo is only [[consistent]] to the [[5-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] {{monzo\| 3 -18 11 }} (quartonic comma) and {{monzo\| -74 13 23 }} (sesesix comma), as well as {{monzo\| 77 -31 -12 }} (lafa comma) in the 5-limit; [[65625/65536]], 420175/419904 and 2460375/2458624 in the 7-limit; 1375/1372, [[4000/3993]], [[19712/19683]], 43923/43904, 180224/180075, and 322102/321489 in the 11-limit. It [[support]]s [[fifthplus]], although [[171edo]] is better suited for that purpose.

			=== Prime harmonics ===
	{{Harmonics in equal\|557}}		{{Harmonics in equal\|557}}
	===Subsets and supersets===
	557edo is the 102nd [[prime ~~EDO~~]].		=== Subsets and supersets ===
	==Regular temperament properties==		557edo is the 102nd [[prime edo]].

			== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|883 -557}}		\| {{monzo\| 883 -557 }}
	\|{{~~val~~\|557 883}}		\| {{mapping\| 557 883 }}
	\| -0.1195		\| -0.1195
	\| 0.1195		\| 0.1195
	\| 5.55		\| 5.55
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|3 -18 11}}, {{monzo\|-74 13 23}}		\| {{monzo\| 3 -18 11 }}, {{monzo\| -74 13 23 }}
	\|{{~~val~~\|557 883 1293}}		\| {{mapping\| 557 883 1293 }}
	\| +0.0174		\| +0.0174
	\| 0.2169		\| 0.2169
	\| 10.07		\| 10.07
	\|}		\|}
	===Rank-2 temperaments===
			=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~		! Generator*
	! Cents~~<br>(reduced)~~		! Cents*
	! Associated<br>~~ratio~~		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|228\557		\| 228\557
	\|491.203		\| 491.203
	\|4/3		\| 3645/2744
	\|[[~~Sesesix~~]]		\| [[Fifthplus]]
	\|}		\|}
	==Scales==		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

			== Scales ==
	* [[Laz5]]		* [[Laz5]]
	* [[Laz9]]		* [[Laz9]]

Francium: Created page with "{{Infobox ET}} {{EDO intro|557}} ==Theory== 557et tempers out 645700815/645657712, 2460375/2458624, 65625/65536 and 420175/419904 in the 7-limit; 820125/819896, 209715..."

2023-10-05T11:57:35Z

Created page with "{{Infobox ET}} {{EDO intro|557}} ==Theory== 557et tempers out 645700815/645657712, 2460375/2458624, 65625/65536 and 420175/419904 in the 7-limit; 820125/819896, 209715..."

New page

{{Infobox ET}}
{{EDO intro|557}}
==Theory==
557et tempers out [[645700815/645657712]], 2460375/2458624, [[65625/65536]] and 420175/419904 in the 7-limit; 820125/819896, 2097152/2096325, [[4000/3993]], 78675968/78594219, [[536870912/535869675]], 180224/180075, 1375/1372, 184549376/184528125, [[19712/19683]], 43923/43904, 20614528/20588575 and 322102/321489 in the 11-limit.
===Prime harmonics===
{{Harmonics in equal|557}}
===Subsets and supersets===
557edo is the 102nd [[prime EDO]].
==Regular temperament properties==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|883 -557}}
|{{val|557 883}}
| -0.1195
| 0.1195
| 5.55
|-
|2.3.5
|{{monzo|3 -18 11}}, {{monzo|-74 13 23}}
|{{val|557 883 1293}}
| +0.0174
| 0.2169
| 10.07
|}
===Rank-2 temperaments===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator (reduced)
! Cents (reduced)
! Associated ratio
! Temperaments
|-
|1
|228\557
|491.203
|4/3
|[[Sesesix]]
|}
==Scales==
* [[Laz5]]
* [[Laz9]]