497edo - 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"

2026-03-13T13:32:05Z

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
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	\| [[Luna]]		\| [[Luna]]
	\|}		\|}
	<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

Francium: changed EDO intro to ED intro

2025-02-21T06:15:46Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:15, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|497~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:48, 15 January 2025

2025-01-15T16:48:09Z

← Older revision		Revision as of 16:48, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	497 factors into 7 × 41, with [[7edo]] and [[~~41edo~~]] as its subset edos. [[1491edo]], which triples it, gives a good correction to harmonics 3 and 7.		497 factors into {{nowrap\|7 × 71}}, with [[7edo]] and [[71edo]] as its subset edos. [[1491edo]], which triples it, gives a good correction to harmonics 3 and 7.

	== Regular temperament properties ==		== Regular temperament properties ==
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	\| {{monzo\| 788 -497 }}		\| {{monzo\| 788 -497 }}
	\| {{mapping\| 497 788 }}		\| {{mapping\| 497 788 }}
	\| -0.2084		\| −0.2084
	\| 0.2084		\| 0.2084
	\| 8.63		\| 8.63
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	\| {{monzo\| 38 -2 -15 }}, {{monzo\| 12 -31 16 }}		\| {{monzo\| 38 -2 -15 }}, {{monzo\| 12 -31 16 }}
	\| {{mapping\| 497 788 1154 }}		\| {{mapping\| 497 788 1154 }}
	\| -0.1396		\| −0.1396
	\| 0.1961		\| 0.1961
	\| 8.12		\| 8.12
Line 54:		Line 54:
	\| [[Luna]]		\| [[Luna]]
	\|}		\|}
	<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

ArrowHead294: Partial undo

2024-11-16T13:19:07Z

Partial undo

← Older revision		Revision as of 13:19, 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
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	\| 0.1961		\| 0.1961
	\| 8.12		\| 8.12
	~~{{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
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	\| 262144/234375		\| 262144/234375
	\| [[Luna]]		\| [[Luna]]
	~~{{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

ArrowHead294 at 01:37, 16 November 2024

2024-11-16T01:37:25Z

← Older revision		Revision as of 01:37, 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 36:		Line 27:
	\| 0.1961		\| 0.1961
	\| 8.12		\| 8.12
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ style="font-size: 105%;" \| Table of~~ rank-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br />per 8ve~~
	! Generator*
	! Cents*
	! Associated<br />Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\| 262144/234375		\| 262144/234375
	\| [[Luna]]		\| [[Luna]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 00:55, 16 November 2024

2024-11-16T00:55:14Z

← Older revision		Revision as of 00:55, 16 November 2024
Line 13:		Line 13:
	== Regular temperament properties ==		== 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
	\|-		\|-
Line 39:		Line 40:
	=== 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		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio*		! Associated<br />Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Luna]]		\| [[Luna]]
	\|}		\|}
	~~<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}}

FloraC: Review

2023-12-13T15:28:34Z

Review

← Older revision		Revision as of 15:28, 13 December 2023
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	== Theory ==		== Theory ==
	497et only is consistent to the 5-limit. Using the patent val, it tempers out ~~67108864~~/~~66976875~~, 48828125/48771072, ~~[[2100875~~/~~2097152]]~~ and 200120949/200000000 in the 7-limit; [[~~117440512~~/~~117406179~~]], ~~26796875~~/~~26763264~~, ~~151263~~/~~151250~~, [[131072/130977]], ~~42875~~/~~42768, 4302592/4296875, [[5632/5625]], 537109375/536870912, 9453125/9437184~~, 160083/160000, ~~1362944/1361367,~~ 391314/390625~~, 43923/43904 and 644204/643125~~ in the 11-limit.		497et only is [[consistent]] to the [[5-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[2100875/2097152]], 48828125/48771072, 67108864/66976875, and 200120949/200000000 in the 7-limit; [[5632/5625]], 42875/42768, 43923/43904, [[131072/130977]], 151263/151250, 160083/160000, and 391314/390625 in the 11-limit.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	497 factors into 7 × 41, with [[7edo]] and [[41edo]] as its subset edos. [[1491edo]], which triples it, gives a good correction to ~~the harmonic~~ 7.		497 factors into 7 × 41, with [[7edo]] and [[41edo]] as its subset edos. [[1491edo]], which triples it, gives a good correction to harmonics 3 and 7.

	== Regular temperament properties ==		== 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\|788 -497}}		\| {{monzo\| 788 -497 }}
	\|{{mapping\|497 788}}		\| {{mapping\| 497 788 }}
	\| -0.2084		\| -0.2084
	\| 0.2084		\| 0.2084
	\| 8.63		\| 8.63
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|38 -2 -15}}, {{~~val~~\|12 -31 16}}		\| {{monzo\| 38 -2 -15 }}, {{monzo\| 12 -31 16 }}
	\|{{mapping\|497 788 1154}}		\| {{mapping\| 497 788 1154 }}
	\| -0.1396		\| -0.1396
	\| 0.1961		\| 0.1961
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	\|+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
	\|80\497		\| 80\497
	\|193.16		\| 193.16
	\|262144/234375		\| 262144/234375
	\|[[Luna]]		\| [[Luna]]
	\|}		\|}

	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

Francium: Created page with "{{Infobox ET}} {{EDO intro|497}} == Theory == 497et only is consistent to the 5-limit. Using the patent val, it tempers out 67108864/66976875, 48828125/48771072, 2100875/20..."

2023-12-13T08:42:45Z

Created page with "{{Infobox ET}} {{EDO intro|497}} == Theory == 497et only is consistent to the 5-limit. Using the patent val, it tempers out 67108864/66976875, 48828125/48771072, 2100875/20..."

New page

{{Infobox ET}}
{{EDO intro|497}}

== Theory ==
497et only is consistent to the 5-limit. Using the patent val, it tempers out 67108864/66976875, 48828125/48771072, [[2100875/2097152]] and 200120949/200000000 in the 7-limit; [[117440512/117406179]], 26796875/26763264, 151263/151250, [[131072/130977]], 42875/42768, 4302592/4296875, [[5632/5625]], 537109375/536870912, 9453125/9437184, 160083/160000, 1362944/1361367, 391314/390625, 43923/43904 and 644204/643125 in the 11-limit.

=== Odd harmonics ===
{{Harmonics in equal|497}}

=== Subsets and supersets ===
497 factors into 7 × 41, with [[7edo]] and [[41edo]] as its subset edos. [[1491edo]], which triples it, gives a good correction to the harmonic 7.

== 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|788 -497}}
|{{mapping|497 788}}
| -0.2084
| 0.2084
| 8.63
|-
|2.3.5
|{{monzo|38 -2 -15}}, {{val|12 -31 16}}
|{{mapping|497 788 1154}}
| -0.1396
| 0.1961
| 8.12
|}

=== 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
|80\497
|193.16
|262144/234375
|[[Luna]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct