470edo - 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"

2026-03-13T13:32:13Z

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 75:		Line 75:
	\| [[Amity]] (5-limit)		\| [[Amity]] (5-limit)
	\|}		\|}
	<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

2025-02-21T06:26:07Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:26, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|470~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:17, 15 January 2025

2025-01-15T18:17:44Z

← Older revision		Revision as of 18:17, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~470 = 5 × 94, and~~ 470edo shares the [[perfect fifth\|fifth]] with [[94edo]]. Unlike 94edo, however, 470edo is only [[consistent]] to the [[5-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[703125/702464]], 823543/820125, and 1500625/1492992 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], [[19712/19683]], and 117649/117128 in the 11-limit. It [[support]]s [[uniwiz]] and [[decimetra]].		470edo shares the [[perfect fifth\|fifth]] with [[94edo]]. Unlike 94edo, however, 470edo is only [[consistent]] to the [[5-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[703125/702464]], 823543/820125, and 1500625/1492992 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], [[19712/19683]], and 117649/117128 in the 11-limit. It [[support]]s [[uniwiz]] and [[decimetra]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 470 factors into ~~2 × 5 × 47~~, 470edo has subset edos {{EDOs\| 2, 5, 10, 47, 94, and 235 }}.		Since 470 factors into {{factorisation\|470}}, 470edo has subset edos {{EDOs\| 2, 5, 10, 47, 94, and 235 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 75:		Line 75:
	\| [[Amity]] (5-limit)		\| [[Amity]] (5-limit)
	\|}		\|}
	<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

2024-11-16T13:06:24Z

Partial undo

← Older revision		Revision as of 13:06, 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]] (%)
	\|-		\|-
	\| 2.3.5		\| 2.3.5
Line 48:		Line 57:
	\| 0.1824		\| 0.1824
	\| 7.14		\| 7.14
	~~{{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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	\| 243/200		\| 243/200
	\| [[Amity]] (5-limit)		\| [[Amity]] (5-limit)
	~~{{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 02:36, 16 November 2024

2024-11-16T02:36:18Z

← Older revision		Revision as of 02:36, 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]] (%)~~
	\|-		\|-
	\| 2.3.5		\| 2.3.5
Line 56:		Line 48:
	\| 0.1824		\| 0.1824
	\| 7.14		\| 7.14
	\|}		{{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
Line 72:		Line 58:
	\| 243/200		\| 243/200
	\| [[Amity]] (5-limit)		\| [[Amity]] (5-limit)
	\|}		{{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}}

FloraC: Review

2024-02-19T13:20:42Z

Review

← Older revision		Revision as of 13:20, 19 February 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~470et is enfactored in~~ the [[~~3-limit~~]] ~~and~~ only consistent to the [[5-odd-limit]]. Using the patent val, it tempers out [[703125/702464]], ~~359661568~~/~~358722675~~, ~~5250987/5242880~~ and ~~200120949~~/~~200000000~~ in the 7-limit; ~~161280~~/~~161051, 820125/819896, 29296875/29218112~~, [[4000/3993]]~~, 22478848/22460625, 759375/758912~~, [[6250/6237]]~~, [[200704/200475]], 352947/352000~~, [[19712/19683]], ~~[[3025/3024]], 16808715/16777216, [[532400/531441]]~~ and ~~[[1771561~~/~~1771470]]~~ in the 11-limit. It [[support]]s [[uniwiz]] and [[decimetra]].		470 = 5 × 94, and 470edo shares the [[perfect fifth\|fifth]] with [[94edo]]. Unlike 94edo, however, 470edo is only [[consistent]] to the [[5-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[703125/702464]], 823543/820125, and 1500625/1492992 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], [[19712/19683]], and 117649/117128 in the 11-limit. It [[support]]s [[uniwiz]] and [[decimetra]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	470 factors into 2 × 5 × 47, ~~with~~ subset edos {{EDOs\|2, 5, 10, 47, 94, and 235}}.		Since 470 factors into 2 × 5 × 47, 470edo has subset edos {{EDOs\| 2, 5, 10, 47, 94, and 235 }}.

	== 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~~		\| 2.3.5
	~~\|{{monzo\|149 -94}}~~		\| 1600000/1594323, {{monzo\|-77 -10 40}}
	~~\|{{mapping\|470 745}}~~		\| {{mapping\| 470 745 1091 }}
	~~\| -0.0545~~
	~~\| 0.0545~~
	~~\| 2.13~~
	\|-
	\|2.3.5
	\|1600000/1594323, {{monzo\|-77 -10 40}}
	\|{{mapping\|470 745 1091}}
	\| +0.0759		\| +0.0759
	\| 0.1897		\| 0.1897
	\| 7.43		\| 7.43
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|1500625/1492992~~, 703125/702464~~, 1600000/1594323		\| 703125/702464, 1500625/1492992, 1600000/1594323
	\|{{mapping\|470 745 1091 1319}}		\| {{mapping\| 470 745 1091 1319 }}
	\| +0.1608		\| +0.1608
	\| 0.2205		\| 0.2205
	\| 8.64		\| 8.64
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|3025/3024, ~~6250~~/~~6237~~, ~~420175~~/~~418176~~, ~~759375~~/~~758912~~		\| 3025/3024, 4000/3993, 19712/19683, 117649/117128
	\|{{mapping\|470 745 1091 1319 1626}}		\| {{mapping\| 470 745 1091 1319 1626 }}
	\| +0.1187		\| +0.1187
	\| 0.2144		\| 0.2144
	\| 8.40		\| 8.40
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|1575/1573, 2080/2079~~, 625/624~~, 13720/13689, ~~218491~~/~~217800~~		\| 625/624, 1575/1573, 2080/2079, 13720/13689, 15379/15360
	\|{{mapping\|470 745 1091 1319 1626 1739}}		\| {{mapping\| 470 745 1091 1319 1626 1739 }}
	\| +0.1227		\| +0.1227
	\| 0.1959		\| 0.1959
	\| 7.67		\| 7.67
	\|-		\|-
	\|2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\|595/594, ~~1575~~/~~1573~~, ~~2080~~/~~2079~~, ~~12376~~/~~12375~~, 3185/3179, 8624/8619		\| 595/594, 625/624, 833/832, 1575/1573, 3185/3179, 8624/8619
	\|{{mapping\|470 745 1091 1319 1626 1739 1921}}		\| {{mapping\| 470 745 1091 1319 1626 1739 1921 }}
	\| +0.1148		\| +0.1148
	\| 0.1824		\| 0.1824
Line 74:		Line 67:
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|133\470		\| 133\470
	\|339.57		\| 339.57
	\|243/200		\| 243/200
	\|[[Amity]]		\| [[Amity]] (5-limit)
	\|}		\|}

	<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|470}} == Theory == 470et is enfactored in the 3-limit and only consistent to the 5-odd-limit. Using the patent val, it tempers out 703125..."

2024-02-19T12:24:05Z

Created page with "{{Infobox ET}} {{EDO intro|470}} == Theory == 470et is enfactored in the 3-limit and only consistent to the 5-odd-limit. Using the patent val, it tempers out 703125..."

New page

{{Infobox ET}}
{{EDO intro|470}}

== Theory ==
470et is enfactored in the [[3-limit]] and only consistent to the [[5-odd-limit]]. Using the patent val, it tempers out [[703125/702464]], 359661568/358722675, 5250987/5242880 and 200120949/200000000 in the 7-limit; 161280/161051, 820125/819896, 29296875/29218112, [[4000/3993]], 22478848/22460625, 759375/758912, [[6250/6237]], [[200704/200475]], 352947/352000, [[19712/19683]], [[3025/3024]], 16808715/16777216, [[532400/531441]] and [[1771561/1771470]] in the 11-limit. It [[support]]s [[uniwiz]] and [[decimetra]].

=== Prime harmonics ===
{{Harmonics in equal|470}}

=== Subsets and supersets ===
470 factors into 2 × 5 × 47, with subset edos {{EDOs|2, 5, 10, 47, 94, and 235}}.

== 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<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|149 -94}}
|{{mapping|470 745}}
| -0.0545
| 0.0545
| 2.13
|-
|2.3.5
|1600000/1594323, {{monzo|-77 -10 40}}
|{{mapping|470 745 1091}}
| +0.0759
| 0.1897
| 7.43
|-
|2.3.5.7
|1500625/1492992, 703125/702464, 1600000/1594323
|{{mapping|470 745 1091 1319}}
| +0.1608
| 0.2205
| 8.64
|-
|2.3.5.7.11
|3025/3024, 6250/6237, 420175/418176, 759375/758912
|{{mapping|470 745 1091 1319 1626}}
| +0.1187
| 0.2144
| 8.40
|-
|2.3.5.7.11.13
|1575/1573, 2080/2079, 625/624, 13720/13689, 218491/217800
|{{mapping|470 745 1091 1319 1626 1739}}
| +0.1227
| 0.1959
| 7.67
|-
|2.3.5.7.11.13.17
|595/594, 1575/1573, 2080/2079, 12376/12375, 3185/3179, 8624/8619
|{{mapping|470 745 1091 1319 1626 1739 1921}}
| +0.1148
| 0.1824
| 7.14
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|1
|133\470
|339.57
|243/200
|[[Amity]]
|}

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