475edo - Revision history

FloraC: /* Regular temperament properties */ + ragitritonic/garitritonic

2026-05-20T12:47:05Z

Regular temperament properties: + ragitritonic/garitritonic

← Older revision		Revision as of 12:47, 20 May 2026
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	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[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
	\|-		\|-
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	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 753 -475 }}		\| {{Monzo\| 753 -475 }}
	\| {{~~mapping~~\| 475 753 }}		\| {{Mapping\| 475 753 }}
	\| −0.1138		\| −0.1138
	\| 0.1138		\| 0.1138
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| -14 -19 19 }}, {{monzo\| 47 -15 -10 }}		\| {{Monzo\| -14 -19 19 }}, {{monzo\| 47 -15 -10 }}
	\| {{~~mapping~~\| 475 753 1103 }}		\| {{Mapping\| 475 753 1103 }}
	\| −0.1064		\| −0.1064
	\| 0.0935		\| 0.0935
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	\|+ style="font-size: 105%;" \| 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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	\| 98304/78125		\| 98304/78125
	\| [[Squarschmidt]]		\| [[Squarschmidt]]
			\|-
			\| 1
			\| 233\475
			\| 588.63
			\| 351/250
			\| [[Ragitritonic]] (475d) / [[garitritonic]] (475e)
	\|-		\|-
	\| 5		\| 5
	\| 329\475<br />(44\475)		\| 329\475<br>(44\475)
	\| 831.16<br />(111.16)		\| 831.16<br>(111.16)
	\| 160/99<br />(16/15)		\| 160/99<br>(16/15)
	\| [[Quintosec]]		\| [[Quintosec]]
	\|-		\|-
	\| 19		\| 19
	\| 197\475<br />(3\475)		\| 197\475<br>(3\475)
	\| 497.68<br />(7.58)		\| 497.68<br>(7.58)
	\| 4/3<br />(225/224)		\| 4/3<br>(225/224)
	\| [[Enneadecal]] (475d)		\| [[Enneadecal]] (475d)
	\|}		\|}
	<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		<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

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"

2026-03-13T13:32:35Z

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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	\| [[Enneadecal]] (475d)		\| [[Enneadecal]] (475d)
	\|}		\|}
	<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

2025-02-21T06:23:12Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:23, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|475~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:05, 15 January 2025

2025-01-15T17:05:04Z

← Older revision		Revision as of 17:05, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 475 factors into ~~5<sup>2</sup> × 19~~, 475edo has subset edos {{EDOs\| 5, 19, 25, and 95 }}. [[950edo]], which doubles it, gives a good correction to the harmonic 7.		Since 475 factors into {{factorisation\|475}}, 475edo has subset edos {{EDOs\| 5, 19, 25, and 95 }}. [[950edo]], which doubles it, gives a good correction to the harmonic 7.

	== Regular temperament properties ==		== Regular temperament properties ==
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	\| {{monzo\| 753 -475 }}		\| {{monzo\| 753 -475 }}
	\| {{mapping\| 475 753 }}		\| {{mapping\| 475 753 }}
	\| ~~−0~~.1138		\| −0.1138
	\| 0.1138		\| 0.1138
	\| 4.50		\| 4.50
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	\| {{monzo\| -14 -19 19 }}, {{monzo\| 47 -15 -10 }}		\| {{monzo\| -14 -19 19 }}, {{monzo\| 47 -15 -10 }}
	\| {{mapping\| 475 753 1103 }}		\| {{mapping\| 475 753 1103 }}
	\| ~~−0~~.1064		\| −0.1064
	\| 0.0935		\| 0.0935
	\| 3.70		\| 3.70
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	\| [[Enneadecal]] (475d)		\| [[Enneadecal]] (475d)
	\|}		\|}
	<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

2024-11-16T13:13:12Z

Partial undo

← Older revision		Revision as of 13:13, 16 November 2024
Line 14:		Line 14:

	== 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\| 753 -475 }}		\| {{monzo\| 753 -475 }}
	\| {{mapping\| 475 753 }}		\| {{mapping\| 475 753 }}
	\| -0.1138		\| −0.1138
	\| 0.1138		\| 0.1138
	\| 4.50		\| 4.50
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	\| {{monzo\| -14 -19 19 }}, {{monzo\| 47 -15 -10 }}		\| {{monzo\| -14 -19 19 }}, {{monzo\| 47 -15 -10 }}
	\| {{mapping\| 475 753 1103 }}		\| {{mapping\| 475 753 1103 }}
	\| -0.1064		\| −0.1064
	\| 0.0935		\| 0.0935
	\| 3.70		\| 3.70
	~~{{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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	\| 4/3<br />(225/224)		\| 4/3<br />(225/224)
	\| [[Enneadecal]] (475d)		\| [[Enneadecal]] (475d)
	~~{{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 01:54, 16 November 2024

2024-11-16T01:54:21Z

← Older revision		Revision as of 01:54, 16 November 2024
Line 14:		Line 14:

	== 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
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	\| 0.0935		\| 0.0935
	\| 3.70		\| 3.70
	\|}		{{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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	\|-		\|-
	\| 5		\| 5
	\| 329\475<br>(44\475)		\| 329\475<br />(44\475)
	\| 831.16<br>(111.16)		\| 831.16<br />(111.16)
	\| 160/99<br>(16/15)		\| 160/99<br />(16/15)
	\| [[Quintosec]]		\| [[Quintosec]]
	\|-		\|-
	\| 19		\| 19
	\| 197\475<br>(3\475)		\| 197\475<br />(3\475)
	\| 497.68<br>(7.58)		\| 497.68<br />(7.58)
	\| 4/3<br>(225/224)		\| 4/3<br />(225/224)
	\| [[Enneadecal]] (475d)		\| [[Enneadecal]] (475d)
	\|}		{{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

2024-02-19T13:30:33Z

Review

← Older revision		Revision as of 13:30, 19 February 2024
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	== Theory ==		== Theory ==
	~~475et~~ is only consistent to the [[5-odd-limit]]. It can be considered for the 2.3.5.11.13.19.23 [[subgroup]], tempering out [[2376/2375]]~~, 11132/11115~~, [[3250/3249]], ~~42757~~/~~42750~~, 11979/11960 ~~and~~ 14300/14283~~. It [[support]]s [[will]], [[countritonic]]~~ and ~~[[cotoneum]]~~.		475edo is only [[consistent]] to the [[5-odd-limit]]. The equal temperament [[tempering out\|tempers out]] {{monzo\| -14 -19 19 }} ([[enneadeca]]) and {{monzo\| 47 -15 -10 }} (quintosec comma) in the 5-limit. In the 7-limit, the 475d [[val]] [[support]]s [[enneadecal]] and the [[patent val]] supports [[cotoneum]].

			It can be considered for the 2.3.5.11.13.19.23 [[subgroup]], tempering out [[2376/2375]], [[3250/3249]], 11132/11115, 11979/11960, 14300/14283 and 42757/42750.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	475 factors into 5<sup>2</sup> × 19, ~~with~~ subset edos {{EDOs\|5, 19, 25, and 95}}. [[950edo]], which doubles it, gives a good correction to the harmonic 7.		Since 475 factors into 5<sup>2</sup> × 19, 475edo has subset edos {{EDOs\| 5, 19, 25, and 95 }}. [[950edo]], which doubles it, gives a good correction to the harmonic 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\|753 -475}}		\| {{monzo\| 753 -475 }}
	\|{{mapping\|475 753}}		\| {{mapping\| 475 753 }}
	\| -0.1138		\| -0.1138
	\| 0.1138		\| 0.1138
	\| 4.50		\| 4.50
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|-14 -19 19}}, {{monzo\|47 -15 -10}}		\| {{monzo\| -14 -19 19 }}, {{monzo\| 47 -15 -10 }}
	\|{{mapping\|475 753 1103}}		\| {{mapping\| 475 753 1103 }}
	\| -0.1064		\| -0.1064
	\| 0.0935		\| 0.0935
Line 46:		Line 48:
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|157\475		\| 157\475
	\|396.63		\| 396.63
	\|98304/78125		\| 98304/78125
	\|[[Squarschmidt]]		\| [[Squarschmidt]]
	\|-		\|-
	\|5		\| 5
	\|329\475<br>(44\475)		\| 329\475<br>(44\475)
	\|831.16<br>(111.16)		\| 831.16<br>(111.16)
	\|80/49<br>(15~~/14~~)		\| 160/99<br>(16/15)
	\|[[~~Qintosec~~]]		\| [[Quintosec]]
	\|-		\|-
	\|19		\| 19
	\|197\475<br>(3\475)		\| 197\475<br>(3\475)
	\|497.68<br>(7.58)		\| 497.68<br>(7.58)
	\|4/3<br>(225/224)		\| 4/3<br>(225/224)
	\|[[Enneadecal]]		\| [[Enneadecal]] (475d)
	\|}		\|}

	<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|475}} == Theory == 475et is only consistent to the 5-odd-limit. It can be considered for the 2.3.5.11.13.19.23 subgroup, tempering out 23..."

2024-02-19T12:52:55Z

Created page with "{{Infobox ET}} {{EDO intro|475}} == Theory == 475et is only consistent to the 5-odd-limit. It can be considered for the 2.3.5.11.13.19.23 subgroup, tempering out 23..."

New page

{{Infobox ET}}
{{EDO intro|475}}

== Theory ==
475et is only consistent to the [[5-odd-limit]]. It can be considered for the 2.3.5.11.13.19.23 [[subgroup]], tempering out [[2376/2375]], 11132/11115, [[3250/3249]], 42757/42750, 11979/11960 and 14300/14283. It [[support]]s [[will]], [[countritonic]] and [[cotoneum]].

=== Prime harmonics ===
{{Harmonics in equal|475}}

=== Subsets and supersets ===
475 factors into 52 × 19, with subset edos {{EDOs|5, 19, 25, and 95}}. [[950edo]], which doubles 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|753 -475}}
|{{mapping|475 753}}
| -0.1138
| 0.1138
| 4.50
|-
|2.3.5
|{{monzo|-14 -19 19}}, {{monzo|47 -15 -10}}
|{{mapping|475 753 1103}}
| -0.1064
| 0.0935
| 3.70
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator*
! Cents*
! Associated Ratio*
! Temperaments
|-
|1
|157\475
|396.63
|98304/78125
|[[Squarschmidt]]
|-
|5
|329\475 (44\475)
|831.16 (111.16)
|80/49 (15/14)
|[[Qintosec]]
|-
|19
|197\475 (3\475)
|497.68 (7.58)
|4/3 (225/224)
|[[Enneadecal]]
|}

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