476edo - 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"

2026-03-13T13:31:41Z

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 13:31, 13 March 2026
Line 75:		Line 75:
	\| [[Oquatonic]] (5-limit)		\| [[Oquatonic]] (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

2025-02-21T06:28:29Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:28, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|476~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:49, 15 January 2025

2025-01-15T17:49:11Z

← Older revision		Revision as of 17:49, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	476 factors into ~~2<sup>2</sup> × 7 × 17~~, with subset edos {{EDOs\| 2, 4, 7, 14, 17, 28, 34, 68, 119, and 238 }}. [[952edo]], which doubles it, gives a good correction to the harmonic 3, but unfortunately it is inconsistent in the [[5-odd-limit]].		476 factors into {{factorisation\|476}}, with subset edos {{EDOs\| 2, 4, 7, 14, 17, 28, 34, 68, 119, and 238 }}. [[952edo]], which doubles it, gives a good correction to the harmonic 3, but unfortunately it is inconsistent in the [[5-odd-limit]].

	== Regular temperament properties ==		== Regular temperament properties ==
Line 28:		Line 28:
	\| {{monzo\| 1509 -476 }}		\| {{monzo\| 1509 -476 }}
	\| {{mapping\| 476 1509 }}		\| {{mapping\| 476 1509 }}
	\| -0.0460		\| −0.0460
	\| 0.0460		\| 0.0460
	\| 1.82		\| 1.82
Line 75:		Line 75:
	\| [[Oquatonic]] (5-limit)		\| [[Oquatonic]] (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

2024-11-16T12:57:56Z

Partial undo

← Older revision		Revision as of 12:57, 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]] (%)
	\|-		\|-
	\| 2.9		\| 2.9
Line 36:		Line 45:
	\| 0.1586		\| 0.1586
	\| 6.29		\| 6.29
	~~{{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 58:		Line 74:
	\| 4/3<br>(105/104)		\| 4/3<br>(105/104)
	\| [[Oquatonic]] (5-limit)		\| [[Oquatonic]] (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 03:04, 16 November 2024

2024-11-16T03:04:37Z

← Older revision		Revision as of 03:04, 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]] (%)~~
	\|-		\|-
	\| 2.9		\| 2.9
Line 44:		Line 36:
	\| 0.1586		\| 0.1586
	\| 6.29		\| 6.29
	\|}		{{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:
	\| 4/3<br>(105/104)		\| 4/3<br>(105/104)
	\| [[Oquatonic]] (5-limit)		\| [[Oquatonic]] (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

2024-01-01T09:50:45Z

Review

← Older revision		Revision as of 09:50, 1 January 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|476}}		{{EDO intro\|476}}

	== Theory ==		== Theory ==
	476edo is consistent to the [[7-odd-limit]] ~~and~~ the [[harmonic]] 3 is about halfway its steps. Using the patent val, it tempers out [[2401/2400]] in the 7-limit; [[~~4000~~/~~3993~~]]~~, 12005~~/~~11979~~, ~~117649~~/~~117612~~, ~~1296000~~/~~1294139~~, [[540/539]], [[~~441~~/~~440~~]]~~, 352947/352000, 24057/24010~~, [[8019/8000]], [[9801/9800]] ~~and 160083/160000 in the~~ 11-limit.		476edo is [[consistent]] to the [[7-odd-limit]], but the [[harmonic]] [[3/1\|3]] is about halfway its steps, while its [[5/1\|5]] and [[7/1\|7]] are both tuned flat. To start with, consider the 2.3.5.7 [[patent val]], as well as 2.9.15.21 and 2.9.5.7 [[subgroup]]s.

			Using the patent val, the equal temperament [[tempering out\|tempers out]] [[2401/2400]] and [[19683/19600]] in the 7-limit, [[support]]ing [[harry]]. The 11-limit 476e val tempers out [[3025/3024]] and [[41503/41472]], whereas the patent val tempers out [[243/242]], [[441/440]], [[540/539]], [[4000/3993]], [[8019/8000]], and [[9801/9800]], supporting 11-limit harry.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 8:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	476 factors into 2<sup>2</sup> × 7 × 17, with subset edos {{EDOs\|2, 4, 7, 14, 17, 28, 34, 68, 119, and 238}}. [[952edo]], which doubles it, gives a good correction to the harmonic 3, but unfortunately it is ~~unconsistent~~ in the [[5-odd-limit]].		476 factors into 2<sup>2</sup> × 7 × 17, with subset edos {{EDOs\| 2, 4, 7, 14, 17, 28, 34, 68, 119, and 238 }}. [[952edo]], which doubles it, gives a good correction to the harmonic 3, but unfortunately it is inconsistent in the [[5-odd-limit]].

	== 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]] (%)
	\|-		\|-
	\|2.9		\| 2.9
	\|{{monzo\|1509 -476}}		\| {{monzo\| 1509 -476 }}
	\|{{mapping\|476 1509}}		\| {{mapping\| 476 1509 }}
	\| -0.0460		\| -0.0460
	\| 0.0460		\| 0.0460
	\| 1.82		\| 1.82
	\|-		\|-
	\|2.9.5		\| 2.9.5
	\|{{monzo\|33 -17 9}}, {{monzo\|-65 0 28}}		\| {{monzo\| 33 -17 9 }}, {{monzo\| -65 0 28 }}
	\|{{mapping\|476 1509 1105}}		\| {{mapping\| 476 1509 1105 }}
	\| +0.0554		\| +0.0554
	\| 0.1482		\| 0.1482
	\| 5.88		\| 5.88
	\|-		\|-
	\|2.9.5.7		\| 2.9.5.7
	\|703125/702464, 4802000/4782969, ~~4202539929/4194304000~~		\| 703125/702464, 4802000/4782969, {{monzo\| 25 3 -3 8 }}
	\|{{mapping\|476 1509 1105 1336}}		\| {{mapping\| 476 1509 1105 1336 }}
	\| +0.1091		\| +0.1091
	\| 0.1586		\| 0.1586
Line 47:		Line 50:
	\|+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
	\|205\476		\| 205\476
	\|516.81		\| 516.81
	\|27/20		\| 27/20
	\|[[~~Gravity~~]]		\| [[Larry]] (476)
	\|-		\|-
	\|2		\| 2
	\|205\476<br>(33\476)		\| 205\476<br>(33\476)
	\|516.81<br>(83.19)		\| 516.81<br>(83.19)
	\|27/20<br>(21/20)		\| 27/20<br>(21/20)
	\|[[Harry]]		\| [[Harry]] (11-limit, 476)
	\|-		\|-
	\|28		\| 28
	\|197\476<br>(6\476)		\| 197\476<br>(6\476)
	\|496.64<br>(15.13)		\| 496.64<br>(15.13)
	\|4/3<br>(105/104)		\| 4/3<br>(105/104)
	\|[[Oquatonic]]		\| [[Oquatonic]] (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 at 14:58, 20 December 2023

2023-12-20T14:58:32Z

← Older revision		Revision as of 14:58, 20 December 2023
Line 2:		Line 2:
	{{EDO intro\|476}}		{{EDO intro\|476}}
	== Theory ==		== Theory ==
	476edo is consistent to the [[7-odd-limit]] and the [[harmonic 3]] is about halfway its steps. Using the patent val, it tempers out [[2401/2400]] in the 7-limit; [[4000/3993]], 12005/11979, 117649/117612, 1296000/1294139, [[540/539]], [[441/440]], 352947/352000, 24057/24010, [[8019/8000]], [[9801/9800]] and 160083/160000 in the 11-limit.		476edo is consistent to the [[7-odd-limit]] and the [[harmonic]] 3 is about halfway its steps. Using the patent val, it tempers out [[2401/2400]] in the 7-limit; [[4000/3993]], 12005/11979, 117649/117612, 1296000/1294139, [[540/539]], [[441/440]], 352947/352000, 24057/24010, [[8019/8000]], [[9801/9800]] and 160083/160000 in the 11-limit.

	=== Odd harmonics ===		=== Odd harmonics ===

Francium: Created page with "{{Infobox ET}} {{EDO intro|476}} == Theory == 476edo is consistent to the 7-odd-limit and the harmonic 3 is about halfway its steps. Using the patent val, it tempers o..."

2023-12-19T16:52:13Z

Created page with "{{Infobox ET}} {{EDO intro|476}} == Theory == 476edo is consistent to the 7-odd-limit and the harmonic 3 is about halfway its steps. Using the patent val, it tempers o..."

New page

{{Infobox ET}}
{{EDO intro|476}}
== Theory ==
476edo is consistent to the [[7-odd-limit]] and the [[harmonic 3]] is about halfway its steps. Using the patent val, it tempers out [[2401/2400]] in the 7-limit; [[4000/3993]], 12005/11979, 117649/117612, 1296000/1294139, [[540/539]], [[441/440]], 352947/352000, 24057/24010, [[8019/8000]], [[9801/9800]] and 160083/160000 in the 11-limit.

=== Odd harmonics ===
{{Harmonics in equal|476}}

=== Subsets and supersets ===
476 factors into 22 × 7 × 17, with subset edos {{EDOs|2, 4, 7, 14, 17, 28, 34, 68, 119, and 238}}. [[952edo]], which doubles it, gives a good correction to the harmonic 3, but unfortunately it is unconsistent in the [[5-odd-limit]].

== 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]] (%)
|-
|2.9
|{{monzo|1509 -476}}
|{{mapping|476 1509}}
| -0.0460
| 0.0460
| 1.82
|-
|2.9.5
|{{monzo|33 -17 9}}, {{monzo|-65 0 28}}
|{{mapping|476 1509 1105}}
| +0.0554
| 0.1482
| 5.88
|-
|2.9.5.7
|703125/702464, 4802000/4782969, 4202539929/4194304000
|{{mapping|476 1509 1105 1336}}
| +0.1091
| 0.1586
| 6.29
|}

=== 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
|205\476
|516.81
|27/20
|[[Gravity]]
|-
|2
|205\476 (33\476)
|516.81 (83.19)
|27/20 (21/20)
|[[Harry]]
|-
|28
|197\476 (6\476)
|496.64 (15.13)
|4/3 (105/104)
|[[Oquatonic]]
|}

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