449edo - 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"

2026-03-13T13:32:37Z

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 49:		Line 49:
	\| [[Amity]] (7-limit)		\| [[Amity]] (7-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

	== Music ==		== Music ==

ArrowHead294 at 12:54, 21 February 2025

2025-02-21T12:54:50Z

← Older revision		Revision as of 12:54, 21 February 2025
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	\| {{monzo\| -1423 449 }}		\| {{monzo\| -1423 449 }}
	\| {{mapping\| 449 1423 }}		\| {{mapping\| 449 1423 }}
	\| 0.1249		\| +0.1249
	\| 0.1249		\| 0.1249
	\| 4.67		\| 4.67

Francium: changed EDO intro to ED intro

2025-02-21T05:54:14Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:54, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|449~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:16, 15 January 2025

2025-01-15T16:16:55Z

← Older revision		Revision as of 16:16, 15 January 2025
Line 49:		Line 49:
	\| [[Amity]] (7-limit)		\| [[Amity]] (7-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

	== Music ==		== Music ==

ArrowHead294: Partial undo

2024-11-16T13:18:05Z

Partial undo

← Older revision		Revision as of 13:18, 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 22:		Line 31:
	\| 0.1249		\| 0.1249
	\| 4.67		\| 4.67
	~~{{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 32:		Line 48:
	\| 243\200		\| 243\200
	\| [[Amity]] (7-limit)		\| [[Amity]] (7-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

	== Music ==		== Music ==

ArrowHead294 at 01:41, 16 November 2024

2024-11-16T01:41:23Z

← Older revision		Revision as of 01:41, 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 31:		Line 22:
	\| 0.1249		\| 0.1249
	\| 4.67		\| 4.67
	\|}		{{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
Line 48:		Line 32:
	\| 243\200		\| 243\200
	\| [[Amity]] (7-limit)		\| [[Amity]] (7-limit)
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 01:00, 16 November 2024

2024-11-16T01:00:07Z

← Older revision		Revision as of 01:00, 16 November 2024
Line 15:		Line 15:
	== 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 34:		Line 35:
	=== 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
	\|-		\|-
Line 47:		Line 49:
	\| [[Amity]] (7-limit)		\| [[Amity]] (7-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~~		{{orf}}

	== Music ==		== Music ==

Francium: +categories

2024-02-13T18:11:53Z

+categories

← Older revision		Revision as of 18:11, 13 February 2024
Line 50:		Line 50:

	== Music ==		== Music ==
	; [[~~User:Francium\|~~Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=vLZuStkREoE ''Little Victorious Dance''] (2023)		* [https://www.youtube.com/watch?v=vLZuStkREoE ''Little Victorious Dance''] (2023)

			[[Category:Listen]]

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

2023-11-03T07:41:24Z

Cleanup; clarify the title row of the rank-2 temp table

← Older revision		Revision as of 07:41, 3 November 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|449}}		{{EDO intro\|449}}

	== Theory ==		== Theory ==
	~~449et tempers out 26873856/26796875 and~~ [[~~4375/4374~~]] in the 7-limit~~; 100663296~~/~~100656875~~, [[~~117440512~~/~~117406179~~]], ~~4302592~~/~~4296875~~, ~~825000/823543~~, ~~85937500~~/~~85766121, 160083~~/~~160000,~~ [[41503/41472]], 539055/537824 ~~and~~ 805255/802816 in the 11-limit.		449edo is [[consistent]] to the [[7-odd-limit]], but the errors of [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] are all quite large, giving us the option of treating it as a full 7-limit temperament, or a 2.9.15.21.11.13 [[subgroup]] temperament.
	===Odd harmonics===
			Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[4375/4374]] and 26873856/26796875 in the 7-limit; [[41503/41472]], 160083/160000, 539055/537824, 805255/802816, and 825000/823543 in the 11-limit.

			=== Odd harmonics ===
	{{Harmonics in equal\|449}}		{{Harmonics in equal\|449}}
	===Subsets and supersets===
			=== Subsets and supersets ===
	449edo is the 87th [[prime edo]]. 898edo, which doubles it, gives a good correction to the harmonic 3, 5 and 7.		449edo is the 87th [[prime edo]]. 898edo, which doubles it, gives a good correction to the harmonic 3, 5 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]] (%)
	\|-		\|-
	\|2.9		\| 2.9
	\|{{monzo\|-1423 449}}		\| {{monzo\| -1423 449 }}
	\|{{~~val~~\|449 1423}}		\| {{mapping\| 449 1423 }}
	\| 0.1249		\| 0.1249
	\| 0.1249		\| 0.1249
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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
	\|127\449		\| 127\449
	\|339.421		\| 339.421
	\|243\200		\| 243\200
	\|[[Amity]] (7-limit)		\| [[Amity]] (7-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

	== Music ==		== Music ==
	*[https://www.youtube.com/watch?v=vLZuStkREoE Little Victorious Dance] ~~by [[User:Francium\|Francium]]~~		; [[User:Francium\|Francium]]
			* [https://www.youtube.com/watch?v=vLZuStkREoE ''Little Victorious Dance''] (2023)

BudjarnLambeth at 06:35, 9 July 2023

2023-07-09T06:35:01Z

← Older revision		Revision as of 06:35, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|449}}		{{EDO intro\|449}}
	== Theory ==		== Theory ==