2048edo - Revision history

ArrowHead294 at 23:06, 20 February 2025

2025-02-20T23:06:55Z

← Older revision		Revision as of 23:06, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|2048~~}}		{{ED intro}}

	== Theory ==		== Theory ==
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	== 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]]
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	\| {{monzo\| 54 -37 2 }}, {{monzo\| -111 -12 56 }}		\| {{monzo\| 54 -37 2 }}, {{monzo\| -111 -12 56 }}
	\| {{mapping\| 2048 3246 4755 }}		\| {{mapping\| 2048 3246 4755 }}
	\| 0.0264		\| +0.0264
	\| 0.0364		\| 0.0364
	\| 6.22		\| 6.22
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	\| 2401/2400, {{monzo\| -18 -13 13 3 }}, {{monzo\| 49 -38 0 4 }}		\| 2401/2400, {{monzo\| -18 -13 13 3 }}, {{monzo\| 49 -38 0 4 }}
	\| {{mapping\| 2048 3246 4755 5749 }}		\| {{mapping\| 2048 3246 4755 5749 }}
	\| 0.0439		\| +0.0439
	\| 0.0438		\| 0.0438
	\| 7.48		\| 7.48
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	\| 2401/2400, 1890625/1889568, 1953125/1951488, 117440512/117406179		\| 2401/2400, 1890625/1889568, 1953125/1951488, 117440512/117406179
	\| {{mapping\| 2048 3246 4755 5749 7085 }}		\| {{mapping\| 2048 3246 4755 5749 7085 }}
	\| 0.0323		\| +0.0323
	\| 0.0456		\| 0.0456
	\| 7.78		\| 7.78

FloraC: +MET-24

2024-11-30T15:00:05Z

+MET-24

← Older revision		Revision as of 15:00, 30 November 2024
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	\| 7.78		\| 7.78
	\|}		\|}

			== Scales ==
			* [[MET-24]]

FloraC: +subset edos

2023-10-30T11:08:10Z

+subset edos

← Older revision		Revision as of 11:08, 30 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	2048edo has an excellent [[3/2\|perfect fifth]], which derives from [[1024edo]]. It tempers out the breedsma ([[2401/2400]]) in the 7-limit, and supports the rank-3 breed temperament.		2048edo has an excellent [[3/2\|perfect fifth]], which derives from [[1024edo]]. It [[tempering out\|tempers out]] the breedsma ([[2401/2400]]) in the 7-limit, and supports the rank-3 breed temperament.

	2048edo is usable as high as 43-limit, with the 2048f val regular temperament having an error of 0.023 cents (0.04 edosteps) per octave, and the no-13's limit patent val is unambiguous and has an error of only 0.019 cents/octave.		2048edo is usable as high as 43-limit, with the 2048f val regular temperament having an error of 0.023 cents (0.04 edosteps) per octave, and the no-13's limit patent val is unambiguous and has an error of only 0.019 cents/octave.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	2048edo is the 11th-power-of-two edo.		2048edo is the 11th-power-of-two edo, with subset edos {{EDOs\| 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024 }}.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: Cleanup; -redundant categories

2023-10-15T13:32:03Z

Cleanup; -redundant categories

← Older revision		Revision as of 13:32, 15 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~{{Harmonics in equal\|2048}}~~		2048edo has an excellent [[3/2\|perfect fifth]], which derives from [[1024edo]]. It tempers out the breedsma ([[2401/2400]]) in the 7-limit, and supports the rank-3 breed temperament.
	2048edo has an excellent perfect fifth, which derives from 1024edo. It tempers out the breedsma (2401/2400) in the 7-limit, and supports the rank 3 breed temperament.

	2048edo is usable as high as 43-limit, with the 2048f val regular temperament having an error of 0.023 cents (0.04 edosteps) per octave, and the no-~~13s~~ limit patent val is unambiguous and has an error of only 0.019 cents/octave.		2048edo is usable as high as 43-limit, with the 2048f val regular temperament having an error of 0.023 cents (0.04 edosteps) per octave, and the no-13's limit patent val is unambiguous and has an error of only 0.019 cents/octave.

	2048edo is the ~~11th power of two EDO~~.		In the 5-limit, it supports [[monzismic]] temperament. In the 11-limit, 2048edo tempers out the [[quartisma]].

	~~In the 5-limit, it supports [[monzismic]] temperament.~~		=== Prime harmonics ===
			{{Harmonics in equal\|2048}}

	In the 11-~~limit, 2048edo tempers out the [[quartisma]]~~.		=== Subsets and supersets ===
			2048edo is the 11th-power-of-two edo.

	== 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]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	8ve ~~stretch~~ (¢)		! colspan="2" \| Tuning Error
	! colspan="2" \|Tuning ~~error~~
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|54, -37, 2}},{{monzo\|-111, -12, 56}}		\| {{monzo\| 54 -37 2 }}, {{monzo\| -111 -12 56 }}
	\|[{{~~val~~\|2048 3246 4755}}]		\| {{mapping\| 2048 3246 4755 }}
	\|0.0264		\| 0.0264
	\|0.0364		\| 0.0364
	\|6.22		\| 6.22
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|2401/2400, {{monzo\|-18, -13, 13, 3}}, {{monzo\|49, -38, 0, 4}}		\| 2401/2400, {{monzo\| -18 -13 13 3 }}, {{monzo\| 49 -38 0 4 }}
	\|[{{~~val~~\|2048 3246 4755 5749}}]		\| {{mapping\| 2048 3246 4755 5749 }}
	\|0.0439		\| 0.0439
	\|0.0438		\| 0.0438
	\|7.48		\| 7.48
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|2401/2400, 1890625/1889568, 1953125/1951488, 117440512/117406179		\| 2401/2400, 1890625/1889568, 1953125/1951488, 117440512/117406179
	\|[{{~~val~~\|2048 3246 4755 5749 7085}}]		\| {{mapping\| 2048 3246 4755 5749 7085 }}
	\|0.0323		\| 0.0323
	\|0.0456		\| 0.0456
	\|7.78		\| 7.78
	\|}		\|}

	~~[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->~~

BudjarnLambeth at 07:00, 9 July 2023

2023-07-09T07:00:34Z

← Older revision		Revision as of 07:00, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2048}}		{{EDO intro\|2048}}

BudjarnLambeth at 04:39, 9 July 2023

2023-07-09T04:39:37Z

← Older revision		Revision as of 04:39, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|2048}}		{{EDO intro\|2048}}

Plumtree: Infobox ET added

2022-10-04T22:14:40Z

Infobox ET added

← Older revision		Revision as of 22:14, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	{{EDO intro\|2048}}		{{EDO intro\|2048}}

Eliora: /* Regular temperament properties */

2022-08-30T11:51:50Z

Regular temperament properties

← Older revision		Revision as of 11:51, 30 August 2022
Line 8:		Line 8:

	2048edo is the 11th power of two EDO.		2048edo is the 11th power of two EDO.

			In the 5-limit, it supports [[monzismic]] temperament.

	In the 11-limit, 2048edo tempers out the [[quartisma]].		In the 11-limit, 2048edo tempers out the [[quartisma]].
Line 26:		Line 28:
	\|{{monzo\|54, -37, 2}},{{monzo\|-111, -12, 56}}		\|{{monzo\|54, -37, 2}},{{monzo\|-111, -12, 56}}
	\|[{{val\|2048 3246 4755}}]		\|[{{val\|2048 3246 4755}}]
	\|		\|0.0264
	\|		\|0.0364
	\|		\|6.22
	\|-		\|-
	\|2.3.5.7		\|2.3.5.7
	\|2401/2400, {{monzo\|-18, -13, 13, 3}}, {{monzo\|49, -38, 0, 4}}		\|2401/2400, {{monzo\|-18, -13, 13, 3}}, {{monzo\|49, -38, 0, 4}}
	\|[{{val\|2048 3246 4755 5749}}]		\|[{{val\|2048 3246 4755 5749}}]
	\|		\|0.0439
	\|		\|0.0438
	\|		\|7.48
	\|-		\|-
	\|2.3.5.7.11		\|2.3.5.7.11
	\|2401/2400, 1890625/1889568, 1953125/1951488, 117440512/117406179		\|2401/2400, 1890625/1889568, 1953125/1951488, 117440512/117406179
	\|[{{val\|2048 3246 4755 5749 7085}}]		\|[{{val\|2048 3246 4755 5749 7085}}]
	\|		\|0.0323
	\|		\|0.0456
	\|		\|7.78
	\|}		\|}

	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->

Eliora at 11:45, 30 August 2022

2022-08-30T11:45:07Z

← Older revision		Revision as of 11:45, 30 August 2022
Line 8:		Line 8:

	2048edo is the 11th power of two EDO.		2048edo is the 11th power of two EDO.

			In the 11-limit, 2048edo tempers out the [[quartisma]].

	== Regular temperament properties ==		== Regular temperament properties ==
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	\|2401/2400, {{monzo\|-18, -13, 13, 3}}, {{monzo\|49, -38, 0, 4}}		\|2401/2400, {{monzo\|-18, -13, 13, 3}}, {{monzo\|49, -38, 0, 4}}
	\|[{{val\|2048 3246 4755 5749}}]		\|[{{val\|2048 3246 4755 5749}}]
			\|
			\|
			\|
			\|-
			\|2.3.5.7.11
			\|2401/2400, 1890625/1889568, 1953125/1951488, 117440512/117406179
			\|[{{val\|2048 3246 4755 5749 7085}}]
	\|		\|
	\|		\|

Fredg999 category edits: Sort key

2022-07-04T01:25:22Z

Sort key

← Older revision		Revision as of 01:25, 4 July 2022
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	\|		\|
	\|}		\|}
	[[Category:Equal divisions of the octave]]
			[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->