424edo - Revision history

ArrowHead294 at 12:39, 21 February 2025

2025-02-21T12:39:39Z

← Older revision		Revision as of 12:39, 21 February 2025
Line 13:		Line 13:
	== 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]]
	! 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]] (%)

Francium: changed EDO intro to ED intro

2025-02-21T06:06:30Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:06, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|424~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Review

2024-01-01T11:33:49Z

Review

← Older revision		Revision as of 11:33, 1 January 2024
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	== Theory ==		== Theory ==
	~~424et~~ is consistent to the [[9-odd-limit]] ~~and~~ the harmonic 5 is halfway between its steps. It ~~tempers out~~ [[~~32805/32768~~]] in the 5-limit~~; 184528125/184473632, 2460375/2458624, 1280000000/1275989841~~, [[~~2401~~/~~2400~~]] ~~and 5250987/5242880 in the 7-limit~~, ~~supporting~~ [[~~enki~~]].		424edo is [[consistent]] to the [[9-odd-limit]], but the [[harmonic]] [[5/1\|5]] is about halfway between its steps. It is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning as [[212edo]]. The approximation to [[11/1\|11]], although closer to just than 212edo's, tends sharp, so its improvement is debatable. All things considered, a 2.3.13.17.19.23 [[subgroup]] interpretation with optional additions of 7, 11, or both, seems most reasonable.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	424 factors into 2<sup>3</sup> × 53, ~~with~~ subset edos {{EDOs\|2, 4, 8, 53, 106, and 212}}. [[848edo]], which doubles it, gives a good correction to the harmonic 11.		Since 424 factors into 2<sup>3</sup> × 53, 424edo has subset edos {{EDOs\| 2, 4, 8, 53, 106, and 212 }}. [[848edo]], which doubles it, gives a good correction to the harmonic 5.

	== 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		\| 2.3.7.11
	\|{{monzo\|-~~84 53~~}}		\| 41503/41472, 117649/117128, {{monzo\| -26 19 1 -2 }}
	\|{{mapping\|424 672}}		\| {{mapping\| 424 672 1190 1467 }}
	\| 0.~~0215~~		\| +0.0499
	\| 0.~~0215~~		\| 0.1747
	\| 0.76		\| 6.17
	\|}		\|}

Francium: /* Subsets and supersets */

2023-12-22T16:38:40Z

Subsets and supersets

← Older revision		Revision as of 16:38, 22 December 2023
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	424 factors into 2<sup>3</sup> × 53, with subset edos {{2, 4, 8, 53, 106, and 212}}. [[848edo]], which doubles it, gives a good correction to the harmonic 11.		424 factors into 2<sup>3</sup> × 53, with subset edos {{EDOs\|2, 4, 8, 53, 106, and 212}}. [[848edo]], which doubles it, gives a good correction to the harmonic 11.

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

Francium: Created page with "{{Infobox ET}} {{EDO intro|424}} == Theory == 424et is consistent to the 9-odd-limit and the harmonic 5 is halfway between its steps. It tempers out 32805/32768 in th..."

2023-12-22T16:38:20Z

Created page with "{{Infobox ET}} {{EDO intro|424}} == Theory == 424et is consistent to the 9-odd-limit and the harmonic 5 is halfway between its steps. It tempers out 32805/32768 in th..."

New page

{{Infobox ET}}
{{EDO intro|424}}

== Theory ==
424et is consistent to the [[9-odd-limit]] and the harmonic 5 is halfway between its steps. It tempers out [[32805/32768]] in the 5-limit; 184528125/184473632, 2460375/2458624, 1280000000/1275989841, [[2401/2400]] and 5250987/5242880 in the 7-limit, supporting [[enki]].

=== Odd harmonics ===
{{Harmonics in equal|424}}

=== Subsets and supersets ===
424 factors into 2<sup>3</sup> × 53, with subset edos {{2, 4, 8, 53, 106, and 212}}. [[848edo]], which doubles it, gives a good correction to the harmonic 11.

== 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|-84 53}}
|{{mapping|424 672}}
| 0.0215
| 0.0215
| 0.76
|}

← Older revision		Revision as of 12:39, 21 February 2025
Line 13:		Line 13:
	== 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]]
	! 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]] (%)