421edo - Revision history

ArrowHead294 at 12:47, 21 February 2025

2025-02-21T12:47:48Z

← Older revision		Revision as of 12:47, 21 February 2025
Line 24:		Line 24:
	== 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]] (%)
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	\| {{monzo\| -667 421 }}		\| {{monzo\| -667 421 }}
	\| {{mapping\| 421 667 }}		\| {{mapping\| 421 667 }}
	\| 0.2421		\| +0.2421
	\| 0.2421		\| 0.2421
	\| 8.49		\| 8.49
Line 43:		Line 44:
	\| {{monzo\| -44 26 1 }}, {{monzo\| 37 5 -16 }}		\| {{monzo\| -44 26 1 }}, {{monzo\| 37 5 -16 }}
	\| {{mapping\| 421 667 1182 }}		\| {{mapping\| 421 667 1182 }}
	\| 0.1263		\| +0.1263
	\| 0.2567		\| 0.2567
	\| 9.01		\| 9.01
Line 50:		Line 51:
	\| 88209/87808, 2893401/2883584, 208971104256/208422380089		\| 88209/87808, 2893401/2883584, 208971104256/208422380089
	\| {{mapping\| 421 667 1182 1456 }}		\| {{mapping\| 421 667 1182 1456 }}
	\| 0.1814		\| +0.1814
	\| 0.2419		\| 0.2419
	\| 8.49		\| 8.49
Line 57:		Line 58:
	\| 24192/24167, 53361/53248, 85293/85184, 88209/87808		\| 24192/24167, 53361/53248, 85293/85184, 88209/87808
	\| {{mapping\| 421 667 1182 1456 1558 }}		\| {{mapping\| 421 667 1182 1456 1558 }}
	\| 0.1274		\| +0.1274
	\| 0.2418		\| 0.2418
	\| 8.48		\| 8.48

Francium: changed EDO intro to ED intro

2025-02-21T06:01:53Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:01, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|421~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: /* Music */ +music

2024-09-29T12:04:36Z

Music: +music

← Older revision		Revision as of 12:04, 29 September 2024
Line 65:		Line 65:
	; [[Francium]]		; [[Francium]]
	* "Cuckoo Muskrat" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/0Gqr9upShTnDW0UXWbHoMK Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-muskrat Bandcamp] \| [https://www.youtube.com/watch?v=YFjcW-tiC-A YouTube]		* "Cuckoo Muskrat" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/0Gqr9upShTnDW0UXWbHoMK Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-muskrat Bandcamp] \| [https://www.youtube.com/watch?v=YFjcW-tiC-A YouTube]
			* "Smash" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/4BScJ5SmSlJWMohlDBvbkw Spotify] \| [https://francium223.bandcamp.com/track/smash Bandcamp] \| [https://www.youtube.com/watch?v=t-80EKfzxW8 YouTube]

	[[Category:Listen]]		[[Category:Listen]]

Francium: +music

2024-03-24T12:34:29Z

+music

← Older revision		Revision as of 12:34, 24 March 2024
Line 61:		Line 61:
	\| 8.48		\| 8.48
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "Cuckoo Muskrat" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/0Gqr9upShTnDW0UXWbHoMK Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-muskrat Bandcamp] \| [https://www.youtube.com/watch?v=YFjcW-tiC-A YouTube]

			[[Category:Listen]]

FloraC: Review

2024-01-21T09:50:20Z

Review

← Older revision		Revision as of 09:50, 21 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~421et~~ is ~~only~~ consistent to the [[3-odd-limit]], with its harmonic 5 being way too sharp. It is suitable for the 2.3.7.11.13.29.37 [[subgroup]], ~~tempering~~ out 638/637~~, 53361/53248, 88209/87808~~, [[5292/5291]], 24192/24167 and 85293/85184.		421edo is in[[consistent]] to the [[5-odd-limit]], with its [[harmonic]] [[5/1\|5]] being way too sharp. To start with, consider the following [[breed]]s:
			* {{val\| 421 667 '''977''' 1182 }} (421c)
			* {{val\| 421 667 '''977''' '''1181''' }} (421cd)
			* {{val\| 421 667 978 1182 }} ([[patent val]])

			The 421c val [[tempering out\|tempers out]] [[4375/4374]] and [[2100875/2097152]], [[support]]ing [[mitonic]].

			The 421cd val tempers out [[1029/1024]] and 823543/820125.

			The 421 val tempers out [[2401/2400]] and [[3136/3125]], supporting [[hemiwürschmidt]].

			Omitting harmonic 5, it is suitable for the 2.3.7.11.13.29.37 [[subgroup]], where it tempers out 638/637, [[5292/5291]], 24192/24167, 53361/53248, 88209/87808 and 85293/85184.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 13:		Line 24:
	== 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\|-667 421}}		\| {{monzo\| -667 421 }}
	\|{{mapping\|421 667}}		\| {{mapping\| 421 667 }}
	\| 0.2421		\| 0.2421
	\| 0.2421		\| 0.2421
	\| 8.49		\| 8.49
	\|-		\|-
	\|2.3.7		\| 2.3.7
	\|{{monzo\|-44 26 1}}, {{monzo\|37 5 -16}}		\| {{monzo\| -44 26 1 }}, {{monzo\| 37 5 -16 }}
	\|{{mapping\|421 667 1182}}		\| {{mapping\| 421 667 1182 }}
	\| 0.1263		\| 0.1263
	\| 0.2567		\| 0.2567
	\| 9.01		\| 9.01
	\|-		\|-
	\|2.3.7.11		\| 2.3.7.11
	\|88209/87808, 2893401/2883584, 208971104256/208422380089		\| 88209/87808, 2893401/2883584, 208971104256/208422380089
	\|{{mapping\|421 667 1182 1456}}		\| {{mapping\| 421 667 1182 1456 }}
	\| 0.1814		\| 0.1814
	\| 0.2419		\| 0.2419
	\| 8.49		\| 8.49
	\|-		\|-
	\|2.3.7.11.13		\| 2.3.7.11.13
	\|53361/53248, 88209/87808~~, 24192/24167, 85293/85184~~		\| 24192/24167, 53361/53248, 85293/85184, 88209/87808
	\|{{mapping\|421 667 1182 1456 1558}}		\| {{mapping\| 421 667 1182 1456 1558 }}
	\| 0.1274		\| 0.1274
	\| 0.2418		\| 0.2418
	\|8.48		\| 8.48
	\|}		\|}

Francium: Created page with "{{Infobox ET}} {{EDO intro|421}} == Theory == 421et is only consistent to the 3-odd-limit, with its harmonic 5 being way too sharp. It is suitable for the 2.3.7.11.13.29...."

2024-01-17T18:58:05Z

Created page with "{{Infobox ET}} {{EDO intro|421}} == Theory == 421et is only consistent to the 3-odd-limit, with its harmonic 5 being way too sharp. It is suitable for the 2.3.7.11.13.29...."

New page

{{Infobox ET}}
{{EDO intro|421}}

== Theory ==
421et is only consistent to the [[3-odd-limit]], with its harmonic 5 being way too sharp. It is suitable for the 2.3.7.11.13.29.37 [[subgroup]], tempering out 638/637, 53361/53248, 88209/87808, [[5292/5291]], 24192/24167 and 85293/85184.

=== Odd harmonics ===
{{Harmonics in equal|421}}

=== Subsets and supersets ===
421edo is the 82nd [[prime edo]]. [[1263edo]], which triples it, gives a good correction to the harmonic 5.

== 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|-667 421}}
|{{mapping|421 667}}
| 0.2421
| 0.2421
| 8.49
|-
|2.3.7
|{{monzo|-44 26 1}}, {{monzo|37 5 -16}}
|{{mapping|421 667 1182}}
| 0.1263
| 0.2567
| 9.01
|-
|2.3.7.11
|88209/87808, 2893401/2883584, 208971104256/208422380089
|{{mapping|421 667 1182 1456}}
| 0.1814
| 0.2419
| 8.49
|-
|2.3.7.11.13
|53361/53248, 88209/87808, 24192/24167, 85293/85184
|{{mapping|421 667 1182 1456 1558}}
| 0.1274
| 0.2418
|8.48
|}