337edo - 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"

2026-03-13T13:31:31Z

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 73:		Line 73:
	\| [[Sqrtphi]] (337, 11-limit)		\| [[Sqrtphi]] (337, 11-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 12:51, 21 February 2025

2025-02-21T12:51:08Z

← Older revision		Revision as of 12:51, 21 February 2025
Line 26:		Line 26:
	\| {{monzo\| -534 337 }}		\| {{monzo\| -534 337 }}
	\| {{mapping\| 337 534 }}		\| {{mapping\| 337 534 }}
	\| 0.1487		\| +0.1487
	\| 0.1487		\| 0.1487
	\| 4.18		\| 4.18
Line 33:		Line 33:
	\| 15625/15552, {{monzo\| -88 57 -1 }}		\| 15625/15552, {{monzo\| -88 57 -1 }}
	\| {{mapping\| 337 534 782 }}		\| {{mapping\| 337 534 782 }}
	\| 0.3495		\| +0.3495
	\| 0.3089		\| 0.3089
	\| 8.67		\| 8.67
Line 40:		Line 40:
	\| 15625/15552, 16875/16807, 7381125/7340032		\| 15625/15552, 16875/16807, 7381125/7340032
	\| {{mapping\| 337 534 782 946 }}		\| {{mapping\| 337 534 782 946 }}
	\| 0.2870		\| +0.2870
	\| 0.2886		\| 0.2886
	\| 8.10		\| 8.10

Francium: changed EDO intro to ED intro

2025-02-21T05:58:43Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:58, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|337~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:02, 15 January 2025

2025-01-15T16:02:21Z

← Older revision		Revision as of 16:02, 15 January 2025
Line 73:		Line 73:
	\| [[Sqrtphi]] (337, 11-limit)		\| [[Sqrtphi]] (337, 11-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

2024-11-16T13:15:24Z

Partial undo

← Older revision		Revision as of 13:15, 16 November 2024
Line 12:		Line 12:

	== 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]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 34:		Line 43:
	\| 0.2886		\| 0.2886
	\| 8.10		\| 8.10
	~~{{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
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	\| 14/11		\| 14/11
	\| [[Sqrtphi]] (337, 11-limit)		\| [[Sqrtphi]] (337, 11-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 01:48, 16 November 2024

2024-11-16T01:48:19Z

← Older revision		Revision as of 01:48, 16 November 2024
Line 12:		Line 12:

	== 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]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
Line 43:		Line 34:
	\| 0.2886		\| 0.2886
	\| 8.10		\| 8.10
	\|}		{{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 72:		Line 56:
	\| 14/11		\| 14/11
	\| [[Sqrtphi]] (337, 11-limit)		\| [[Sqrtphi]] (337, 11-limit)
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 01:08, 16 November 2024

2024-11-16T01:08:50Z

← Older revision		Revision as of 01:08, 16 November 2024
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\|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 46:		Line 47:
	=== 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 71:		Line 73:
	\| [[Sqrtphi]] (337, 11-limit)		\| [[Sqrtphi]] (337, 11-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]]		; [[Francium]]
	* "The End Of A Good Day" from ''Mysteries'' (2023) – [https://open.spotify.com/track/1yaSXn4u2TVWClwXBtMVs4 Spotify] \| [https://francium223.bandcamp.com/track/the-end-of-a-good-day Bandcamp] \| [https://www.youtube.com/watch?v=2ixL8YQmJig YouTube]		* "The End Of A Good Day" from ''Mysteries'' (2023) – [https://open.spotify.com/track/1yaSXn4u2TVWClwXBtMVs4 Spotify] \| [https://francium223.bandcamp.com/track/the-end-of-a-good-day Bandcamp] \| [https://www.youtube.com/watch?v=2ixL8YQmJig YouTube]

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

Francium: +categories

2024-02-13T18:01:20Z

+categories

← Older revision		Revision as of 18:01, 13 February 2024
Line 76:		Line 76:
	; [[Francium]]		; [[Francium]]
	* "The End Of A Good Day" from ''Mysteries'' (2023) – [https://open.spotify.com/track/1yaSXn4u2TVWClwXBtMVs4 Spotify] \| [https://francium223.bandcamp.com/track/the-end-of-a-good-day Bandcamp] \| [https://www.youtube.com/watch?v=2ixL8YQmJig YouTube]		* "The End Of A Good Day" from ''Mysteries'' (2023) – [https://open.spotify.com/track/1yaSXn4u2TVWClwXBtMVs4 Spotify] \| [https://francium223.bandcamp.com/track/the-end-of-a-good-day Bandcamp] \| [https://www.youtube.com/watch?v=2ixL8YQmJig YouTube]

			[[Category:Listen]]

FloraC: Review + 1

2024-01-22T07:22:32Z

Review + 1

← Older revision		Revision as of 07:22, 22 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	337edo is [[consistent]] to the [[9-odd-limit]], but the error of [[harmonic]] [[5/1\|5]] is quite large. If the harmonic is used at all, it tends very flat. The equal temperament [[tempering out\|tempers out]] [[16875/16807]], 420175/419904, and 5250987/5242880 in the 7-limit. It [[support]]s ~~the~~ [[~~kleirtismic~~]] ~~temperament~~.		337edo is [[consistent]] to the [[9-odd-limit]], but the error of [[harmonic]] [[5/1\|5]] is quite large. If the harmonic is used at all, it tends very flat. The equal temperament [[tempering out\|tempers out]] [[16875/16807]], [[420175/419904]], and 5250987/5242880 in the 7-limit. It [[support]]s [[tokko]] and [[sqrtphi]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 43:		Line 43:
	\| 8.10		\| 8.10
	\|}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
Line 63:		Line 64:
	\| 6/5		\| 6/5
	\| [[Hanson]]		\| [[Hanson]]
			\|-
			\| 1
			\| 117\337
			\| 416.62
			\| 14/11
			\| [[Sqrtphi]] (337, 11-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
Line 68:		Line 75:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "The End Of A Good Day" from ''Mysteries'' (2023) [https://open.spotify.com/track/1yaSXn4u2TVWClwXBtMVs4 Spotify] \| [https://francium223.bandcamp.com/track/the-end-of-a-good-day Bandcamp] \| [https://www.youtube.com/watch?v=2ixL8YQmJig YouTube]		* "The End Of A Good Day" from ''Mysteries'' (2023) – [https://open.spotify.com/track/1yaSXn4u2TVWClwXBtMVs4 Spotify] \| [https://francium223.bandcamp.com/track/the-end-of-a-good-day Bandcamp] \| [https://www.youtube.com/watch?v=2ixL8YQmJig YouTube]

Francium: /* Music */

2023-11-20T05:35:48Z

Music

← Older revision		Revision as of 05:35, 20 November 2023
Line 68:		Line 68:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "The End Of A Good Day" from ''Mysteries'' [https://open.spotify.com/track/1yaSXn4u2TVWClwXBtMVs4 Spotify] \| [https://francium223.bandcamp.com/track/the-end-of-a-good-day Bandcamp] \| [https://www.youtube.com/watch?v=2ixL8YQmJig YouTube]		* "The End Of A Good Day" from ''Mysteries'' (2023) [https://open.spotify.com/track/1yaSXn4u2TVWClwXBtMVs4 Spotify] \| [https://francium223.bandcamp.com/track/the-end-of-a-good-day Bandcamp] \| [https://www.youtube.com/watch?v=2ixL8YQmJig YouTube]