457edo - 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"

2026-03-13T13:33:11Z

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 13:33, 13 March 2026
Line 94:		Line 94:
	\| [[Tritriple]]		\| [[Tritriple]]
	\|}		\|}
	<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 ==

Francium: changed EDO intro to ED intro

2025-02-21T06:09:37Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:09, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|457~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */

2025-01-17T16:20:26Z

Theory

← Older revision		Revision as of 16:20, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	457edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1\|3]] is quite large. As an equal temperament, it [[tempers out]] [[19683/19600]] and [[65625/65536]] in the 7-limit; [[540/539]], [[8019/8000]], and 43923/43904 in the 11-limit.		457edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1\|3]] is quite large. As an equal temperament, it [[tempering out\|tempers out]] [[19683/19600]] and [[65625/65536]] in the [[7-limit]]; [[540/539]], [[8019/8000]], and 43923/43904 in the [[11-limit]].

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: /* Theory */ cleanup

2025-01-17T16:18:50Z

Theory: cleanup

← Older revision		Revision as of 16:18, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	457edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1\|3]] is quite large. It [[tempers out]] [[19683/19600]] and [[65625/65536]] in the 7-limit; [[540/539]], [[8019/8000]], and 43923/43904 in the 11-limit.		457edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1\|3]] is quite large. As an equal temperament, it [[tempers out]] [[19683/19600]] and [[65625/65536]] in the 7-limit; [[540/539]], [[8019/8000]], and 43923/43904 in the 11-limit.

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	457edo is the 88th [[prime edo]].		457edo is the 88th [[prime edo]].

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

ArrowHead294 at 19:32, 15 January 2025

2025-01-15T19:32:53Z

← Older revision		Revision as of 19:32, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	457edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1\|3]] is quite large. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] [[19683/19600]] and [[65625/65536]] in the 7-limit; [[540/539]], [[8019/8000]], and 43923/43904 in the 11-limit.		457edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1\|3]] is quite large. It [[tempers out]] [[19683/19600]] and [[65625/65536]] in the 7-limit; [[540/539]], [[8019/8000]], and 43923/43904 in the 11-limit.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 26:		Line 26:
	\| {{monzo\| -724 457 }}		\| {{monzo\| -724 457 }}
	\| {{mapping\| 457 724 }}		\| {{mapping\| 457 724 }}
	\| 0.2716		\| +0.2716
	\| 0.2716		\| 0.2716
	\| 10.34		\| 10.34
Line 33:		Line 33:
	\| {{monzo\| -36 11 8 }}, {{monzo\| -5 31 -19 }}		\| {{monzo\| -36 11 8 }}, {{monzo\| -5 31 -19 }}
	\| {{mapping\| 457 724 1061 }}		\| {{mapping\| 457 724 1061 }}
	\| 0.2267		\| +0.2267
	\| 0.2307		\| 0.2307
	\| 8.79		\| 8.79
Line 40:		Line 40:
	\| 19683/19600, 65625/65536, 7381125/7340032		\| 19683/19600, 65625/65536, 7381125/7340032
	\| {{mapping\| 457 724 1061 1283 }}		\| {{mapping\| 457 724 1061 1283 }}
	\| 0.1609		\| +0.1609
	\| 0.2300		\| 0.2300
	\| 8.76		\| 8.76
Line 47:		Line 47:
	\| 540/539, 8019/8000, 19683/19600, 43923/43904		\| 540/539, 8019/8000, 19683/19600, 43923/43904
	\| {{mapping\| 457 724 1061 1283 1581 }}		\| {{mapping\| 457 724 1061 1283 1581 }}
	\| 0.1227		\| +0.1227
	\| 0.2194		\| 0.2194
	\| 8.36		\| 8.36
Line 54:		Line 54:
	\| 540/539, 1716/1715, 4225/4224, 41067/40960, 43940/43923		\| 540/539, 1716/1715, 4225/4224, 41067/40960, 43940/43923
	\| {{mapping\| 457 724 1061 1283 1581 1691 }}		\| {{mapping\| 457 724 1061 1283 1581 1691 }}
	\| 0.1142		\| +0.1142
	\| 0.2012		\| 0.2012
	\| 7.66		\| 7.66
Line 61:		Line 61:
	\| 936/935, 1089/1088, 1275/1274, 1575/1573, 2601/2600, 4225/4224		\| 936/935, 1089/1088, 1275/1274, 1575/1573, 2601/2600, 4225/4224
	\| {{mapping\| 457 724 1061 1283 1581 1691 1868 }}		\| {{mapping\| 457 724 1061 1283 1581 1691 1868 }}
	\| 0.0952		\| +0.0952
	\| 0.1920		\| 0.1920
	\| 7.31		\| 7.31
Line 94:		Line 94:
	\| [[Tritriple]]		\| [[Tritriple]]
	\|}		\|}
	<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 ==
	; [[Francium]]		; [[Francium]]
	* "Less and Less" from ''Take Advantage'' (2024) ~~–~~ [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] \| [https://francium223.bandcamp.com/track/less-and-less Bandcamp] \| [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]		* "Less and Less" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] \| [https://francium223.bandcamp.com/track/less-and-less Bandcamp] \| [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]
	* "Porcelain Stoneware" from ''Scoop'' (2024) ~~–~~ [https://open.spotify.com/track/055lRdMBKr37MU8HQqlvus Spotify] \| [https://francium223.bandcamp.com/track/porcelain-stoneware Bandcamp] \| [https://www.youtube.com/watch?v=bzycN6PYMQQ YouTube]		* "Porcelain Stoneware" from ''Scoop'' (2024) – [https://open.spotify.com/track/055lRdMBKr37MU8HQqlvus Spotify] \| [https://francium223.bandcamp.com/track/porcelain-stoneware Bandcamp] \| [https://www.youtube.com/watch?v=bzycN6PYMQQ YouTube]

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

ArrowHead294: Partial undo

2024-11-16T13:01:58Z

Partial undo

← Older revision		Revision as of 13:01, 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 55:		Line 64:
	\| 0.1920		\| 0.1920
	\| 7.31		\| 7.31
	~~{{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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	\| 864/625		\| 864/625
	\| [[Tritriple]]		\| [[Tritriple]]
	~~{{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 02:49, 16 November 2024

2024-11-16T02:49:39Z

← Older revision		Revision as of 02:49, 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 63:		Line 55:
	\| 0.1920		\| 0.1920
	\| 7.31		\| 7.31
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\| 864/625		\| 864/625
	\| [[Tritriple]]		\| [[Tritriple]]
	\|}		{{rank-2 end}}
	~~<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]]
	* "Less and Less" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] \| [https://francium223.bandcamp.com/track/less-and-less Bandcamp] \| [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]		* "Less and Less" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] \| [https://francium223.bandcamp.com/track/less-and-less Bandcamp] \| [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]
	* "Porcelain Stoneware" from ''Scoop'' (2024) – [https://open.spotify.com/track/055lRdMBKr37MU8HQqlvus Spotify] \| [https://francium223.bandcamp.com/track/porcelain-stoneware Bandcamp] \| [https://www.youtube.com/watch?v=bzycN6PYMQQ YouTube]		* "Porcelain Stoneware" from ''Scoop'' (2024) – [https://open.spotify.com/track/055lRdMBKr37MU8HQqlvus Spotify] \| [https://francium223.bandcamp.com/track/porcelain-stoneware Bandcamp] \| [https://www.youtube.com/watch?v=bzycN6PYMQQ YouTube]

			[[Category:Listen]]

Francium: /* Music */ +music

2024-11-12T13:34:18Z

Music: +music

← Older revision		Revision as of 13:34, 12 November 2024
Line 97:		Line 97:
	; [[Francium]]		; [[Francium]]
	* "Less and Less" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] \| [https://francium223.bandcamp.com/track/less-and-less Bandcamp] \| [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]		* "Less and Less" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] \| [https://francium223.bandcamp.com/track/less-and-less Bandcamp] \| [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]
			* "Porcelain Stoneware" from ''Scoop'' (2024) – [https://open.spotify.com/track/055lRdMBKr37MU8HQqlvus Spotify] \| [https://francium223.bandcamp.com/track/porcelain-stoneware Bandcamp] \| [https://www.youtube.com/watch?v=bzycN6PYMQQ YouTube]

Francium: +music

2024-09-14T18:58:10Z

+music

← Older revision		Revision as of 18:58, 14 September 2024
Line 93:		Line 93:
	\|}		\|}
	<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

			== Music ==
			; [[Francium]]
			* "Less and Less" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] \| [https://francium223.bandcamp.com/track/less-and-less Bandcamp] \| [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]

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

2023-11-03T07:12:54Z

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

← Older revision		Revision as of 07:12, 3 November 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|457}}		{{EDO intro\|457}}

	== Theory ==		== Theory ==
	~~457et~~ tempers out ~~283115520~~/~~282475249, 1220703125/1219784832, 26873856/26796875,~~ [[65625/65536]] ~~and 200120949/200000000~~ in the 7-limit; ~~95703125/95664294, 100663296/100656875, 161280/161051, 29296875/29218112, 166698/166375, 1953125/1951488, 151263/151250, 2359296/2358125,~~ [[540/539]]~~, 5767168/5764801, 825000/823543~~, [[8019/8000]], ~~160083/160000, 16808715/16777216, 539055/537824, 244515348/244140625, 67110351/67108864~~ and 43923/43904 in the 11-limit.		457edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1\|3]] is quite large. The equal temperament [[tempering out\|tempers out]] [[19683/19600]] and [[65625/65536]] in the 7-limit; [[540/539]], [[8019/8000]], and 43923/43904 in the 11-limit.
	===Odd harmonics===
			=== Odd harmonics ===
	{{Harmonics in equal\|457}}		{{Harmonics in equal\|457}}
	===Subsets and supersets===
			=== Subsets and supersets ===
	457edo is the 88th [[prime edo]].		457edo is the 88th [[prime 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\|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\|-724 457}}		\| {{monzo\| -724 457 }}
	\|{{~~val~~\|457 724}}		\| {{mapping\| 457 724 }}
	\| 0.2716		\| 0.2716
	\| 0.2716		\| 0.2716
	\| 10.34		\| 10.34
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|-36 11 8}}, {{monzo\|-5 31 -19}}		\| {{monzo\| -36 11 8 }}, {{monzo\| -5 31 -19 }}
	\|{{~~val~~\|457 724 1061}}		\| {{mapping\| 457 724 1061 }}
	\| 0.2267		\| 0.2267
	\| 0.2307		\| 0.2307
	\| 8.79		\| 8.79
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|19683/19600, 65625/65536, 7381125/7340032		\| 19683/19600, 65625/65536, 7381125/7340032
	\|{{~~val~~\|457 724 1061 1283}}		\| {{mapping\| 457 724 1061 1283 }}
	\| 0.1609		\| 0.1609
	\| 0.2300		\| 0.2300
	\| 8.76		\| 8.76
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|540/539, 8019/8000, 19683/19600, 43923/43904		\| 540/539, 8019/8000, 19683/19600, 43923/43904
	\|{{~~val~~\|457 724 1061 1283 1581}}		\| {{mapping\| 457 724 1061 1283 1581 }}
	\| 0.1227		\| 0.1227
	\| 0.2194		\| 0.2194
	\| 8.36		\| 8.36
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|540/539, 1716/1715, 4225/4224, 41067/40960, 43940/43923		\| 540/539, 1716/1715, 4225/4224, 41067/40960, 43940/43923
	\|{{~~val~~\|457 724 1061 1283 1581 1691}}		\| {{mapping\| 457 724 1061 1283 1581 1691 }}
	\| 0.1142		\| 0.1142
	\| 0.2012		\| 0.2012
	\| 7.66		\| 7.66
	\|-		\|-
	\|2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\|936/935, 1089/1088, 1275/1274, 1575/1573, 2601/2600, 4225/4224		\| 936/935, 1089/1088, 1275/1274, 1575/1573, 2601/2600, 4225/4224
	\|{{~~val~~\|457 724 1061 1283 1581 1691 1868}}		\| {{mapping\| 457 724 1061 1283 1581 1691 1868 }}
	\| 0.0952		\| 0.0952
	\| 0.1920		\| 0.1920
Line 65:		Line 69:
	\|+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
	\|10\457		\| 10\457
	\|26.258		\| 26.258
	\|49/48		\| 49/48
	\|[[Sfourth]]		\| [[Sfourth]]
	\|-		\|-
	\|1		\| 1
	\|136\457		\| 136\457
	\|357.11		\| 357.11
	\|49/40		\| 49/40
	\|[[Dodifo]]		\| [[Dodifo]]
	\|-		\|-
	\|1		\| 1
	\|213\457		\| 213\457
	\|559.30		\| 559.30
	\|864/625		\| 864/625
	\|[[Tritriple]]		\| [[Tritriple]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct