523edo - 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"

2026-03-13T13:31:57Z

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 87:		Line 87:
	\| [[Amity]]		\| [[Amity]]
	\|}		\|}
	<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

2025-02-21T06:03:32Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:03, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|523~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 19:23, 15 January 2025

2025-01-15T19:23:40Z

← Older revision		Revision as of 19:23, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	523et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, [[6250/6237]], 42875/42768, [[19712/19683]], 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400 and 322102/321489 in the 11-limit.		523et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, [[6250/6237]], 42875/42768, [[19712/19683]], 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400, and 322102/321489 in the 11-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 26:		Line 26:
	\| {{monzo\|829 -523}}		\| {{monzo\|829 -523}}
	\| {{mapping\|523 829}}		\| {{mapping\|523 829}}
	\| ~~−0~~.0468		\| −0.0468
	\| 0.0468		\| 0.0468
	\| 2.04		\| 2.04
Line 87:		Line 87:
	\| [[Amity]]		\| [[Amity]]
	\|}		\|}
	<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]]
	* "(not) stuck" from ''hope in dark times'' (2024) ~~–~~ [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] \| [https://francium223.bandcamp.com/track/not-stuck Bandcamp] \| [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]		* "(not) stuck" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] \| [https://francium223.bandcamp.com/track/not-stuck Bandcamp] \| [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]

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

ArrowHead294: Partial undo

2024-11-16T13:10:11Z

Partial undo

← Older revision		Revision as of 13:10, 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 48:		Line 57:
	\| 0.1497		\| 0.1497
	\| 6.52		\| 6.52
	~~{{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
Line 70:		Line 86:
	\| 243/200		\| 243/200
	\| [[Amity]]		\| [[Amity]]
	~~{{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 02:10, 16 November 2024

2024-11-16T02:10:01Z

← Older revision		Revision as of 02:10, 16 November 2024
Line 5:		Line 5:
	523et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, [[6250/6237]], 42875/42768, [[19712/19683]], 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400 and 322102/321489 in the 11-limit.		523et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, [[6250/6237]], 42875/42768, [[19712/19683]], 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400 and 322102/321489 in the 11-limit.

	===Prime harmonics===		=== Prime harmonics ===
	{{Harmonics in equal\|523}}		{{Harmonics in equal\|523}}

	===Subsets and supersets===		=== Subsets and supersets ===
	523edo is the 99th [[prime edo]].		523edo is the 99th [[prime edo]].

	==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
	\|{{monzo\|829 -523}}		\| {{monzo\|829 -523}}
	\|{{mapping\|523 829}}		\| {{mapping\|523 829}}
	\| -0.0468		\| −0.0468
	\| 0.0468		\| 0.0468
	\| 2.04		\| 2.04
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|1600000/1594323, {{monzo\|-101 11 36}}		\| 1600000/1594323, {{monzo\|-101 11 36}}
	\|{{mapping\|523 829 1214}}		\| {{mapping\|523 829 1214}}
	\| +0.0901		\| +0.0901
	\| 0.1974		\| 0.1974
	\| 8.60		\| 8.60
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|2401/2400, 1600000/1594323, 341796875/339738624		\| 2401/2400, 1600000/1594323, 341796875/339738624
	\|{{mapping\|523 829 1214 1468}}		\| {{mapping\|523 829 1214 1468}}
	\| +0.1180		\| +0.1180
	\| 0.1776		\| 0.1776
	\| 7.74		\| 7.74
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|6250/6237, 2401/2400, 19712/19683, 166375/165888		\| 6250/6237, 2401/2400, 19712/19683, 166375/165888
	\|{{mapping\|523 829 1214 1468 1809}}		\| {{mapping\|523 829 1214 1468 1809}}
	\| +0.1319		\| +0.1319
	\| 0.1613		\| 0.1613
	\| 7.03		\| 7.03
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|2080/2079, 625/624, 4459/4455, 19712/19683, 50193/50176		\| 2080/2079, 625/624, 4459/4455, 19712/19683, 50193/50176
	\|{{mapping\|523 829 1214 1468 1809 1935}}		\| {{mapping\|523 829 1214 1468 1809 1935}}
	\| +0.1440		\| +0.1440
	\| 0.1497		\| 0.1497
	\| 6.52		\| 6.52
	\|}		{{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
	\|37\523		\| 37\523
	\|84.89		\| 84.89
	\|21/20		\| 21/20
	\|[[Amicable]]		\| [[Amicable]]
	\|-		\|-
	\|1		\| 1
	\|52\523		\| 52\523
	\|119.31		\| 119.31
	\|15/14		\| 15/14
	\|[[Septidiasemi]]		\| [[Septidiasemi]]
	\|-		\|-
	\|1		\| 1
	\|148\523		\| 148\523
	\|339.58		\| 339.58
	\|243/200		\| 243/200
	\|[[Amity]]		\| [[Amity]]
	\|}		{{rank-2 end}}
			{{orf}}
	~~<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 ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "(not) stuck" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] \| [https://francium223.bandcamp.com/track/not-stuck Bandcamp] \| [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]		* "(not) stuck" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] \| [https://francium223.bandcamp.com/track/not-stuck Bandcamp] \| [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]

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

Francium: +categories

2024-02-13T18:15:54Z

+categories

← Older revision		Revision as of 18:15, 13 February 2024
Line 91:		Line 91:
	; [[Francium]]		; [[Francium]]
	* "(not) stuck" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] \| [https://francium223.bandcamp.com/track/not-stuck Bandcamp] \| [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]		* "(not) stuck" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] \| [https://francium223.bandcamp.com/track/not-stuck Bandcamp] \| [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]

			[[Category:Listen]]

Francium: /* Music */ +year

2024-01-03T11:27:54Z

Music: +year

← Older revision		Revision as of 11:27, 3 January 2024
Line 90:		Line 90:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "(not) stuck" from ''hope in dark times'' – [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] \| [https://francium223.bandcamp.com/track/not-stuck Bandcamp] \| [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]		* "(not) stuck" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] \| [https://francium223.bandcamp.com/track/not-stuck Bandcamp] \| [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]

Francium: +music

2024-01-03T11:27:23Z

+music

← Older revision		Revision as of 11:27, 3 January 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|523}}		{{EDO intro\|523}}

	== Theory ==		== Theory ==
	523et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, [[6250/6237]], 42875/42768, [[19712/19683]], 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400 and 322102/321489 in the 11-limit.		523et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, [[6250/6237]], 42875/42768, [[19712/19683]], 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400 and 322102/321489 in the 11-limit.

	===Prime harmonics===		===Prime harmonics===
	{{Harmonics in equal\|523}}		{{Harmonics in equal\|523}}

	===Subsets and supersets===		===Subsets and supersets===
	523edo is the 99th [[prime edo]].		523edo is the 99th [[prime edo]].

	==Regular temperament properties==		==Regular temperament properties==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
Line 83:		Line 87:

	<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]]
			* "(not) stuck" from ''hope in dark times'' – [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] \| [https://francium223.bandcamp.com/track/not-stuck Bandcamp] \| [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]

Francium: Created page with "{{Infobox ET}} {{EDO intro|523}} == Theory == 523et tempers out 2401/2400 in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/49..."

2023-11-21T08:02:24Z

Created page with "{{Infobox ET}} {{EDO intro|523}} == Theory == 523et tempers out 2401/2400 in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/49..."

New page

{{Infobox ET}}
{{EDO intro|523}}
== Theory ==
523et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, [[6250/6237]], 42875/42768, [[19712/19683]], 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400 and 322102/321489 in the 11-limit.
===Prime harmonics===
{{Harmonics in equal|523}}
===Subsets and supersets===
523edo is the 99th [[prime edo]].
==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|829 -523}}
|{{mapping|523 829}}
| -0.0468
| 0.0468
| 2.04
|-
|2.3.5
|1600000/1594323, {{monzo|-101 11 36}}
|{{mapping|523 829 1214}}
| +0.0901
| 0.1974
| 8.60
|-
|2.3.5.7
|2401/2400, 1600000/1594323, 341796875/339738624
|{{mapping|523 829 1214 1468}}
| +0.1180
| 0.1776
| 7.74
|-
|2.3.5.7.11
|6250/6237, 2401/2400, 19712/19683, 166375/165888
|{{mapping|523 829 1214 1468 1809}}
| +0.1319
| 0.1613
| 7.03
|-
|2.3.5.7.11.13
|2080/2079, 625/624, 4459/4455, 19712/19683, 50193/50176
|{{mapping|523 829 1214 1468 1809 1935}}
| +0.1440
| 0.1497
| 6.52
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|1
|37\523
|84.89
|21/20
|[[Amicable]]
|-
|1
|52\523
|119.31
|15/14
|[[Septidiasemi]]
|-
|1
|148\523
|339.58
|243/200
|[[Amity]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct