9539edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:44:02Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:44, 13 March 2026
Line 61:		Line 61:
	\|}		\|}

	<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 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]]		; [[Francium]]
	* "You Are My Dear Fog Man" from ''Void'' (2025) – [https://open.spotify.com/track/3ozYLaXbjMusrw3FJWG85G Spotify] \| [https://francium223.bandcamp.com/track/you-are-my-dear-fog-man Bandcamp] \| [https://www.youtube.com/watch?v=gbBKjQkWxCU YouTube]		* "You Are My Dear Fog Man" from ''Void'' (2025) – [https://open.spotify.com/track/3ozYLaXbjMusrw3FJWG85G Spotify] \| [https://francium223.bandcamp.com/track/you-are-my-dear-fog-man Bandcamp] \| [https://www.youtube.com/watch?v=gbBKjQkWxCU YouTube]

Francium: /* Music */ +links

2025-05-20T14:06:52Z

Music: +links

← Older revision		Revision as of 14:06, 20 May 2025
Line 64:		Line 64:

	== Music ==		== Music ==
	* ''[https://www.youtube.com/watch?v=gbBKjQkWxCU ~~You Are My Dear Fog Man~~]~~'' - [[Francium]] (2025)~~		; [[Francium]]
			* "You Are My Dear Fog Man" from ''Void'' (2025) – [https://open.spotify.com/track/3ozYLaXbjMusrw3FJWG85G Spotify] \| [https://francium223.bandcamp.com/track/you-are-my-dear-fog-man Bandcamp] \| [https://www.youtube.com/watch?v=gbBKjQkWxCU YouTube]

BudjarnLambeth: add music

2025-05-20T11:17:03Z

add music

← Older revision		Revision as of 11:17, 20 May 2025
Line 62:		Line 62:

	<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 it is distinct

			== Music ==
			* ''[https://www.youtube.com/watch?v=gbBKjQkWxCU You Are My Dear Fog Man]'' - [[Francium]] (2025)

Francium: /* Theory */ +word

2025-03-22T19:16:16Z

Theory: +word

← Older revision		Revision as of 19:16, 22 March 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	9539edo is [[consistent]] to the [[9-odd-limit]] due to its [[harmonic]]s [[11/1\|11]] and [[13/1\|13]] being between its steps. It is strong in the 2.3.5.19.31.37.43 [[subgroup]], [[tempering out]] 5000211/5000000, 320013/320000, 3486880000/3486784401, 79456894976/79449609375, 94470144/94465625 and 30294016/30292137. Using the 2.3.5.31.41 subgroup, it tempers out [[15376/15375]].		9539edo is [[consistent]] to the [[9-odd-limit]] due to its [[harmonic]]s [[11/1\|11]] and [[13/1\|13]] being halfway between its steps. It is strong in the 2.3.5.19.31.37.43 [[subgroup]], [[tempering out]] 5000211/5000000, 320013/320000, 3486880000/3486784401, 79456894976/79449609375, 94470144/94465625 and 30294016/30292137. Using the 2.3.5.31.41 subgroup, it tempers out [[15376/15375]].

	=== Prime harmonics ===		=== Prime harmonics ===

Francium: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 9539edo is consistent to the 9-odd-limit due to its harmonics 11 and 13 being between its steps. It is..."

2025-03-22T19:15:37Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 9539edo is consistent to the 9-odd-limit due to its harmonics 11 and 13 being between its steps. It is..."

New page

{{Infobox ET}}
{{ED intro}}

== Theory ==
9539edo is [[consistent]] to the [[9-odd-limit]] due to its [[harmonic]]s [[11/1|11]] and [[13/1|13]] being between its steps. It is strong in the 2.3.5.19.31.37.43 [[subgroup]], [[tempering out]] 5000211/5000000, 320013/320000, 3486880000/3486784401, 79456894976/79449609375, 94470144/94465625 and 30294016/30292137. Using the 2.3.5.31.41 subgroup, it tempers out [[15376/15375]].

=== Prime harmonics ===
{{Harmonics in equal|9539}}

=== Subsets and supersets ===
9539edo is the 1181st [[prime edo]]. [[19078edo]], which doubles it, gives a good correction to its harmonics 11 and 13.

== 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|15119 -9539}}
| {{mapping|9539 15119}}
| −0.0017
| 0.0017
| 1.35
|-
| 2.3.5
| {{monzo|-17 62 -35}}, {{monzo|380 -38 -107}}
| {{mapping|9539 15119 22149}}
| −0.0034
| 0.0028
| 2.23
|-
| 2.3.5.7
| {{monzo|-5 -12 -9 16}}, {{monzo|-52 6 5 11}}, {{monzo|6 -37 13 8}}
| {{mapping|9539 15119 22149 26779}}
| +0.0014
| 0.0088
| 7.00
|}

=== 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
| 2566\9539
| 322.8011
| {{monzo|-6 23 -13}}
| [[Senior]]
|}

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