3889edo - Revision history

FloraC: Review

2026-04-17T14:46:38Z

Review

← Older revision		Revision as of 14:46, 17 April 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	3889edo is [[consistent]] to the [[27-odd-limit]], [[tempering out]] [[~~12376/12375~~]], [[~~14400/14399~~]], [[~~6175~~/~~6174~~]]~~, 8625/8624, 89376/89375~~, [[123201/123200]]~~, 1549184/1549125~~ and [[1990656/1990625]] in the [[23-limit]]~~. It is strong~~ in the ~~2.3.5.7.13.~~17~~.19.23.31~~ [[~~subgroup~~]], ~~tempering out~~ 6175/6174, 14365/14364, ~~426496~~/~~426465~~, ~~52326~~/~~52325~~, ~~52003~~/~~52000~~, ~~1549184~~/~~1549125~~, ~~1990656/1990625~~ and ~~22816~~/~~22815. The equal temperament also tempers out [[19251/19250]]~~ in the ~~2.3.5.7.11.23.31 subgroup and~~ [[~~5440/5439~~]] ~~in the 2.3.5.7.17.37 subgroup~~.		3889edo is [[consistent]] to the [[27-odd-limit]], and except for [[29/19]] and its [[octave complement]], it is consistent to the [[31-odd-limit]].

			As an equal temperament, it [[tempering out\|tempers out]] the [[pirate comma]], the [[starscape comma]], and the [[quartisma]]. Some of the simpler commas it tempers out in the higher limits include [[6656/6655]], [[123201/123200]] and [[1990656/1990625]] in the [[13-limit]]; [[12376/12375]], [[14400/14399]] in the [[17-limit]]; [[5776/5775]], [[6175/6174]], 14365/14364, 23409/23408, 28900/28899, 43681/43680 in the [[19-limit]]; [[5083/5082]], 7866/7865, and 8625/8624 in the [[23-limit]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 39:		Line 41:
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| ~~{{Monzo\| -4 17 1 -9 }}~~, {{monzo\| 2 -20 14 -1 }}, {{monzo\| 46 -14 -3 -6 }}		\| 645700815/645657712, {{monzo\| 2 -20 14 -1 }}, {{monzo\| 46 -14 -3 -6 }}
	\| {{Mapping\| 3889 6164 9030 10918 }}		\| {{Mapping\| 3889 6164 9030 10918 }}
	\| −0.0101		\| −0.0101
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	\|-		\|-
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| ~~21437500~~/~~21434787~~, ~~47265625~~/~~47258883~~, ~~56953125~~/~~56942116~~, 104857600/104825259		\| 1771875/1771561, 3294225/3294172, 14348907/14348180, 104857600/104825259
	\| {{Mapping\| 3889 6164 9030 10918 13454 }}		\| {{Mapping\| 3889 6164 9030 10918 13454 }}
	\| −0.0129		\| −0.0129
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	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 6656/6655, 123201/123200, 492128/492075, 1990656/1990625~~, 29046875/29042496~~		\| 6656/6655, 123201/123200, 492128/492075, 823680/823543, 1990656/1990625
	\| {{Mapping\| 3889 6164 9030 10918 13454 14391 }}		\| {{Mapping\| 3889 6164 9030 10918 13454 14391 }}
	\| −0.0106		\| −0.0106
Line 60:		Line 62:
	\|-		\|-
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 12376/12375, ~~14400/14399, 123201~~/~~123200~~, 37180/37179, ~~1990656~~/~~1990625~~, ~~361250~~/~~361179~~		\| 6656/6655, 12376/12375, 28561/28560, 37180/37179, 361250/361179, 937125/937024
	\| {{Mapping\| 3889 6164 9030 10918 13454 14391 15896 }}		\| {{Mapping\| 3889 6164 9030 10918 13454 14391 15896 }}
	\| −0.0075		\| −0.0075

FloraC: Standardize format

2026-04-17T14:31:37Z

Standardize format

← Older revision		Revision as of 14:31, 17 April 2026
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|3889}}		{{Harmonics in equal\|3889\|columns=11}}
			{{Harmonics in equal\|3889\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 3889edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
Line 15:		Line 16:
	\|-		\|-
	! 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]] (¢)
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	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\|6164 -3889}}		\| {{Monzo\| 6164 -3889 }}
	\| {{~~mapping~~\|3889 6164}}		\| {{Mapping\| 3889 6164 }}
	\| −0.0079		\| −0.0079
	\| 0.0079		\| 0.0079
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\|-90 -15 49}}, {{monzo\|56 -91 38}}		\| {{Monzo\| -90 -15 49 }}, {{monzo\| 56 -91 38 }}
	\| {{~~mapping~~\|3889 6164 9030}}		\| {{Mapping\| 3889 6164 9030 }}
	\| −0.0062		\| −0.0062
	\| 0.0068		\| 0.0068
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	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| {{~~monzo~~\|-4 17 1 -9}}, {{monzo\|2 -20 14 -1}}, {{monzo\|46 -14 -3 -6}}		\| {{Monzo\| -4 17 1 -9 }}, {{monzo\| 2 -20 14 -1 }}, {{monzo\| 46 -14 -3 -6 }}
	\| {{~~mapping~~\|3889 6164 9030 10918}}		\| {{Mapping\| 3889 6164 9030 10918 }}
	\| −0.0101		\| −0.0101
	\| 0.0089		\| 0.0089
Line 46:		Line 47:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 21437500/21434787, 47265625/47258883, 56953125/56942116, 104857600/104825259		\| 21437500/21434787, 47265625/47258883, 56953125/56942116, 104857600/104825259
	\| {{~~mapping~~\|3889 6164 9030 10918 13454}}		\| {{Mapping\| 3889 6164 9030 10918 13454 }}
	\| −0.0129		\| −0.0129
	\| 0.0098		\| 0.0098
Line 52:		Line 53:
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 123201/123200, ~~6656~~/~~6655~~, 1990656/1990625~~, 492128/492075~~, 29046875/29042496		\| 6656/6655, 123201/123200, 492128/492075, 1990656/1990625, 29046875/29042496
	\| {{~~mapping~~\|3889 6164 9030 10918 13454 14391}}		\| {{Mapping\| 3889 6164 9030 10918 13454 14391 }}
	\| −0.0106		\| −0.0106
	\| 0.0103		\| 0.0103
Line 60:		Line 61:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 12376/12375, 14400/14399, 123201/123200, 37180/37179, 1990656/1990625, 361250/361179		\| 12376/12375, 14400/14399, 123201/123200, 37180/37179, 1990656/1990625, 361250/361179
	\| {{~~mapping~~\|3889 6164 9030 10918 13454 14391 15896}}		\| {{Mapping\| 3889 6164 9030 10918 13454 14391 15896 }}
	\| −0.0075		\| −0.0075
	\| 0.0121		\| 0.0121
Line 70:		Line 71:
	\|+ style="font-size: 105%;" \| 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
	\|-		\|-
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	\| 602\3889		\| 602\3889
	\| 185.755		\| 185.755
	\| {{~~monzo~~\|24 4 -13}}		\| {{Monzo\| 24 4 -13 }}
	\| [[Pirate]]		\| [[Pirate]]
	\|}		\|}
	<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		<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]]
	* "Don't Stop Interrupting People" from ''Don't'' (2025) – [https://open.spotify.com/track/2W1M2taD9SRU2MIz7YqpxQ Spotify] \| [https://francium223.bandcamp.com/track/dont-stop-interrupting-people Bandcamp] \| [https://www.youtube.com/watch?v=nOoXjJ6dqhk YouTube]		* "Don't Stop Interrupting People" from ''Don't'' (2025) – [https://open.spotify.com/track/2W1M2taD9SRU2MIz7YqpxQ Spotify] \| [https://francium223.bandcamp.com/track/dont-stop-interrupting-people Bandcamp] \| [https://www.youtube.com/watch?v=nOoXjJ6dqhk YouTube]

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"

2026-03-13T13:31:58Z

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
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	\| [[Pirate]]		\| [[Pirate]]
	\|}		\|}
	<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]]		; [[Francium]]
	* "Don't Stop Interrupting People" from ''Don't'' (2025) – [https://open.spotify.com/track/2W1M2taD9SRU2MIz7YqpxQ Spotify] \| [https://francium223.bandcamp.com/track/dont-stop-interrupting-people Bandcamp] \| [https://www.youtube.com/watch?v=nOoXjJ6dqhk YouTube]		* "Don't Stop Interrupting People" from ''Don't'' (2025) – [https://open.spotify.com/track/2W1M2taD9SRU2MIz7YqpxQ Spotify] \| [https://francium223.bandcamp.com/track/dont-stop-interrupting-people Bandcamp] \| [https://www.youtube.com/watch?v=nOoXjJ6dqhk YouTube]

Francium: /* Music */ +link

2025-07-03T11:58:53Z

Music: +link

← Older revision		Revision as of 11:58, 3 July 2025
Line 86:		Line 86:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Don't Stop Interrupting People" from ''Don't'' (2025) – [https://francium223.bandcamp.com/track/dont-stop-interrupting-people Bandcamp] \| [https://www.youtube.com/watch?v=nOoXjJ6dqhk YouTube]		* "Don't Stop Interrupting People" from ''Don't'' (2025) – [https://open.spotify.com/track/2W1M2taD9SRU2MIz7YqpxQ Spotify] \| [https://francium223.bandcamp.com/track/dont-stop-interrupting-people Bandcamp] \| [https://www.youtube.com/watch?v=nOoXjJ6dqhk YouTube]

Francium: +music

2025-06-29T11:21:39Z

+music

← Older revision		Revision as of 11:21, 29 June 2025
Line 83:		Line 83:
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

			== Music ==
			; [[Francium]]
			* "Don't Stop Interrupting People" from ''Don't'' (2025) – [https://francium223.bandcamp.com/track/dont-stop-interrupting-people Bandcamp] \| [https://www.youtube.com/watch?v=nOoXjJ6dqhk YouTube]

Francium: changed EDO intro to ED intro

2025-02-19T18:16:31Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:16, 19 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|3889~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294: Phormatting

2025-02-04T19:02:10Z

Phormatting

← Older revision		Revision as of 19:02, 4 February 2025
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" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| [[Mapping]]
	! colspan="2" \|Tuning Error		! rowspan="2" \| Optimal<br />8ve Stretch (¢)
			! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\|6164 -3889}}		\| {{monzo\|6164 -3889}}
	\| {{mapping\|3889 6164}}		\| {{mapping\|3889 6164}}
	\| -0.0079		\| −0.0079
	\| 0.0079		\| 0.0079
	\| 2.56		\| 2.56
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	\| {{monzo\|-90 -15 49}}, {{monzo\|56 -91 38}}		\| {{monzo\|-90 -15 49}}, {{monzo\|56 -91 38}}
	\| {{mapping\|3889 6164 9030}}		\| {{mapping\|3889 6164 9030}}
	\| -0.0062		\| −0.0062
	\| 0.0068		\| 0.0068
	\| 2.20		\| 2.20
Line 39:		Line 40:
	\| {{monzo\|-4 17 1 -9}}, {{monzo\|2 -20 14 -1}}, {{monzo\|46 -14 -3 -6}}		\| {{monzo\|-4 17 1 -9}}, {{monzo\|2 -20 14 -1}}, {{monzo\|46 -14 -3 -6}}
	\| {{mapping\|3889 6164 9030 10918}}		\| {{mapping\|3889 6164 9030 10918}}
	\| -0.0101		\| −0.0101
	\| 0.0089		\| 0.0089
	\| 2.88		\| 2.88
Line 46:		Line 47:
	\| 21437500/21434787, 47265625/47258883, 56953125/56942116, 104857600/104825259		\| 21437500/21434787, 47265625/47258883, 56953125/56942116, 104857600/104825259
	\| {{mapping\|3889 6164 9030 10918 13454}}		\| {{mapping\|3889 6164 9030 10918 13454}}
	\| -0.0129		\| −0.0129
	\| 0.0098		\| 0.0098
	\| 3.18		\| 3.18
Line 53:		Line 54:
	\| 123201/123200, 6656/6655, 1990656/1990625, 492128/492075, 29046875/29042496		\| 123201/123200, 6656/6655, 1990656/1990625, 492128/492075, 29046875/29042496
	\| {{mapping\|3889 6164 9030 10918 13454 14391}}		\| {{mapping\|3889 6164 9030 10918 13454 14391}}
	\| -0.0106		\| −0.0106
	\| 0.0103		\| 0.0103
	\| 3.34		\| 3.34
Line 60:		Line 61:
	\| 12376/12375, 14400/14399, 123201/123200, 37180/37179, 1990656/1990625, 361250/361179		\| 12376/12375, 14400/14399, 123201/123200, 37180/37179, 1990656/1990625, 361250/361179
	\| {{mapping\|3889 6164 9030 10918 13454 14391 15896}}		\| {{mapping\|3889 6164 9030 10918 13454 14391 15896}}
	\| -0.0075		\| −0.0075
	\| 0.0121		\| 0.0121
	\| 3.92		\| 3.92
Line 67:		Line 68:
	=== 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*
Line 80:		Line 82:
	\| [[Pirate]]		\| [[Pirate]]
	\|}		\|}
			<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct

Francium: Created page with "{{Infobox ET}} {{EDO intro|3889}} == Theory == 3889edo is consistent to the 27-odd-limit, tempering out 12376/12375, 14400/14399, 6175/6174, 8625/8624..."

2025-02-04T12:05:11Z

Created page with "{{Infobox ET}} {{EDO intro|3889}} == Theory == 3889edo is consistent to the 27-odd-limit, tempering out 12376/12375, 14400/14399, 6175/6174, 8625/8624..."

New page

{{Infobox ET}}
{{EDO intro|3889}}

== Theory ==
3889edo is [[consistent]] to the [[27-odd-limit]], [[tempering out]] [[12376/12375]], [[14400/14399]], [[6175/6174]], 8625/8624, 89376/89375, [[123201/123200]], 1549184/1549125 and [[1990656/1990625]] in the [[23-limit]]. It is strong in the 2.3.5.7.13.17.19.23.31 [[subgroup]], tempering out 6175/6174, 14365/14364, 426496/426465, 52326/52325, 52003/52000, 1549184/1549125, 1990656/1990625 and 22816/22815. The equal temperament also tempers out [[19251/19250]] in the 2.3.5.7.11.23.31 subgroup and [[5440/5439]] in the 2.3.5.7.17.37 subgroup.

=== Prime harmonics ===
{{Harmonics in equal|3889}}

=== Subsets and supersets ===
3889edo is the 539th [[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|6164 -3889}}
| {{mapping|3889 6164}}
| -0.0079
| 0.0079
| 2.56
|-
| 2.3.5
| {{monzo|-90 -15 49}}, {{monzo|56 -91 38}}
| {{mapping|3889 6164 9030}}
| -0.0062
| 0.0068
| 2.20
|-
| 2.3.5.7
| {{monzo|-4 17 1 -9}}, {{monzo|2 -20 14 -1}}, {{monzo|46 -14 -3 -6}}
| {{mapping|3889 6164 9030 10918}}
| -0.0101
| 0.0089
| 2.88
|-
| 2.3.5.7.11
| 21437500/21434787, 47265625/47258883, 56953125/56942116, 104857600/104825259
| {{mapping|3889 6164 9030 10918 13454}}
| -0.0129
| 0.0098
| 3.18
|-
| 2.3.5.7.11.13
| 123201/123200, 6656/6655, 1990656/1990625, 492128/492075, 29046875/29042496
| {{mapping|3889 6164 9030 10918 13454 14391}}
| -0.0106
| 0.0103
| 3.34
|-
| 2.3.5.7.11.13.17
| 12376/12375, 14400/14399, 123201/123200, 37180/37179, 1990656/1990625, 361250/361179
| {{mapping|3889 6164 9030 10918 13454 14391 15896}}
| -0.0075
| 0.0121
| 3.92
|}

=== 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
| 602\3889
| 185.755
| {{monzo|24 4 -13}}
| [[Pirate]]
|}

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