1361edo - Revision history

Francium: +music

2025-02-23T12:05:23Z

+music

← Older revision		Revision as of 12:05, 23 February 2025
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	\| 5.34		\| 5.34
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "The Nights Get Better and Better." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/11VP8L05cT6pDNQX8SJ0u6 Spotify] \| [https://francium223.bandcamp.com/track/the-nights-get-better-and-better Bandcamp] \| [https://www.youtube.com/watch?v=WmjKnu0OzLQ Bandcamp] – in Beattic, 1361edo tuning

ArrowHead294 at 13:01, 21 February 2025

2025-02-21T13:01:20Z

← Older revision		Revision as of 13:01, 21 February 2025
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	== 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]]		! 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]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
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	\| {{monzo\| -2157 1361 }}		\| {{monzo\| -2157 1361 }}
	\| {{mapping\| 1361 2157 }}		\| {{mapping\| 1361 2157 }}
	\| 0.0373		\| +0.0373
	\| 0.0373		\| 0.0373
	\| 4.23		\| 4.23
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	\| {{monzo\| -31 43 -16 }}, {{monzo\| -67 -9 35 }}		\| {{monzo\| -31 43 -16 }}, {{monzo\| -67 -9 35 }}
	\| {{mapping\| 1361 2157 3160 }}		\| {{mapping\| 1361 2157 3160 }}
	\| 0.0431		\| +0.0431
	\| 0.0315		\| 0.0315
	\| 3.57		\| 3.57
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	\| 703125/702464, 14348907/14336000, {{monzo\| 37 2 -4 -11 }}		\| 703125/702464, 14348907/14336000, {{monzo\| 37 2 -4 -11 }}
	\| {{mapping\| 1361 2157 3160 3821 }}		\| {{mapping\| 1361 2157 3160 3821 }}
	\| 0.0174		\| +0.0174
	\| 0.0522		\| 0.0522
	\| 5.92		\| 5.92
Line 46:		Line 47:
	\| 3025/3024, 759375/758912, 14348907/14336000, 262766592/262609375		\| 3025/3024, 759375/758912, 14348907/14336000, 262766592/262609375
	\| {{mapping\| 1361 2157 3160 3821 4708 }}		\| {{mapping\| 1361 2157 3160 3821 4708 }}
	\| 0.0285		\| +0.0285
	\| 0.0517		\| 0.0517
	\| 5.86		\| 5.86
Line 53:		Line 54:
	\| 1716/1715, 3025/3024, 4225/4224, 91125/91091, 131107977/131072000		\| 1716/1715, 3025/3024, 4225/4224, 91125/91091, 131107977/131072000
	\| {{mapping\| 1361 2157 3160 3821 4708 5036 }}		\| {{mapping\| 1361 2157 3160 3821 4708 5036 }}
	\| 0.0356		\| +0.0356
	\| 0.0498		\| 0.0498
	\| 5.65		\| 5.65
Line 60:		Line 61:
	\| 1716/1715, 2500/2499, 3025/3024, 4225/4224, 57375/57344, 3536379/3536000		\| 1716/1715, 2500/2499, 3025/3024, 4225/4224, 57375/57344, 3536379/3536000
	\| {{mapping\| 1361 2157 3160 3821 4708 5036 5563 }}		\| {{mapping\| 1361 2157 3160 3821 4708 5036 5563 }}
	\| 0.0317		\| +0.0317
	\| 0.0471		\| 0.0471
	\| 5.34		\| 5.34
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-21T05:50:09Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:50, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1361~~}}		{{ED intro}}

	== Theory ==		== Theory ==

BudjarnLambeth: Used the todo template to make the todo message findable for editors browsing the todo categories

2025-01-10T22:19:52Z

Used the todo template to make the todo message findable for editors browsing the todo categories

← Older revision		Revision as of 22:19, 10 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1361edo is [[consistent]] in the [[17-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[3025/3024]], [[1716/1715]], [[2500/2499]], [[4225/4224]], [[57375/57344]] and 3536379/3536000. Using the 2.3.5.13.17.43 [[subgroup]]~~<!--~~ todo: explain why this subgroup is good to consider ~~-->~~, it tempers out [[2925/2924]]. It [[support]]s [[galaxy]] and [[geb]].		1361edo is [[consistent]] in the [[17-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[3025/3024]], [[1716/1715]], [[2500/2499]], [[4225/4224]], [[57375/57344]] and 3536379/3536000. Using the 2.3.5.13.17.43 [[subgroup]]{{todo\|clarify\|comment=explain why this subgroup is good to consider}}, it tempers out [[2925/2924]]. It [[support]]s [[galaxy]] and [[geb]].

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

FloraC: Misc. cleanup. Request explanation

2025-01-10T16:36:42Z

Misc. cleanup. Request explanation

← Older revision		Revision as of 16:36, 10 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1361edo is [[consistent]] in the [[17-odd-limit]], [[tempering out]] [[3025/3024]], [[1716/1715]], [[2500/2499]], [[4225/4224]], [[57375/57344]] and 3536379/3536000. Using the 2.3.5.13.17.43 [[subgroup]], it tempers out [[2925/2924]]. It [[support]]s [[galaxy]] and [[geb]].		1361edo is [[consistent]] in the [[17-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[3025/3024]], [[1716/1715]], [[2500/2499]], [[4225/4224]], [[57375/57344]] and 3536379/3536000. Using the 2.3.5.13.17.43 [[subgroup]]<!-- todo: explain why this subgroup is good to consider -->, it tempers out [[2925/2924]]. It [[support]]s [[galaxy]] and [[geb]].

	=== Prime harmonics ===		=== Prime harmonics ===
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]]
	! 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\|-2157 1361}}		\| {{monzo\| -2157 1361 }}
	\| {{mapping\|1361 2157}}		\| {{mapping\| 1361 2157 }}
	\| 0.0373		\| 0.0373
	\| 0.0373		\| 0.0373
Line 30:		Line 30:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{monzo\|-31 43 -16}}, {{monzo\|-67 -9 35}}		\| {{monzo\| -31 43 -16 }}, {{monzo\| -67 -9 35 }}
	\| {{mapping\|1361 2157 3160}}		\| {{mapping\| 1361 2157 3160 }}
	\| 0.0431		\| 0.0431
	\| 0.0315		\| 0.0315
Line 37:		Line 37:
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| 703125/702464, 14348907/14336000, {{monzo\|37 2 -4 -11}}		\| 703125/702464, 14348907/14336000, {{monzo\| 37 2 -4 -11 }}
	\| {{mapping\|1361 2157 3160 3821}}		\| {{mapping\| 1361 2157 3160 3821 }}
	\| 0.0174		\| 0.0174
	\| 0.0522		\| 0.0522
Line 45:		Line 45:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 759375/758912, 14348907/14336000, 262766592/262609375		\| 3025/3024, 759375/758912, 14348907/14336000, 262766592/262609375
	\| {{mapping\|1361 2157 3160 3821 4708}}		\| {{mapping\| 1361 2157 3160 3821 4708 }}
	\| 0.0285		\| 0.0285
	\| 0.0517		\| 0.0517
Line 51:		Line 51:
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 3025/3024~~, 1716/1715~~, 4225/4224, 91125/91091, 131107977/131072000		\| 1716/1715, 3025/3024, 4225/4224, 91125/91091, 131107977/131072000
	\| {{mapping\|1361 2157 3160 3821 4708 5036}}		\| {{mapping\| 1361 2157 3160 3821 4708 5036 }}
	\| 0.0356		\| 0.0356
	\| 0.0498		\| 0.0498
Line 58:		Line 58:
	\|-		\|-
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| ~~3025/3024,~~ 1716/1715, 2500/2499, 4225/4224, 57375/57344, 3536379/3536000		\| 1716/1715, 2500/2499, 3025/3024, 4225/4224, 57375/57344, 3536379/3536000
	\| {{mapping\|1361 2157 3160 3821 4708 5036 5563}}		\| {{mapping\| 1361 2157 3160 3821 4708 5036 5563 }}
	\| 0.0317		\| 0.0317
	\| 0.0471		\| 0.0471
	\| 5.34		\| 5.34
	\|}		\|}

Francium: Created page with "{{Infobox ET}} {{EDO intro|1361}} == Theory == 1361edo is consistent in the 17-odd-limit, tempering out 3025/3024, 1716/1715, 2500/2499, 4225/4224..."

2025-01-10T12:02:15Z

Created page with "{{Infobox ET}} {{EDO intro|1361}} == Theory == 1361edo is consistent in the 17-odd-limit, tempering out 3025/3024, 1716/1715, 2500/2499, 4225/4224..."

New page

{{Infobox ET}}
{{EDO intro|1361}}

== Theory ==
1361edo is [[consistent]] in the [[17-odd-limit]], [[tempering out]] [[3025/3024]], [[1716/1715]], [[2500/2499]], [[4225/4224]], [[57375/57344]] and 3536379/3536000. Using the 2.3.5.13.17.43 [[subgroup]], it tempers out [[2925/2924]]. It [[support]]s [[galaxy]] and [[geb]].

=== Prime harmonics ===
{{Harmonics in equal|1361}}

=== Subsets and supersets ===
1361edo is the 218th [[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|-2157 1361}}
| {{mapping|1361 2157}}
| 0.0373
| 0.0373
| 4.23
|-
| 2.3.5
| {{monzo|-31 43 -16}}, {{monzo|-67 -9 35}}
| {{mapping|1361 2157 3160}}
| 0.0431
| 0.0315
| 3.57
|-
| 2.3.5.7
| 703125/702464, 14348907/14336000, {{monzo|37 2 -4 -11}}
| {{mapping|1361 2157 3160 3821}}
| 0.0174
| 0.0522
| 5.92
|-
| 2.3.5.7.11
| 3025/3024, 759375/758912, 14348907/14336000, 262766592/262609375
| {{mapping|1361 2157 3160 3821 4708}}
| 0.0285
| 0.0517
| 5.86
|-
| 2.3.5.7.11.13
| 3025/3024, 1716/1715, 4225/4224, 91125/91091, 131107977/131072000
| {{mapping|1361 2157 3160 3821 4708 5036}}
| 0.0356
| 0.0498
| 5.65
|-
| 2.3.5.7.11.13.17
| 3025/3024, 1716/1715, 2500/2499, 4225/4224, 57375/57344, 3536379/3536000
| {{mapping|1361 2157 3160 3821 4708 5036 5563}}
| 0.0317
| 0.0471
| 5.34
|}