2081edo - 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 67:		Line 67:
	\| [[Vavoom]]		\| [[Vavoom]]
	\|}		\|}
	<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]]
	* "Fluffy Pants" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/19RLlJT3xTUmnIk9u9p1dT Spotify] \| [https://francium223.bandcamp.com/track/fluffy-pants Bandcamp] \| [https://www.youtube.com/watch?v=nNQjh8ZUtVc YouTube]		* "Fluffy Pants" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/19RLlJT3xTUmnIk9u9p1dT Spotify] \| [https://francium223.bandcamp.com/track/fluffy-pants Bandcamp] \| [https://www.youtube.com/watch?v=nNQjh8ZUtVc YouTube]

Francium: +music

2025-06-09T11:41:39Z

+music

← Older revision		Revision as of 11:41, 9 June 2025
Line 68:		Line 68:
	\|}		\|}
	<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 ==
			; [[Francium]]
			* "Fluffy Pants" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/19RLlJT3xTUmnIk9u9p1dT Spotify] \| [https://francium223.bandcamp.com/track/fluffy-pants Bandcamp] \| [https://www.youtube.com/watch?v=nNQjh8ZUtVc YouTube]

Francium: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 2081edo is consistent to the 7-odd-limit, tempering out 2460375/2458624, 1312993546389/1310720000000 and {{monzo|24 13 -18 -1}}. It is strong in the 2.5.7.11.17.19 subgroup, tempering out 10241/10240, 495635/495616, 184877/184832, 163498496/163480075 and 244248928/244140625. === Odd harmonics === {{Harmonics in equal|2081}} === Subsets and supersets === 2081edo is the 313th prime edo. == Regular tempera..."

2025-04-16T13:57:37Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 2081edo is consistent to the 7-odd-limit, tempering out 2460375/2458624, 1312993546389/1310720000000 and {{monzo|24 13 -18 -1}}. It is strong in the 2.5.7.11.17.19 subgroup, tempering out 10241/10240, 495635/495616, 184877/184832, 163498496/163480075 and 244248928/244140625. === Odd harmonics === {{Harmonics in equal|2081}} === Subsets and supersets === 2081edo is the 313th prime edo. == Regular tempera..."

New page

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

== Theory ==
2081edo is [[consistent]] to the [[7-odd-limit]], [[tempering out]] [[2460375/2458624]], 1312993546389/1310720000000 and {{monzo|24 13 -18 -1}}. It is strong in the 2.5.7.11.17.19 [[subgroup]], tempering out 10241/10240, 495635/495616, 184877/184832, 163498496/163480075 and 244248928/244140625.

=== Odd harmonics ===
{{Harmonics in equal|2081}}

=== Subsets and supersets ===
2081edo is the 313th [[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|-3298 2081}}
| {{mapping|2081 3298}}
| 0.0558
| 0.0558
| 9.68
|-
| 2.3.5
| {{monzo|-68 18 17}}, {{monzo|-30 79 -41}}
| {{mapping|2081 3298 4832}}
| 0.0316
| 0.0570
| 9.88
|-
| 2.3.5.7
| 2460375/2458624, {{monzo|-24 13 -7 7}}, {{monzo|24 13 -18 -1}}
| {{mapping|2081 3298 4832 5842}}
| 0.0291
| 0.0496
| 8.60
|-
| 2.3.5.7.11
| 160083/160000, 2460375/2458624, 3750705/3748096, 204073344/203809375
| {{mapping|2081 3298 4832 5842 7199}}
| 0.0259
| 0.0448
| 7.77
|}

=== 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
| 194\2081
| 111.869
| 16/15
| [[Vavoom]]
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct