User:Francium/6091edo - Revision history

Francium: /* Theory */ typo

2026-02-02T12:21:54Z

Theory: typo

← Older revision		Revision as of 12:21, 2 February 2026
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	== Theory ==		== Theory ==
	6091edo is [[consistent]] to the [[9-odd-limit]], [[tempering out]] 184528125/184473632, 8796093022208/8792724609375 and {{monzo\|-15 42 -21 -1}} in the [[7-limit]]. It has a remarkably low relative error in its [[harmonic]]s [[3/1\|3]], [[23/1\|23]], [[29/1\|29]] and [[31/1]], being strong in the 2.3.5.19.23.29.31 [[subgroup]], tempering out 655371/655360, 323116128/323078125, 183353344/183347145, 484416/484375, 32506245/32505856 and 46405467/46400000.		6091edo is [[consistent]] to the [[9-odd-limit]], [[tempering out]] 184528125/184473632, 8796093022208/8792724609375 and {{monzo\|-15 42 -21 -1}} in the [[7-limit]]. It has a remarkably low relative error in its [[harmonic]]s [[3/1\|3]], [[23/1\|23]], [[29/1\|29]] and [[31/1\|31]], being strong in the 2.3.5.19.23.29.31 [[subgroup]], tempering out 655371/655360, 323116128/323078125, 183353344/183347145, 484416/484375, 32506245/32505856 and 46405467/46400000.

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

Francium: +music

2026-02-02T12:21:14Z

+music

← Older revision		Revision as of 12:21, 2 February 2026
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	<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]]
			* "Hammin" from ''Bumbos'' (2026) – [https://open.spotify.com/track/0PHcvPz6zasF4TXV1lLc4H Spotify] \| [https://francium223.bandcamp.com/track/hammin Bandcamp] \| [https://www.youtube.com/watch?v=OO2wf9vS33M YouTube] – in Hamity, 6091edo tuning

Francium: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 6091edo is consistent to the 9-odd-limit, tempering out 184528125/184473632, 8796093022208/8792724609375 and {{monzo|-15 42 -21 -1}} in the 7-limit. It has a remarkably low relative error in its harmonics 3, 23, 29 and 31/1, being strong in the 2.3.5.19.23.29.31 subgroup, tempering out 655371/655360, 323116128/323078125, 183353344/183347145, 484416/484375, 32506245/32505856 an..."

2025-12-17T18:17:00Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 6091edo is consistent to the 9-odd-limit, tempering out 184528125/184473632, 8796093022208/8792724609375 and {{monzo|-15 42 -21 -1}} in the 7-limit. It has a remarkably low relative error in its harmonics 3, 23, 29 and 31/1, being strong in the 2.3.5.19.23.29.31 subgroup, tempering out 655371/655360, 323116128/323078125, 183353344/183347145, 484416/484375, 32506245/32505856 an..."

New page

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

== Theory ==
6091edo is [[consistent]] to the [[9-odd-limit]], [[tempering out]] 184528125/184473632, 8796093022208/8792724609375 and {{monzo|-15 42 -21 -1}} in the [[7-limit]]. It has a remarkably low relative error in its [[harmonic]]s [[3/1|3]], [[23/1|23]], [[29/1|29]] and [[31/1]], being strong in the 2.3.5.19.23.29.31 [[subgroup]], tempering out 655371/655360, 323116128/323078125, 183353344/183347145, 484416/484375, 32506245/32505856 and 46405467/46400000.

=== Prime harmonics ===
{{Harmonics in equal|6091}}

=== Subsets and supersets ===
6091edo is the 795th [[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|-9654 6091}}
| {{mapping|6091 9654}}
| +0.0004
| 0.0004
| 0.20
|-
| 2.3.5
| {{monzo|91 -12 -31}}, {{monzo|-103 169 -71}}
| {{mapping|6091 9654 14143}}
| −0.0036
| 0.0056
| 2.8
|-
| 2.3.5.7
| 184528125/184473632, 8796093022208/8792724609375, {{monzo|-15 42 -21 -1}}
| {{mapping|6091 9654 14143 17100}}
| −0.0097
| 0.0117
| 5.94
|}

=== 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
| 671\6091
| 132.1950
| {{monzo|-38 5 13}}
| [[Astro]]
|}

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