User:Francium/4243edo - Revision history

Francium: +music

2025-10-21T14:59:52Z

+music

← Older revision		Revision as of 14:59, 21 October 2025
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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 ==
			; "you ABSOLUTE GRAPE!!" from ''Things to Scream at People'' (2025) – [https://open.spotify.com/track/18b08eK8l9HF1SrLozKCLr Spotify] \| [https://francium223.bandcamp.com/track/you-absolute-grape Bandcamp] \| [https://www.youtube.com/watch?v=CyfAURQlWrs YouTube]

FloraC: Text replacement - "{{Infobox ET}}" to "{{Infobox ET|debug=1}}"

2025-08-20T16:53:41Z

Text replacement - "{{Infobox ET}}" to "{{Infobox ET|debug=1}}"

← Older revision		Revision as of 16:53, 20 August 2025
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	{{ED intro}}		{{ED intro}}

Francium: /* Theory */

2025-08-04T13:44:39Z

Theory

← Older revision		Revision as of 13:44, 4 August 2025
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	== Theory ==		== Theory ==
	4243edo is [[consistent]] to the [[9-odd-limit]], [[tempering out]] [[78125000/78121827]], {{monzo\|46 -14 -3 -6}} and {{monzo\|-14 26 4 -13}} in the [[7-limit]]. Its [[harmonic]] [[3/1\|3]] has a remarkably low relative error of 0.4 percent. As an equal temperament, 4243edo is strong in the 2.3.5.13.17.19 [[subgroup]], tempering out 104976/104975, 28900/28899, 19922944/19921875, 8450649/8450000 and 18051780123/18050000000. It also tempers out the [[lakisma]] in the ~~full [[~~19~~-limit]]~~ and [[7956/7955]] in the 2.3.5.13.17.37.43 subgroup. 4243edo [[support]]s [[whoosh]].		4243edo is [[consistent]] to the [[9-odd-limit]], [[tempering out]] [[78125000/78121827]], {{monzo\|46 -14 -3 -6}} and {{monzo\|-14 26 4 -13}} in the [[7-limit]]. Its [[harmonic]] [[3/1\|3]] has a remarkably low relative error of 0.4 percent. As an equal temperament, 4243edo is strong in the 2.3.5.13.17.19 [[subgroup]], tempering out 104976/104975, 28900/28899, 19922944/19921875, 8450649/8450000 and 18051780123/18050000000. It also tempers out the [[lakisma]] in the 2.3.5.17.19 subgroup and [[7956/7955]] in the 2.3.5.13.17.37.43 subgroup. 4243edo [[support]]s [[whoosh]].

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

Francium: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 4243edo is consistent to the 9-odd-limit, tempering out 78125000/78121827, {{monzo|46 -14 -3 -6}} and {{monzo|-14 26 4 -13}} in the 7-limit. Its harmonic 3 has a remarkably low relative error of 0.4 percent. As an equal temperament, 4243edo is strong in the 2.3.5.13.17.19 subgroup, tempering out 104976/104975, 28900/28899, 19922944/19921875, 8450649/8450000 and 18051780123/18050000000. It also..."

2025-08-03T21:33:49Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 4243edo is consistent to the 9-odd-limit, tempering out 78125000/78121827, {{monzo|46 -14 -3 -6}} and {{monzo|-14 26 4 -13}} in the 7-limit. Its harmonic 3 has a remarkably low relative error of 0.4 percent. As an equal temperament, 4243edo is strong in the 2.3.5.13.17.19 subgroup, tempering out 104976/104975, 28900/28899, 19922944/19921875, 8450649/8450000 and 18051780123/18050000000. It also..."

New page

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

== Theory ==
4243edo is [[consistent]] to the [[9-odd-limit]], [[tempering out]] [[78125000/78121827]], {{monzo|46 -14 -3 -6}} and {{monzo|-14 26 4 -13}} in the [[7-limit]]. Its [[harmonic]] [[3/1|3]] has a remarkably low relative error of 0.4 percent. As an equal temperament, 4243edo is strong in the 2.3.5.13.17.19 [[subgroup]], tempering out 104976/104975, 28900/28899, 19922944/19921875, 8450649/8450000 and 18051780123/18050000000. It also tempers out the [[lakisma]] in the full [[19-limit]] and [[7956/7955]] in the 2.3.5.13.17.37.43 subgroup. 4243edo [[support]]s [[whoosh]].

=== Prime harmonics ===
{{Harmonics in equal|4243}}

=== Subsets and supersets ===
4243edo is the 582nd [[prime edo]]. [[8486edo]], which doubles it, gives a good correction to the harmonic [[11/1|11]].

== 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|6725 -4243}}
| {{mapping|4243 6725}}
| −0.0004
| 0.0004
| 0.14
|-
| 2.3.5
| {{monzo|37 25 -33}}, {{monzo|215 -121 -10}}
| {{mapping|4243 6725 9852}}
| −0.0026
| 0.0032
| 1.31
|-
| 2.3.5.7
| 78125000/78121827, {{monzo|46 -14 -3 -6}}, {{monzo|-14 26 4 -13}}
| {{mapping|4243 6725 9852 11912}}
| −0.0119
| 0.0162
| 5.73
|}

=== 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
| 1982\4243
| 560.5468
| 864/625
| [[Whoosh]]
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct