2243edo - 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"

2026-03-13T13:44:00Z

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
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	\| [[Counterschismic]]		\| [[Counterschismic]]
	\|}		\|}
	<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

Lériendil: tempers out 19/18?????

2025-04-07T05:48:00Z

tempers out 19/18?????

← Older revision		Revision as of 05:48, 7 April 2025
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	== Theory ==		== Theory ==
	2243edo is [[consistent]] to the [[9-odd-limit]] [[tempering out]] [[43046721/43025920]], [[78125000/78121827]] and 281484423828125/281474976710656 in the 7-limit. It is strong in the 2.3.5.7.13.17.19 [[subgroup]], tempering out [[5832/5831]], [[6175/6174]], 14365/14364, 121875/121856, 1003833/1003520 and 1101600/1101373. Using ~~the 2.3.19 subgroup, it tempers out [[19/18]], using~~ the 2.3.5.17.19 subgroup it tempers out the [[lakisma]]. Using the 2.3.7.13.31.37 subgroup, it tempers out [[3627/3626]]. It [[support]]s [[hemiegads]].		2243edo is [[consistent]] to the [[9-odd-limit]] [[tempering out]] [[43046721/43025920]], [[78125000/78121827]] and 281484423828125/281474976710656 in the 7-limit. It is strong in the 2.3.5.7.13.17.19 [[subgroup]], tempering out [[5832/5831]], [[6175/6174]], 14365/14364, 121875/121856, 1003833/1003520 and 1101600/1101373. Using the 2.3.5.17.19 subgroup it tempers out the [[lakisma]]. Using the 2.3.7.13.31.37 subgroup, it tempers out [[3627/3626]]. It [[support]]s [[hemiegads]].

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

Francium: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 2243edo is consistent to the 9-odd-limit tempering out 43046721/43025920, 78125000/78121827 and 281484423828125/281474976710656 in the 7-limit. It is strong in the 2.3.5.7.13.17.19 subgroup, tempering out 5832/5831, 6175/6174, 14365/14364, 121875/121856, 1003833/1003520 and 1101600/1101373. Using the 2.3.19 subgroup, it tempers out 19/18, using the 2.3.5.17.19 subgroup it tempers out the laki..."

2025-04-06T19:23:41Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 2243edo is consistent to the 9-odd-limit tempering out 43046721/43025920, 78125000/78121827 and 281484423828125/281474976710656 in the 7-limit. It is strong in the 2.3.5.7.13.17.19 subgroup, tempering out 5832/5831, 6175/6174, 14365/14364, 121875/121856, 1003833/1003520 and 1101600/1101373. Using the 2.3.19 subgroup, it tempers out 19/18, using the 2.3.5.17.19 subgroup it tempers out the laki..."

New page

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

== Theory ==
2243edo is [[consistent]] to the [[9-odd-limit]] [[tempering out]] [[43046721/43025920]], [[78125000/78121827]] and 281484423828125/281474976710656 in the 7-limit. It is strong in the 2.3.5.7.13.17.19 [[subgroup]], tempering out [[5832/5831]], [[6175/6174]], 14365/14364, 121875/121856, 1003833/1003520 and 1101600/1101373. Using the 2.3.19 subgroup, it tempers out [[19/18]], using the 2.3.5.17.19 subgroup it tempers out the [[lakisma]]. Using the 2.3.7.13.31.37 subgroup, it tempers out [[3627/3626]]. It [[support]]s [[hemiegads]].

=== Prime harmonics ===
{{Harmonics in equal|2243}}

=== Subsets and supersets ===
2243edo is the 334th [[prime edo]]. [[4486edo]], which doubles it, gives a good correction to its [[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|-3555 2243}}
| {{mapping| 2243 3555}}
| 0.0120
| 0.0120
| 2.24
|-
| 2.3.5
| {{monzo|-69 45 -1}}, {{monzo|-36 -52 51}}
| {{mapping| 2243 3555 5208}}
| 0.0145
| 0.0104
| 1.94
|-
| 2.3.5.7
| 43046721/43025920, 78125000/78121827, {{monzo|-48 0 11 8}}
| {{mapping| 2243 3555 5208 6297}}
| 0.0060
| 0.0173
| 3.23
|}

=== 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
| 590\2243
| 315.649
| 6/5
| [[Egads]]
|-
| 1
| 931\2243
| 498.083
| 4/3
| [[Counterschismic]]
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct