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Created page with "{{Infobox ET}} {{EDO intro|361}} == Theory == 361et is consistent to the 9-odd-limit, tempering out 43046721/43025920, 2460375/2458624, 703125/702464, 48828125/48..."
 
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|361}}
{{ED intro}}


== Theory ==
== Theory ==
361et is consistent to the [[9-odd-limit]], tempering out [[43046721/43025920]], 2460375/2458624, [[703125/702464]], 48828125/48771072 and [[4375/4374]] in the 7-limit. It [[support]]s [[submajor]].
361et is [[consistent]] to the [[9-odd-limit]] with flat tunings of [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]]. The equal temperament [[tempering out|tempers out]] [[4375/4374]], [[703125/702464]], 2460375/2458624, [[43046721/43025920]], and 48828125/48771072 in the 7-limit. It [[support]]s the 5-limit [[submajor]] temperament.


=== Odd harmonics ===
=== Odd harmonics ===
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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" |[[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
! rowspan="2" | [[Subgroup]]
|{{monzo|-572 361}}
! rowspan="2" | [[Comma list]]
|{{mapping|361 572}}
! rowspan="2" | [[Mapping]]
| 0.1798
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -572 361 }}
| {{mapping| 361 572 }}
| +0.1798
| 0.1798
| 0.1798
| 5.41
| 5.41
|-
|-
|2.3.5
| 2.3.5
|{{monzo|-36 11 8}}, {{monzo|-14 -19 19}}
| {{monzo| -36 11 8 }}, {{monzo| -14 -19 19 }}
|{{mapping|361 572 838}}
| {{mapping| 361 572 838 }}
| 0.2230
| +0.2230
| 0.1590
| 0.1590
| 4.78
| 4.78
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, 2460375/2458624, 823543/819200
| 4375/4374, 823543/819200, 2460375/2458624
|{{mapping|361 572 838 1013}}
| {{mapping| 361 572 838 1013 }}
| 0.3020
| +0.3020
| 0.1941
| 0.1941
| 5.84
| 5.84
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=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
! Periods<br>per 8ve
|-
! Periods<br />per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|166\361
| 166\361
|551.80
| 551.80
|48/35
| 48/35
|[[Emka]]
| [[Emka]]
|-
|-
|19
| 19
|150\361<br>(2\361)
| 150\361<br />(2\361)
|498.61<br>(6.65)
| 498.61<br />(6.65)
|4/3<br>(225/224)
| 4/3<br />(225/224)
|[[Enneadecal]]
| [[Enneadecal]]
|}
|}
 
<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
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
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