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{{Infobox ET}}
{{Infobox ET}}
The '''202 equal temperament''' divides the octave into 202 equal parts of 5.941 cents each.
{{ED intro}}


202et tempers out [[2401/2400]], 19683/19600 and 65625/65536 in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, and the rank-4 rastmic temperament tempering out 243/242.
== Theory ==
{{harmonics in equal|202|start=2|prec=3}}
202et [[tempering out|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, and the rank-4 rastmic temperament tempering out 243/242.


==Regular temperament properties==
=== Prime harmonics ===
{{Harmonics in equal|202}}
 
=== Subsets and supersets ===
Since 202 factors into {{factorization|202}}, 202edo contains [[2edo]] and [[101edo]] as its subsets.
 
== 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|-160 101}}
! rowspan="2" | [[Comma list]]
|{{val|202 320}}
! rowspan="2" | [[Mapping]]
| 0.3044
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -160 101 }}
| {{mapping| 202 320 }}
| +0.3044
| 0.3045
| 0.3045
| 5.13
| 5.13
|-
|-
|2.3.5
| 2.3.5
|{{monzo|-13 17 -6}}, {{monzo|23 6 -14}}
| {{monzo| -13 17 -6 }}, {{monzo| 23 6 -14 }}
|{{val|202 320 469}}
| {{mapping| 202 320 469 }}
| 0.2280
| +0.2280
| 0.2710
| 0.2710
| 4.56
| 4.56
|-
|-
|2.3.5.7
| 2.3.5.7
|2401/2400, 19683/19600, 65625/65536
| 2401/2400, 19683/19600, 65625/65536
|{{val|202 320 469 567}}
| {{mapping| 202 320 469 567 }}
| 0.2164
| +0.2164
| 0.2356
| 0.2356
| 3.97
| 3.97
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|243/242, 441/440, 540/539, 2401/2400
| 243/242, 441/440, 4000/3993, 65625/65536
|{{val|202 320 469 567 699}}
| {{mapping| 202 320 469 567 699 }}
| 0.1061
| +0.1061
| 0.3049
| 0.3049
| 5.13
| 5.13
Line 47: Line 54:
=== 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
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|13\202
| 13\202
|77.23
| 77.23
|256/245
| 256/245
|[[Tertiaseptal]]
| [[Tertiaseptal]]
|-
|-
|1
| 1
|51\202
| 51\202
|302.97
| 302.97
|25/21
| 25/21
|[[Quinmite]]
| [[Quinmite]]
|-
|-
|1
| 1
|85\202
| 85\202
|504.95
| 504.95
|104976/78125
| 104976/78125
|[[Countermeantone]]
| [[Countermeantone]]
|-
|-
|1
| 1
|87\202
| 87\202
|516.83
| 516.83
|27/20
| 27/20
|[[Gravity]]
| [[Larry]]
|-
|-
|2
| 2
|12\202
| 12\202
|71.29
| 71.29
|25/24
| 25/24
|[[Vishnu]]
| [[Narayana]]
|-
|-
|2
| 2
|87\202<br>(14\202)
| 87\202<br />(14\202)
|516.83<br>(83.17)
| 516.83<br />(83.17)
|27/20<br>(21/20)
| 27/20<br />(21/20)
|[[Harry]]
| [[Harry]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct


== Scales ==
== Scales ==
* [[Jove1]]
* [[Jove1]], [[jove2]], [[jove3]], [[jove4]], [[jove5]], [[jove6]]
* [[Jove2]]
* [[Elfjove7]], [[elfjove8d]], [[elfjove10]], [[elfjove11c]], [[elfjove12]]
* [[Jove3]]
* [[Oktone]]
* [[Jove4]]
* [[Jove5]]
* [[Jove6]]


== Music ==
== Music ==
[https://www.youtube.com/watch?v=_bNbb2o5K80 Home Planet Nostalgia] by Mundoworld
; [[Mundoworld]]
* [https://www.youtube.com/watch?v=_bNbb2o5K80 ''Home Planet Nostalgia''] – in Oktone scale


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Harry]]
[[Category:Harry]]
[[Category:Tertiaseptal]]
[[Category:Tertiaseptal]]
[[Category:Jove]]
[[Category:Jove]]
[[Category:Rastmic]]
[[Category:Rastmic]]
[[Category:Quartismic]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/202edo"