202edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|202}} | |||
==Theory== | == Theory == | ||
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. | 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. | ||
==Regular temperament properties== | === Prime harmonics === | ||
{{Harmonics in equal|202}} | |||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|-160 101}} | | {{monzo| -160 101 }} | ||
|{{val|202 320}} | | {{val| 202 320 }} | ||
| 0.3044 | | 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}} | | {{val| 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}} | | {{val| 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, 540/539, 2401/2400 | ||
|{{val|202 320 469 567 699}} | | {{val| 202 320 469 567 699 }} | ||
| 0.1061 | | 0.1061 | ||
| 0.3049 | | 0.3049 | ||
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|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator<br>( | ! Generator<br>(Reduced) | ||
! Cents<br>( | ! Cents<br>(Reduced) | ||
! Associated<br> | ! 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]] | | [[Gravity]] | ||
|- | |- | ||
|2 | | 2 | ||
|12\202 | | 12\202 | ||
|71.29 | | 71.29 | ||
|25/24 | | 25/24 | ||
|[[Vishnu]] | | [[Vishnu]] | ||
|- | |- | ||
|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]] | ||
|} | |} | ||
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== Music == | == Music == | ||
[https://www.youtube.com/watch?v=_bNbb2o5K80 Home Planet Nostalgia] | ; [[Mundoworld]] | ||
* [https://www.youtube.com/watch?v=_bNbb2o5K80 ''Home Planet Nostalgia''] | |||
[[Category:Harry]] | [[Category:Harry]] | ||
[[Category:Tertiaseptal]] | [[Category:Tertiaseptal]] | ||