202edo: Difference between revisions
m category |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| (21 intermediate revisions by 9 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | |||
{{ED intro}} | |||
[[ | == Theory == | ||
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. | |||
=== 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" | |||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[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| -160 101 }} | |||
| {{mapping| 202 320 }} | |||
| +0.3044 | |||
| 0.3045 | |||
| 5.13 | |||
|- | |||
| 2.3.5 | |||
| {{monzo| -13 17 -6 }}, {{monzo| 23 6 -14 }} | |||
| {{mapping| 202 320 469 }} | |||
| +0.2280 | |||
| 0.2710 | |||
| 4.56 | |||
|- | |||
| 2.3.5.7 | |||
| 2401/2400, 19683/19600, 65625/65536 | |||
| {{mapping| 202 320 469 567 }} | |||
| +0.2164 | |||
| 0.2356 | |||
| 3.97 | |||
|- | |||
| 2.3.5.7.11 | |||
| 243/242, 441/440, 4000/3993, 65625/65536 | |||
| {{mapping| 202 320 469 567 699 }} | |||
| +0.1061 | |||
| 0.3049 | |||
| 5.13 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 13\202 | |||
| 77.23 | |||
| 256/245 | |||
| [[Tertiaseptal]] | |||
|- | |||
| 1 | |||
| 51\202 | |||
| 302.97 | |||
| 25/21 | |||
| [[Quinmite]] | |||
|- | |||
| 1 | |||
| 85\202 | |||
| 504.95 | |||
| 104976/78125 | |||
| [[Countermeantone]] | |||
|- | |||
| 1 | |||
| 87\202 | |||
| 516.83 | |||
| 27/20 | |||
| [[Larry]] | |||
|- | |||
| 2 | |||
| 12\202 | |||
| 71.29 | |||
| 25/24 | |||
| [[Narayana]] | |||
|- | |||
| 2 | |||
| 87\202<br />(14\202) | |||
| 516.83<br />(83.17) | |||
| 27/20<br />(21/20) | |||
| [[Harry]] | |||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Scales == | |||
* [[Jove1]], [[jove2]], [[jove3]], [[jove4]], [[jove5]], [[jove6]] | |||
* [[Elfjove7]], [[elfjove8d]], [[elfjove10]], [[elfjove11c]], [[elfjove12]] | |||
* [[Oktone]] | |||
== Music == | |||
; [[Mundoworld]] | |||
* [https://www.youtube.com/watch?v=_bNbb2o5K80 ''Home Planet Nostalgia''] – in Oktone scale | |||
[[Category:Harry]] | |||
[[Category:Tertiaseptal]] | |||
[[Category:Jove]] | |||
[[Category:Rastmic]] | |||
[[Category:Listen]] | |||