202edo: Difference between revisions
Correct comma bases; formatting; +links to more scales |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== 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 [[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 === | === Prime harmonics === | ||
{{Harmonics in equal|202}} | {{Harmonics in equal|202}} | ||
=== Subsets and supersets === | |||
Since 202 factors into {{factorization|202}}, 202edo contains [[2edo]] and [[101edo]] as its subsets. | |||
== 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" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
| Line 22: | Line 26: | ||
| {{monzo| -160 101 }} | | {{monzo| -160 101 }} | ||
| {{mapping| 202 320 }} | | {{mapping| 202 320 }} | ||
| 0.3044 | | +0.3044 | ||
| 0.3045 | | 0.3045 | ||
| 5.13 | | 5.13 | ||
| Line 29: | Line 33: | ||
| {{monzo| -13 17 -6 }}, {{monzo| 23 6 -14 }} | | {{monzo| -13 17 -6 }}, {{monzo| 23 6 -14 }} | ||
| {{mapping| 202 320 469 }} | | {{mapping| 202 320 469 }} | ||
| 0.2280 | | +0.2280 | ||
| 0.2710 | | 0.2710 | ||
| 4.56 | | 4.56 | ||
| Line 36: | Line 40: | ||
| 2401/2400, 19683/19600, 65625/65536 | | 2401/2400, 19683/19600, 65625/65536 | ||
| {{mapping| 202 320 469 567 }} | | {{mapping| 202 320 469 567 }} | ||
| 0.2164 | | +0.2164 | ||
| 0.2356 | | 0.2356 | ||
| 3.97 | | 3.97 | ||
| Line 43: | Line 47: | ||
| 243/242, 441/440, 4000/3993, 65625/65536 | | 243/242, 441/440, 4000/3993, 65625/65536 | ||
| {{mapping| 202 320 469 567 699 }} | | {{mapping| 202 320 469 567 699 }} | ||
| 0.1061 | | +0.1061 | ||
| 0.3049 | | 0.3049 | ||
| 5.13 | | 5.13 | ||
| Line 50: | 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 | ! Periods<br />per 8ve | ||
! Cents | ! Generator* | ||
! Associated<br> | ! Cents* | ||
! Associated<br />ratio* | |||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 88: | Line 93: | ||
|- | |- | ||
| 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 == | ||
| Line 107: | Line 113: | ||
[[Category:Jove]] | [[Category:Jove]] | ||
[[Category:Rastmic]] | [[Category:Rastmic]] | ||
[[Category: | [[Category:Listen]] | ||