202edo: Difference between revisions
Added music section |
Added regular temperament properties and rank-2 temperaments |
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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. | ||
{{harmonics in equal|202|start=2|prec=3}} | {{harmonics in equal|202|start=2|prec=3}} | ||
==Regular temperament properties== | |||
{| 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 | |||
|{{monzo|-160 101}} | |||
|{{val|202 320}} | |||
| 0.3044 | |||
| 0.3045 | |||
| 5.13 | |||
|- | |||
|2.3.5 | |||
|{{monzo|-13 17 -6}}, {{monzo|23 6 -14}} | |||
|{{val|202 320 469}} | |||
| 0.2280 | |||
| 0.2710 | |||
| 4.56 | |||
|- | |||
|2.3.5.7 | |||
|2401/2400, 19683/19600, 65625/65536 | |||
|{{val|202 320 469 567}} | |||
| 0.2164 | |||
| 0.2356 | |||
| 3.97 | |||
|- | |||
|2.3.5.7.11 | |||
|243/242, 441/440, 540/539, 2401/2400 | |||
|{{val|202 320 469 567 699}} | |||
| 0.1061 | |||
| 0.3049 | |||
| 5.13 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! 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 | |||
|[[Gravity]] | |||
|- | |||
|2 | |||
|12\202 | |||
|71.29 | |||
|25/24 | |||
|[[Vishnu]] | |||
|- | |||
|2 | |||
|87\202<br>(14\202) | |||
|516.83<br>(83.17) | |||
|27/20<br>(21/20) | |||
|[[Harry]] | |||
|} | |||
== Scales == | == Scales == | ||