285edo: Difference between revisions
Cleanup |
m changed EDO intro to ED intro |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 285 factors into | Since 285 factors into {{factorisation|285}}, 285edo has subset edos {{EDOs| 3, 5, 15, 19, 57, and 95 }}. | ||
== 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]] (¢) | ||
| Line 25: | Line 26: | ||
| {{monzo| 452 -285 }} | | {{monzo| 452 -285 }} | ||
| {{mapping| 285 452 }} | | {{mapping| 285 452 }} | ||
| | | −0.3795 | ||
| 0.3794 | | 0.3794 | ||
| 9.01 | | 9.01 | ||
| Line 32: | Line 33: | ||
| 67108864/66430125, {{monzo| -14 -19 19 }} | | 67108864/66430125, {{monzo| -14 -19 19 }} | ||
| {{mapping| 285 452 662 }} | | {{mapping| 285 452 662 }} | ||
| | | −0.4043 | ||
| 0.3117 | | 0.3117 | ||
| 7.41 | | 7.41 | ||
| Line 39: | Line 40: | ||
| 3136/3125, 5120/5103, 40353607/39858075 | | 3136/3125, 5120/5103, 40353607/39858075 | ||
| {{mapping| 285 452 662 800 }} | | {{mapping| 285 452 662 800 }} | ||
| | | −0.2673 | ||
| 0.3596 | | 0.3596 | ||
| 8.54 | | 8.54 | ||
| Line 46: | Line 47: | ||
| 3025/3024, 3136/3125, 5120/5103, 12005/11979 | | 3025/3024, 3136/3125, 5120/5103, 12005/11979 | ||
| {{mapping| 285 452 662 800 986 }} | | {{mapping| 285 452 662 800 986 }} | ||
| | | −0.2289 | ||
| 0.3307 | | 0.3307 | ||
| 7.85 | | 7.85 | ||
| Line 53: | Line 54: | ||
| 352/351, 676/675, 847/845, 3025/3024, 12005/11979 | | 352/351, 676/675, 847/845, 3025/3024, 12005/11979 | ||
| {{mapping| 285 452 662 800 986 1055 }} | | {{mapping| 285 452 662 800 986 1055 }} | ||
| | | −0.2618 | ||
| 0.3107 | | 0.3107 | ||
| 7.38 | | 7.38 | ||
| Line 60: | Line 61: | ||
=== 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 | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 74: | Line 76: | ||
|- | |- | ||
| 3 | | 3 | ||
| 59\285<br>(36\285) | | 59\285<br />(36\285) | ||
| 248.42<br>(151.58) | | 248.42<br />(151.58) | ||
| 15/13<br>(12/11) | | 15/13<br />(12/11) | ||
| [[Hemimist]] | | [[Hemimist]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 59\285<br>(23\285) | | 59\285<br />(23\285) | ||
| 496.84<br>(96.84) | | 496.84<br />(96.84) | ||
| 4/3<br>(256/243) | | 4/3<br />(256/243) | ||
| [[Misty]] | | [[Misty]] | ||
|- | |- | ||
| 19 | | 19 | ||
| 118\285<br>(2\285) | | 118\285<br />(2\285) | ||
| 496.84<br>(8.42) | | 496.84<br />(8.42) | ||
| 4/3<br>(15625/15552) | | 4/3<br />(15625/15552) | ||
| [[Enneadecal]] (5-limit) | | [[Enneadecal]] (5-limit) | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||