327edo: Difference between revisions
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m changed EDO intro to ED intro |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 327 factors into | Since 327 factors into {{factorisation|327}}, 327edo has [[3edo]] and [[109edo]] 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 25: | Line 26: | ||
| {{monzo| -518 327 }} | | {{monzo| -518 327 }} | ||
| {{mapping| 327 518 }} | | {{mapping| 327 518 }} | ||
| 0.3273 | | +0.3273 | ||
| 0.3274 | | 0.3274 | ||
| 8.92 | | 8.92 | ||
| Line 32: | Line 33: | ||
| 2109375/2097152, {{monzo| -20 39 -18 }} | | 2109375/2097152, {{monzo| -20 39 -18 }} | ||
| {{mapping| 327 518 759 }} | | {{mapping| 327 518 759 }} | ||
| 0.3608 | | +0.3608 | ||
| 0.2715 | | 0.2715 | ||
| 7.40 | | 7.40 | ||
| Line 39: | Line 40: | ||
| 16875/16807, 19683/19600, 2100875/2097152 | | 16875/16807, 19683/19600, 2100875/2097152 | ||
| {{mapping| 327 518 759 918 }} | | {{mapping| 327 518 759 918 }} | ||
| 0.2722 | | +0.2722 | ||
| 0.2807 | | 0.2807 | ||
| 7.65 | | 7.65 | ||
| Line 46: | Line 47: | ||
| 540/539, 1375/1372, 8019/8000, 2100875/2097152 | | 540/539, 1375/1372, 8019/8000, 2100875/2097152 | ||
| {{mapping| 327 518 759 918 1131 }} | | {{mapping| 327 518 759 918 1131 }} | ||
| 0.2674 | | +0.2674 | ||
| 0.2512 | | 0.2512 | ||
| 6.85 | | 6.85 | ||
| Line 53: | Line 54: | ||
| 540/539, 625/624, 1575/1573, 2200/2197, 8019/8000 | | 540/539, 625/624, 1575/1573, 2200/2197, 8019/8000 | ||
| {{mapping| 327 518 759 918 1131 1210 }} | | {{mapping| 327 518 759 918 1131 1210 }} | ||
| 0.2301 | | +0.2301 | ||
| 0.2441 | | 0.2441 | ||
| 6.65 | | 6.65 | ||
| 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 85: | Line 87: | ||
| [[Mirkat]] | | [[Mirkat]] | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||