275edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 275 factors into | Since 275 factors into {{factorisation|275}}, 275edo has subset edos {{EDOs| 5, 11, 25 and 55 }}. | ||
== 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]] (¢) | ||
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| {{monzo| 436 -275 }} | | {{monzo| 436 -275 }} | ||
| {{mapping| 275 436 }} | | {{mapping| 275 436 }} | ||
| | | −0.1863 | ||
| 0.1862 | | 0.1862 | ||
| 4.27 | | 4.27 | ||
Line 36: | Line 37: | ||
| {{monzo| 24 -21 4 }}, {{monzo| 19 10 -15 }} | | {{monzo| 24 -21 4 }}, {{monzo| 19 10 -15 }} | ||
| {{mapping| 275 436 639 }} | | {{mapping| 275 436 639 }} | ||
| | | −0.4184 | ||
| 0.3618 | | 0.3618 | ||
| 8.29 | | 8.29 | ||
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| 6144/6125, 10976/10935, 9882516/9765625 | | 6144/6125, 10976/10935, 9882516/9765625 | ||
| {{mapping| 275 436 639 772 }} | | {{mapping| 275 436 639 772 }} | ||
| | | −0.3051 | ||
| 0.3698 | | 0.3698 | ||
| 8.48 | | 8.48 | ||
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| 441/440, 4000/3993, 6144/6125, 10976/10935 | | 441/440, 4000/3993, 6144/6125, 10976/10935 | ||
| {{mapping| 275 436 639 772 952 }} (275e) | | {{mapping| 275 436 639 772 952 }} (275e) | ||
| | | −0.4096 | ||
| 0.3912 | | 0.3912 | ||
| 8.97 | | 8.97 | ||
Line 57: | Line 58: | ||
| 364/363, 441/440, 676/675, 6144/6125, 10976/10935 | | 364/363, 441/440, 676/675, 6144/6125, 10976/10935 | ||
| {{mapping| 275 436 639 772 952 1018 }} (275e) | | {{mapping| 275 436 639 772 952 1018 }} (275e) | ||
| | | −0.4158 | ||
| 0.3574 | | 0.3574 | ||
| 8.19 | | 8.19 | ||
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=== 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 | ||
|- | |- | ||
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|- | |- | ||
| 11 | | 11 | ||
| 114\275<br>(11\275) | | 114\275<br />(11\275) | ||
| 497.45<br>(48.00) | | 497.45<br />(48.00) | ||
| 4/3<br>(36/35) | | 4/3<br />(36/35) | ||
| [[Hendecatonic]] | | [[Hendecatonic]] | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct |