275edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|275}}
{{ED intro}}


== Theory ==
== Theory ==
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=== Subsets and supersets ===
=== Subsets and supersets ===
Since 275 factors into 5<sup>2</sup> × 11, 275edo has subset edos {{EDOs| 5, 11, 25 and 55 }}.  
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|Comma List]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning Error
! 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
| −0.1863
| 0.1862
| 0.1862
| 4.27
| 4.27
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| {{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
| −0.4184
| 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
| −0.3051
| 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
| −0.4096
| 0.3912
| 0.3912
| 8.97
| 8.97
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| 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
| −0.4158
| 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>Ratio*
! 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 it is distinct
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct