275edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! 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
| 2.3
| {{monzo| 436 -275 }}
| {{monzo| 436 -275 }}
| {{mapping| 275 436 }}
| {{mapping| 275 436 }}
| -0.1863
| &minus;0.1863
| 0.1862
| 0.1862
| 4.27
| 4.27
Line 36: Line 28:
| {{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
| &minus;0.4184
| 0.3618
| 0.3618
| 8.29
| 8.29
Line 43: Line 35:
| 6144/6125, 10976/10935, 9882516/9765625
| 6144/6125, 10976/10935, 9882516/9765625
| {{mapping| 275 436 639 772 }}
| {{mapping| 275 436 639 772 }}
| -0.3051
| &minus;0.3051
| 0.3698
| 0.3698
| 8.48
| 8.48
Line 50: Line 42:
| 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
| &minus;0.4096
| 0.3912
| 0.3912
| 8.97
| 8.97
Line 57: Line 49:
| 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
| &minus;0.4158
| 0.3574
| 0.3574
| 8.19
| 8.19
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 96: Line 82:
|-
|-
| 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]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}