65edo: Difference between revisions

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{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-all right-2 left-3"
|-
|-
! #
! #
! [[Cent]]s
! [[Cent]]s
! Approximate Ratios *
! Approximate ratios*
! colspan="2" | [[Ups and Downs Notation]]
! colspan="2" | [[Ups and downs notation]]
|-
|-
| 0
| 0
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| D
| D
|}
|}
<nowiki>*</nowiki> based on treating 65edo as a 2.3.5.11.13/7.17.19.23.29.31.47 subgroup temperament.
<nowiki />* {{sg|2.3.5.11.13/7.17.19.23.29.31.47 subgroup}}


== 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
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| 32805/32768, 78732/78125
| 32805/32768, 78732/78125
| {{mapping| 65 103 151 }}
| {{mapping| 65 103 151 }}
| -0.110
| &minus;0.110
| 0.358
| 0.358
| 1.94
| 1.94
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| 243/242, 4000/3993, 5632/5625
| 243/242, 4000/3993, 5632/5625
| {{mapping| 65 103 151 225 }}
| {{mapping| 65 103 151 225 }}
| -0.266
| &minus;0.266
| 0.410
| 0.410
| 2.22
| 2.22
|}
{{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
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|-
|-
| 5
| 5
| 20\65<br>(6\65)
| 20\65<br />(6\65)
| 369.23<br>(110.77)
| 369.23<br />(110.77)
| 99/80<br>(16/15)
| 99/80<br />(16/15)
| [[Quintosec]]
| [[Quintosec]]
|-
|-
| 5
| 5
| 27\65<br>(1\65)
| 27\65<br />(1\65)
| 498.46<br>(18.46)
| 498.46<br />(18.46)
| 4/3<br>(81/80)
| 4/3<br />(81/80)
| [[Pental (temperament)|Pental]]
| [[Pental (temperament)|Pental]]
|-
|-
| 5
| 5
| 30\65<br>(4\65)
| 30\65<br />(4\65)
| 553.85<br>(73.85)
| 553.85<br />(73.85)
| 11/8<br>(25/24)
| 11/8<br />(25/24)
| [[Countdown]]
| [[Countdown]]
|}
{{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}}


== Scales ==
== Scales ==
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[[Category:Listen]]
[[Category:Listen]]
[[Category:Subgroup temperaments]]
[[Category:Schismic]]
[[Category:Schismic]]
[[Category:Sensipent]]
[[Category:Sensipent]]
[[Category:Subgroup temperaments]]
[[Category:Würschmidt]]
[[Category:Würschmidt]]