468edo: 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|371 -234}}
| {{monzo|371 -234}}
|{{mapping|468 742}}
| {{mapping|468 742}}
| -0.1922
| &minus;0.1922
| 0.1921
| 0.1921
| 7.49
| 7.49
|-
|-
|2.3.5
| 2.3.5
|2199023255552/2179240250625, 7629394531250/7625597484987
| 2199023255552/2179240250625, 7629394531250/7625597484987
|{{mapping|468 742 1087}}
| {{mapping|468 742 1087}}
| -0.2524
| &minus;0.2524
| 0.1785
| 0.1785
| 6.96
| 6.96
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, 2401/2400, 47141561040896/46708681640625
| 4375/4374, 2401/2400, 47141561040896/46708681640625
|{{mapping|468 742 1087 1314}}
| {{mapping|468 742 1087 1314}}
| -0.2253
| &minus;0.2253
| 0.1615
| 0.1615
| 6.30
| 6.30
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|3025/3024, 4375/4374, 2401/2400, 5767168/5740875
| 3025/3024, 4375/4374, 2401/2400, 5767168/5740875
|{{mapping|468 742 1087 1314 1619}}
| {{mapping|468 742 1087 1314 1619}}
| -0.1782
| &minus;0.1782
| 0.1725
| 0.1725
| 6.73
| 6.73
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|2080/2079, 1001/1000, 3025/3024, 1716/1715, 1982464/1974375
| 2080/2079, 1001/1000, 3025/3024, 1716/1715, 1982464/1974375
|{{mapping|468 742 1087 1314 1619 1732}}
| {{mapping|468 742 1087 1314 1619 1732}}
| -0.1709
| &minus;0.1709
| 0.1583
| 0.1583
| 6.17
| 6.17
|-
|-
|2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
|2080/2079, 1001/1000, 3025/3024, 1716/1715, 17920/17901, 30464/30375
| 2080/2079, 1001/1000, 3025/3024, 1716/1715, 17920/17901, 30464/30375
|{{mapping|468 742 1087 1314 1619 1732 1913}}
| {{mapping|468 742 1087 1314 1619 1732 1913}}
| -0.1526
| &minus;0.1526
| 0.1533
| 0.1533
| 5.98
| 5.98
|}
{{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<br>(reduced)*
! Cents<br>(reduced)*
! Associated<br>Ratio*
! Temperaments
|-
|-
|1
| 1
|179\468
| 179\468
|458.97
| 458.97
|125/96
| 125/96
|[[Majvam]]
| [[Majvam]]
|-
|-
|4
| 4
|194\468<br>(40\468)
| 194\468<br />(40\468)
|497.44<br>(102.56)
| 497.44<br />(102.56)
|4/3<br>(35/33)
| 4/3<br />(35/33)
|[[Undim]]
| [[Undim]]
|-
|-
|9
| 9
|123\468<br>(19\468)
| 123\468<br />(19\468)
|315.38<br>(48.72)
| 315.38<br />(48.72)
|6/5<br>(36/35)
| 6/5<br />(36/35)
|[[Ennealimmal]]
| [[Ennealimmal]]
|-
|-
|18
| 18
|97\468<br>(7\468)
| 97\468<br />(7\468)
|248.72<br>(17.95)
| 248.72<br />(17.95)
|231/200<br>(99/98)
| 231/200<br />(99/98)
|[[Hemiennealimmal]]
| [[Hemiennealimmal]]
|}
{{rank-2 end}}
 
{{orf}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct