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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]] (%)
|-
|-
| 2.3.5
| 2.3.5
| {{monzo| 32 -7 -9 }}, {{monzo| -7 22 -12 }}
| {{monzo| 32 -7 -9 }}, {{monzo| -7 22 -12 }}
| {{mapping| 282 447 655 }}
| {{mapping| 282 447 655 }}
| -0.1684
| &minus;0.1684
| 0.1671
| 0.1671
| 3.93
| 3.93
Line 36: Line 28:
| 6144/6125, 118098/117649, 250047/250000
| 6144/6125, 118098/117649, 250047/250000
| {{mapping| 282 447 655 792 }}
| {{mapping| 282 447 655 792 }}
| -0.2498
| &minus;0.2498
| 0.2020
| 0.2020
| 4.75
| 4.75
Line 43: Line 35:
| 540/539, 4000/3993, 5632/5625, 137781/137500
| 540/539, 4000/3993, 5632/5625, 137781/137500
| {{mapping| 282 447 655 792 976 }}
| {{mapping| 282 447 655 792 976 }}
| -0.3081
| &minus;0.3081
| 0.2151
| 0.2151
| 5.06
| 5.06
Line 50: Line 42:
| 540/539, 729/728, 1575/1573, 2200/2197, 3584/3575
| 540/539, 729/728, 1575/1573, 2200/2197, 3584/3575
| {{mapping| 282 447 655 792 976 1044 }}
| {{mapping| 282 447 655 792 976 1044 }}
| -0.3480
| &minus;0.3480
| 0.2156
| 0.2156
| 5.07
| 5.07
Line 57: Line 49:
| 540/539, 729/728, 936/935, 1156/1155, 1575/1573, 2200/2197
| 540/539, 729/728, 936/935, 1156/1155, 1575/1573, 2200/2197
| {{mapping| 282 447 655 792 976 1044 1153 }}
| {{mapping| 282 447 655 792 976 1044 1153 }}
| -0.3481
| &minus;0.3481
| 0.1996
| 0.1996
| 4.69
| 4.69
Line 64: Line 56:
| 456/455, 540/539, 729/728, 936/935, 969/968, 1156/1155, 1575/1573
| 456/455, 540/539, 729/728, 936/935, 969/968, 1156/1155, 1575/1573
| {{mapping| 282 447 655 792 976 1044 1153 1198 }}
| {{mapping| 282 447 655 792 976 1044 1153 1198 }}
| -0.3152
| &minus;0.3152
| 0.2061
| 0.2061
| 4.84
| 4.84
Line 71: Line 63:
| 456/455, 540/539, 729/728, 760/759, 936/935, 969/968, 1156/1155, 1288/1287
| 456/455, 540/539, 729/728, 760/759, 936/935, 969/968, 1156/1155, 1288/1287
| {{mapping| 282 447 655 792 976 1044 1153 1198 1276 }}
| {{mapping| 282 447 655 792 976 1044 1153 1198 1276 }}
| -0.3173
| &minus;0.3173
| 0.1944
| 0.1944
| 4.57
| 4.57
|}
{{comma basis end}}
* 282et has a lower relative error than any previous equal temperaments in the 23-limit, past [[270edo|270]] and before [[311edo|311]].  
* 282et has a lower relative error than any previous equal temperaments in the 23-limit, past [[270edo|270]] and before [[311edo|311]].  


=== 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 123: Line 109:
|-
|-
| 6
| 6
| 51\282<br>(4\282)
| 51\282<br />(4\282)
| 217.02<br>(17.02)
| 217.02<br />(17.02)
| 17/15<br>(105/104)
| 17/15<br />(105/104)
| [[Stearnscape]]
| [[Stearnscape]]
|-
|-
| 6
| 6
| 80\282<br>(14\282)
| 80\282<br />(14\282)
| 340.43<br>(59.57)
| 340.43<br />(59.57)
| 162/133<br>(88/85)
| 162/133<br />(88/85)
| [[Semiseptichrome]]
| [[Semiseptichrome]]
|-
|-
| 6
| 6
| 117\282<br>(23\282)
| 117\282<br />(23\282)
| 497.87<br>(97.87)
| 497.87<br />(97.87)
| 4/3<br>(128/121)
| 4/3<br />(128/121)
| [[Sextile]]
| [[Sextile]]
|}
{{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}}


[[Category:Jupiter]]
[[Category:Septisuperfourth]]
[[Category:Septisuperfourth]]
[[Category:Jupiter]]
Retrieved from "https://en.xen.wiki/w/282edo"