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58edo: Difference between revisions

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== 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]]
! rowspan="2" | [[Comma list|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]] (¢)
Line 335: Line 335:
|}
|}


58et is lower in relative error than any previous equal temperaments in the 13-limit, and the next ET that does better in this subgroup is 72.  
58et has a lower relative error than any previous equal temperaments in the 13-limit, and the next equal temperament that does better in this subgroup is [[72edo|72]].  


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-1 center-2"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
|-
|-
! Period<br>per Octave
! Period<br>per 8ve
! Generator
! Generator
! Cents
! Associated Ratio
! Temperament
! Temperament
|-
| 1
| 1\58
|
|-
|-
| 1
| 1
| 3\58
| 3\58
|  
| 62.07
|-
| 28/27
| 1
| [[Unicorn]] / alicorn / qilin
| 5\58
|
|-
| 1
| 7\58
|
|-
| 1
| 9\58
|  
|-
|-
| 1
| 1
| 11\58
| 11\58
| [[Llywelyn clan|Llywelyn]] / [[Gorgik]]
| 227.59
| 8/7
| [[Gorgik]]
|-
|-
| 1
| 1
| 13\58
| 13\58
| 268.97
| 7/6
| [[Infraorwell]]
| [[Infraorwell]]
|-
|-
| 1
| 1
| 15\58
| 15\58
| 310.34
| 6/5
| [[Myna]]
| [[Myna]]
|-
|-
| 1
| 1
| 17\58
| 17\58
| 351.72
| 49/40
| [[Hemififths]]
| [[Hemififths]]
|-
|-
| 1
| 1
| 19\58
| 19\58
|  
| 393.10
|-
| 64/51
| 1
| [[Emmthird]]
| 21\58
|  
|-
|-
| 1
| 1
| 23\58
| 23\58
| [[Vulture]] / [[buzzard]]<br>[[Subfourth]]
| 475.86
|-
| 21/16
| 1
| [[Buzzard]] / [[subfourth]]
| 25\58
|
|-
|-
| 1
| 1
| 27\58
| 27\58
| 558.62
| 11/8
| [[Thuja]]
| [[Thuja]]
|-
| 2
| 1\58
| [[Commatic]]
|-
| 2
| 2\58
|
|-
|-
| 2
| 2
| 3\58
| 3\58
|  
| 62.07
| 28/27
| [[Monocerus]]
|-
|-
| 2
| 2
| 4\58
| 1\58
| [[Harry]]
| 20.69
|-
| 81/80
| 2
| [[Commatic]]
| 5\58
| [[Srutal]] / [[diaschismic]]
|-
| 2
| 6\58
|
|-
| 2
| 7\58
|
|-
| 2
| 8\58
| [[Echidna]]<br>[[Supers]]
|-
|-
| 2
| 2
| 9\58
| 9\58
| 186.21
| 10/9
| [[Secant]]
| [[Secant]]
|-
|-
| 2
| 2
| 10\58
| 17\58<br>(12\58)
|  
| 351.72<br>(248.28)
| 11/9<br>(15/13)
| [[Sruti]]
|-
|-
| 2
| 2
| 11\58
| 21\58<br>(8\58)
|  
| 434.48<br>(165.52)
| 9/7<br>(11/10)
| [[Echidna]]
|-
|-
| 2
| 2
| 12\58
| 24\58<br>(5\58)
| [[Sruti]]<br>[[Semihemi]]
| 496.55<br>(103.45)
| 4/3<br>(17/16)
| [[Diaschismic]]
|-
|-
| 2
| 2
| 13\58
| 25\58<br>(4\58)
|  
| 517.24<br>(82.76)
|-
| 27/20<br>(21/20)
| 2
| [[Harry]]
| 14\58
|  
|-
|-
| 29
| 29
| 1\58
| 19\58<br>(1\58)
| 393.10<br>(20.69)
| 5/4<br>(91/90)
| [[Mystery]]
| [[Mystery]]
|}
|}
58et can also be detempered to [[semihemi]] (58 & 140), [[supers]] (58 & 152), [[condor]] (58 & 159), and [[eagle]] (58 & 212).


== Scales ==
== Scales ==
Retrieved from "https://en.xen.wiki/w/58edo"