559edo: Difference between revisions

5-limit notability
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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| 886 -559 }}
| {{monzo| 886 -559 }}
| {{mapping| 559 886 }}
| {{mapping| 559 886 }}
| -0.0040
| &minus;0.0040
| 0.0040
| 0.0040
| 0.19
| 0.19
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| {{monzo| 38 -2 -15 }}, {{monzo| -16 35 -17 }}
| {{monzo| 38 -2 -15 }}, {{monzo| -16 35 -17 }}
| {{mapping| 559 886 1298 }}
| {{mapping| 559 886 1298 }}
| -0.0157
| &minus;0.0157
| 0.0168
| 0.0168
| 0.78
| 0.78
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| 0.1175
| 0.1175
| 5.48
| 5.48
|}
{{comma basis end}}
* 559et has a lower relative error than any previous equal temperaments in the 5-limit, past [[441edo|441]] and before [[612edo|612]].  
* 559et has a lower relative error than any previous equal temperaments in the 5-limit, past [[441edo|441]] and before [[612edo|612]].  


=== 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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| [[Acrokleismic]]
| [[Acrokleismic]]
|-
|-
|13
| 13
|232\559<br>(17\559)
| 232\559<br />(17\559)
|498.03<br>(36.494)
| 498.03<br />(36.494)
|4/3<br>(?)
| 4/3<br />(?)
|[[Aluminium]]
| [[Aluminium]]
|-
|-
| 43
| 43
| 232\559<br>(2\559)
| 232\559<br />(2\559)
| 498.03<br>(4.29)
| 498.03<br />(4.29)
| 4/3<br>(385/384)
| 4/3<br />(385/384)
| [[Meridic]]
| [[Meridic]]
|}
{{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}}