559edo: Difference between revisions

m Cleanup; update prime error table
+infobox; +RTT table and rank-2 temperaments
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{{EDO intro|559}} 559edo [[tempering out|tempers out]] the luna comma, {{monzo| 38 -2 -15 }} and the minortone comma, {{monzo| -16 35 -17 }} in the [[5-limit]], as well as the [[monzisma]], {{monzo| 54 -37 2 }}; [[4375/4374]], [[2100875/2097152]], and 282475249/281250000 in the [[7-limit]]; 12005/11979, [[41503/41472]], 160083/160000, and 172032/171875 in the [[11-limit]]. Rank-2 temperaments it [[support]]s include [[mitonic]], [[lunatic]], [[acrokleismic]], [[monzism]], and [[meridic]].
{{Infobox ET
| Prime factorization = 13 × 43
| Step size = 2.14669¢
| Fifth = 327\559 (701.97¢)
| Semitones = 53:42 (113.77¢ : 90.16¢)
| Consistency = 11
}}
{{EDO intro|559}}
 
== Theory ==
559edo [[tempering out|tempers out]] the luna comma, {{monzo| 38 -2 -15 }} and the minortone comma, {{monzo| -16 35 -17 }} in the [[5-limit]], as well as the [[monzisma]], {{monzo| 54 -37 2 }}; [[4375/4374]], [[2100875/2097152]], and 282475249/281250000 in the [[7-limit]]; 12005/11979, [[41503/41472]], 160083/160000, and 172032/171875 in the [[11-limit]]. Rank-2 temperaments it [[support]]s include [[mitonic]], [[lunatic]], [[acrokleismic]], [[monzism]], and [[meridic]].


{{Harmonics in equal|559|columns=11}}
{{Harmonics in equal|559|columns=11}}
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 886 -559 }}
| [{{val| 559 886 }}]
| -0.0040
| 0.0040
| 0.19
|-
| 2.3.5
| {{monzo| 38 -2 -15 }}, {{monzo| -16 35 -17 }}
| [{{val| 559 886 1298 }}]
| -0.0157
| 0.0168
| 0.78
|-
| 2.3.5.7
| 4375/4374, 2100875/2097152, {{monzo| -4 -2 -9 10 }}
| [{{val| 559 886 1298 1569 }}]
| +0.0478
| 0.1109
| 5.16
|-
| 2.3.5.7.11
| 4375/4374, 12005/11979, 41503/41472, 172032/171875
| [{{val| 559 886 1298 1569 1934 }}]
| 0.0161
| 0.1175
| 5.48
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per octave
! Generator<br>(reduced)
! Cents<br>(reduced)
! Associated<br>ratio
! Temperaments
|-
| 1
| 90\559
| 182.47
| 10/9
| [[Mitonic]]
|-
| 1
| 90\559
| 193.20
| 352/315
| [[Lunatic]]
|-
| 1
| 116\559
| 249.02
| {{monzo| -26 18 -1 }}
| [[Monzismic]]
|-
| 1
| 147\559
| 315.56
| 6/5
| [[Acrokleismic]]
|}


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->