559edo: Difference between revisions
m Cleanup; update prime error table |
+infobox; +RTT table and rank-2 temperaments |
||
| Line 1: | Line 1: | ||
{{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 --> | ||