559edo: Difference between revisions
ArrowHead294 (talk | contribs) m Partial undo |
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
559edo is a very strong 5-limit system. | 559edo is a very strong 5-limit system. It [[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]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 26: | Line 26: | ||
| {{monzo| 886 -559 }} | | {{monzo| 886 -559 }} | ||
| {{mapping| 559 886 }} | | {{mapping| 559 886 }} | ||
| | | −0.0040 | ||
| 0.0040 | | 0.0040 | ||
| 0.19 | | 0.19 | ||
| Line 33: | Line 33: | ||
| {{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 | ||
| 0.0168 | | 0.0168 | ||
| 0.78 | | 0.78 | ||
| Line 99: | Line 99: | ||
| [[Meridic]] | | [[Meridic]] | ||
|} | |} | ||
<nowiki />* [[Normal | <nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||