444edo: Difference between revisions
ArrowHead294 (talk | contribs) m Partial undo |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
444edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. 444 = 4 × 111, | 444edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. Since {{nowrap|444 {{=}} 4 × 111}}, its harmonic [[3/1|3]] derives from [[111edo]]. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[250047/250000]], 29360128/29296875, 67108864/66976875 and in the 7-limit; [[3025/3024]], [[5632/5625]], 42592/42525, 102487/102400, [[131072/130977]], 160083/160000, 172032/171875, 322102/321489, 391314/390625 and [[1771561/1769472]] in the 11-limit. It [[support]]s the [[magnesium]] temperament. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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| {{monzo| 41 -20 -4 }}, {{monzo| -29 -11 20 }} | | {{monzo| 41 -20 -4 }}, {{monzo| -29 -11 20 }} | ||
| {{mapping| 444 704 1031 }} | | {{mapping| 444 704 1031 }} | ||
| | | −0.1821 | ||
| 0.2071 | | 0.2071 | ||
| 7.66 | | 7.66 | ||
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| [[Undim]] (444d) | | [[Undim]] (444d) | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||