253edo: Difference between revisions
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== Theory == | == Theory == | ||
253edo is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the [[prime harmonic]]s from 5 to 17 are all slightly flat. | 253edo is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the [[prime harmonic]]s from 5 to 17 are all slightly flat. It [[tempers out]] [[32805/32768]] in the 5-limit; [[2401/2400]] in the 7-limit; [[385/384]], 1375/1372 and [[4000/3993]] in the 11-limit; [[325/324]], [[1575/1573]] and [[2200/2197]] in the 13-limit; [[375/374]] and [[595/594]] in the 17-limit. It provides the [[optimal patent val]] for the [[tertiaschis]] temperament, and a good tuning for the [[sesquiquartififths]] temperament in the higher limits. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
253 | Since 253 factors into {{factorisation|253}}, and has subset edos [[11edo]] and [[23edo]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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| {{monzo| 401 -253 }} | | {{monzo| 401 -253 }} | ||
| {{mapping| 253 401 }} | | {{mapping| 253 401 }} | ||
| | | −0.007 | ||
| 0.007 | | 0.007 | ||
| 0.14 | | 0.14 | ||
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| [[Cotritone]] | | [[Cotritone]] | ||
|} | |} | ||
<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 | ||
== Scales == | == Scales == | ||