253edo: Difference between revisions

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== 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 harmonics 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.

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 harmonics 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 ===

=== Subsets and supersets ===

253 = 11 × 23, and has subset edos [[11edo]] and [[23edo]].

~~=== Prime harmonics ===~~

~~{{Harmonics in equal|253|columns=11}}~~

== Regular temperament properties ==

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* 20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s|Ketradektriatoh scale]]

~~[[Category:Equal divisions of the octave|###]] ~~

[[Category:Tertiaschis]]

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 == Theory ==
-edo 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 harmonics 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.
+edo 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 harmonics 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 ===
+{{Harmonics in equal|253}}
+=== Subsets and supersets ===
 = 11 × 23, and has subset edos [[11edo]] and [[23edo]].
-=== Prime harmonics ===
-{{Harmonics in equal|253|columns=11}}
 == Regular temperament properties ==
@@ Line 108: / Line 109: @@
 * 20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s|Ketradektriatoh scale]]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Tertiaschis]]