236edo: Difference between revisions

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The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer. Alternately, sharpening it to 236b gives a fifth that is in the golden [[diaschismic]] sequence.

The 236dghin val makes for a reasonable flat-tending system as far as the [[43-limit]], and is in fact [[diamond monotone]] in the [[43-odd-limit]]. This works best with a stretched octave.

The 236dghin val (using the second-best mappings of primes 7, 17, 19, 23, and 43) makes for a reasonable flat-tending system as far as the [[43-limit]], and is in fact [[diamond monotone]] in the [[45-odd-limit]]. This works best with a stretched octave.

=== Prime harmonics ===

{{Harmonics in equal|236|start=12|columns=11|collapsed=1|title=Approximation of prime harmonics in 236edo (continued)}}

=== Subsets and supersets ===

Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs| 2, 4, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.

Since 236 factors into 2<sup>2</sup> × 59, 236edo has subset edos {{EDOs| 2, 4, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.

== Regular temperament properties ==

@@ Line 7: / Line 7: @@
 The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer. Alternately, sharpening it to 236b gives a fifth that is in the golden [[diaschismic]] sequence.
-The 236dghin val makes for a reasonable flat-tending system as far as the [[43-limit]], and is in fact [[diamond monotone]] in the [[43-odd-limit]]. This works best with a stretched octave.
+The 236dghin val (using the second-best mappings of primes 7, 17, 19, 23, and 43) makes for a reasonable flat-tending system as far as the [[43-limit]], and is in fact [[diamond monotone]] in the [[45-odd-limit]]. This works best with a stretched octave.
 === Prime harmonics ===
-{{Harmonics in equal|236}}
+{{Harmonics in equal|236|columns=11}}
-{{Harmonics in equal|236|start=12}}
+{{Harmonics in equal|236|start=12|columns=11|collapsed=1|title=Approximation of prime harmonics in 236edo (continued)}}
 === Subsets and supersets ===
-Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs| 2, 4, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.
+Since 236 factors into 2<sup>2</sup> × 59, 236edo has subset edos {{EDOs| 2, 4, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.
 == Regular temperament properties ==