256edo: Difference between revisions

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-The 256 equal division divides the [[Octave|octave]] into 256 equal parts of exactly 4.6875 [[cent|cent]]s each.  It is contorted in the 3-limit in such a way as to lead to inconsistency, which is likely one of the reasons this EDO attracts little interest.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave]]
+edo is [[enfactoring|enfactored]] in the [[5-limit]] with the same tuning as [[128edo]], and the error of [[harmonic]] [[7/1|7]] leads to in[[consistency]], which is likely one of the reasons this edo attracts little interest. To start with, consider the sharp-tending 256c [[val]] {{val| 256 406 '''595''' 719 886 }}, which [[tempering out|tempers out]] [[2401/2400]], [[3388/3375]], [[5120/5103]], so that it [[support]]s 7-limit [[hemififths]] and [[11-limit]] [[semihemi]]. The [[patent val]] {{val| 256 406 '''594''' 719 886 }} tempers out [[540/539]], 2200/2187, [[4000/3969]], 12005/11979, among others. It is best tuned in the 2.3.7.11 [[subgroup]], in which it is consistent to the [[11-odd-limit]] minus intervals involving [[5/1|5]].
+In the higher limits, it approximates harmonics 23, 43, and 47 quite accurately.
+=== Odd harmonics ===
+{{Harmonics in equal|256}}
+=== Subsets and supersets ===
+Since 256 factors into {{factorization|256}}, 256edo has subset edos {{EDOs| 2, 4, 8, 16, 32, 64, and 128 }}.