256edo: Difference between revisions

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~~== Theory ==~~

~~{{harmonics in equal}}~~

256edo is [[contorted]] in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO attracts little interest. 256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit.

256edo ~~can also be played using non~~-~~contorted harmonics, no matter how bad~~ the ~~approximation. Under such rule~~, ~~256edo supports~~ the 2.7~~.13.19 subgroup. In~~ the 2.~~7.13.19 subgroup in~~ the ~~patent~~ val, ~~256edo~~ tempers out ~~32851~~/~~32768~~, ~~and~~ [[support]]s the ~~corresponding 20 & 73 & 256 rank~~ 3 ~~temperament~~.

256edo 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]].

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

In the higher limits, it approximates harmonics 23, 43, and 47 quite accurately.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 256 factors into {{factorization|256}}, 256edo has subset edos {{EDOs| 2, 4, 8, 16, 32, 64, and 128 }}.

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 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
-== Theory ==
-{{harmonics in equal}}
-edo is [[contorted]] in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO attracts little interest. 256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit.
-edo can also be played using non-contorted harmonics, no matter how bad the approximation. Under such rule, 256edo supports the 2.7.13.19 subgroup. In the 2.7.13.19 subgroup in the patent val, 256edo tempers out 32851/32768, and [[support]]s the corresponding 20 & 73 & 256 rank 3 temperament.
+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]].
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+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 }}.