1778edo: Difference between revisions

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 {{Infobox ET}}
+{{ED intro}}
-{{EDO intro|1778}}
+edo is [[consistent]] to the [[9-odd-limit]], but the errors of both [[harmonic]]s [[5/1|5]] and [[7/1|7]] are quite large. It is [[enfactoring|enfactored]] in the 5-limit, with the same tuning as [[889edo]], [[tempering out|tempering out]] {{monzo| -29 -11 20 }} (gammic comma) and {{monzo| -69 45 -1 }} ([[counterschisma]]). In the 7-limit, the equal temperament tempers out 2401/2400 ([[breedsma]]) and 48828125/48771072 (neptunisma). It provides the [[optimal patent val]] for the 7-limit [[neptune]] temperament.
-== Theory ==
+For higher harmonics, it is suitable for a 2.3.11.19.23.43.47.61 [[subgroup]] interpretation.
+=== Odd harmonics ===
 {{Harmonics in equal|1778}}
-Prime harmonics with less than 1 standard deviation in 1778edo are: 2, 3, 11, 23, 43, 47, 61. As such, it is best for use with the 2.3.11.23.43.47.61 subgroup.
-In the 7-limit, in which it is consistent, it provides the optimal patent val for the [[neptune]] temperament.
+=== Subsets and supersets ===
+Since 1778 factors into {{factorization|1778}}, 1778edo has subset edos {{EDOs| 2, 7, 14, 127, 254, and 889 }}.
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+[[Category:Neptune]]