1612edo: Difference between revisions

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 {{Infobox ET}}
-{{EDO intro|1612}}
+{{ED intro}}
-edo is a strong [[5-limit]] system, providing the tuning for [[quasithird]], [[aluminium]] and [[counterorson]] temperaments.
+edo is a strong [[5-limit]] system, but it is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]]s [[7/1|7]] and [[11/1|11]] are about halfway between its steps. Nonetheless, the [[patent val]] is a strong 2.3.5.13.17.23.29.31 [[subgroup]] tuning.
+It provides a tuning for [[quasithird]], [[aluminium]] and [[counterorson]] temperaments in the 5-limit.
-While it is only consistent up to 5-limit, there are higher-limit mappings to be considered. 1612df val is the unique system supporting both the [[silicon]] and [[iron]] temperaments. The patent val is a strong 2.3.5.13.17.23.29.31 subgroup tuning.
 === Prime harmonics ===
-{{harmonics in equal|1612}}
+{{Harmonics in equal|1612}}
 === Subsets and supersets ===
-[[3224edo]], which doubles 1612edo, corrects mapping for 7 and 11.
+Since 1612 factors into {{factorization|1612}}, 1612edo has subset edos {{EDOs| 2, 4, 13, 26, 31, 52, 62, 124, 403, and 806 }}. [[3224edo]], which doubles 1612edo, corrects the mapping for 7 and 11.