618edo: Difference between revisions

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 {{Infobox ET}}
-{{EDO intro|618}}
+{{ED intro}}
-== Theory ==
+edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1|3]] is about halfway between its steps. Nonetheless, as every other step of [[1236edo]], 618edo is excellent in approximating harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], and [[17/1|17]], making it suitable for a 2.9.5.7.11.13.17 [[subgroup]] interpretation, where the equal temperament notably [[tempering out|tempers out]] [[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], and [[10648/10647]]. With a reasonable approximation of 19, it further tempers out 2926/2925, 5985/5984, and 6175/6174.
-As every other step of [[1236edo]], 618edo is excellent in the 2.9.5.7.11.13.17 subgroup, where it notably tempers out [[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], and [[10648/10647]]. With a reasonable approximation of 19, it further tempers out 2926/2925, 5985/5984, and 6175/6174.
 === Odd harmonics ===
 {{Harmonics in equal|618}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+=== Subsets and supersets ===
+Since 618 factors into {{factorization|618}}, 618edo has subset edos {{EDOs| 2, 3, 6, 103, 206, and 309 }}. 1236edo, which doubles it, provides a good correction for harmonic 3.