177edo: Difference between revisions

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-The ''177 equal division'' divides the octave into 177 equal parts of 6.780 cents each. The patent val tempers out 245/243 and 2401/2400 in the 7-limit, supporting and providing a good tuning for [[Tetracot_family#Octacot|octacot temperament]].
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1|3]] is about halfway between its steps. It has good approximations to [[5/1|5]], [[7/1|7]], [[9/1|9]], [[13/1|13]], and [[19/1|19]], making it suitable for a 2.9.5.7.13.19 [[subgroup]] interpretation, which is equivalent to every other step of [[354edo]].
+Consider the full 7-limit patent val nonetheless, the equal temperament [[tempering out|tempers out]] [[245/243]] and [[2401/2400]], [[support]]ing and providing a good tuning for the [[octacot]] temperament.
+=== Odd harmonics ===
+{{Harmonics in equal|177}}
+=== Subsets and supersets ===
+Since 177 factors into {{factorization|177}}, 177edo contains [[3edo]] and [[59edo]] as its subsets. 354edo, which doubles it, provides good correction for the approximation of harmonic 3.