410edo

The 410 equal divisions of the octave (410edo) is the equal division of the octave into 410 parts of 2.9268 cents each.

410edo is closely related to 205edo, but the patent val differs on the mappings for 7 and 13. It is contorted in the 5-limit, tempering out 1600000/1594323 (amity comma) and [38 -2 -15⟩ (luna/hemithirds comma), as well as [-29 -11 20⟩ (gammic comma) and [47 -15 -10⟩ (qintosec comma). It tempers out 2401/2400 (breedsma), 4802000/4782969 (canousma), and 48828125/48771072 (neptunisma) in the 7-limit; 5632/5625, 9801/9800, 14641/14580, and 117649/117612 in the 11-limit; 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095, 4225/4224 and 73205/73008 in the 13-limit.

It provides the optimal patent val for the 11- and 13-limit semiluna, hemiluna, and floral temperament, the rank-3 semicanou temperament, and the rank-4 temperament tempering out 14641/14580.