318edo

318edo is the 318 equal division of the octave into equal parts of 3.774 cents each.

318 = 2 × 3 × 53, and 318edo is contorted in the 5-limit, sharing the same mapping with 53edo. Besides, it shares its representations of the 11th and 17th harmonics with 159edo. However, compared to 159edo, the patent vals differ on the mappings for 7, 13, and 19. In the 5-limit, it tempers out the schisma (32805/32768), the kleisma (15625/15552), the amity comma (1600000/1594323), the semicomma (2109375/2097152), and the vulture comma (10485760000/10460353203). In the 11-limit it tempers out the swetisma (540/539), the wizardharry comma (4000/3993), the kalisma (9801/9800) and the nexus comma (1771561/1769472). So far, none of the 7-limit commas that are tempered out by this EDO have been found, while only one 13-limit comma, the cantonisma (10985/10976) has been found to be tempered out by this EDO. It is of note that 318edo divides the 4/3 perfect fourth into two even halves through means other than tempering out the island comma (676/675), and that this EDO likewise divides the apotome (2187/2048) in half by means other than tempering out the rastma (243/242).