318edo

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

Mappings

318 = 2 × 3 × 53, and 318edo is contorted in both the 3-limit and the 5-limit, sharing the same mappings with 53edo, with inconsistency developing for the 3-limit as a result. 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.

Commas

In the 5-limit, it tempers out the same commas as 53edo, including the schisma (32805/32768), the kleisma (15625/15552), the amity comma (1600000/1594323), the semicomma (2109375/2097152), the vulture comma (10485760000/10460353203), etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out the swetisma (540/539), the wizardharry (4000/3993), the kalisma (9801/9800) and the nexus comma (1771561/1769472). In the 13-limit, 1575/1573, 2080/2079, the schismina (4096/4095), and the cantonisma (10985/10976) have 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).