318edo

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

Theory

Approximation of primary intervals in 318 EDO
Prime number 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.00 -0.07 -1.41 +0.99 -0.37 +0.98 +0.70 +0.60 -1.86 +0.61 -1.64
relative (%) +0 -2 -37 +26 -10 +26 +19 +16 -49 +16 -43
Steps (reduced) 318 (0) 504 (186) 738 (102) 893 (257) 1100 (146) 1177 (223) 1300 (28) 1351 (79) 1438 (166) 1545 (273) 1575 (303)

At only slightly more than 3.5 cents, the step size of 318edo is really close to being unnoticeable as is the case with other Mega-EDOs in this vicinity, so the steps themselves run a pretty high risk of blending completely into one another.

Mappings

318 = 2 × 3 × 53, and 318edo is contorted in both the 3-limit and the 5-limit, sharing the same mappings 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.

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.