318edo: Difference between revisions
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Revision as of 11:17, 7 January 2021
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 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.
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). 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, 4096/4095, and 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).