218edo

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218edo, having a step size of 5.50458715596 cents, contains very accurate ratios, such as 7/4, 9/7, 8/7, 9/8, 10/9, 11/10 and 17/16 which are approximated within 0.55¢ deviation (10% the step size).

The following table shows the nearest matches for the interval, not the matches from the patent val. Bold numbers are off within less than 0.1 (10%) of the step size.

Interval fraction 3/2 4/3 5/4 8/5 5/3 6/5 7/4 8/7 10/9 9/5 9/8 16/9
Steps in 218edo 128 90 70 148 161 57 176 42 33 185 37 181

Suggested subgroups: 2.9.7.17 and 2.9.5.7.11.17.

Also explore 436edo.

Commas using the 13-limit patent val:

5-limit
20000/19683, 1220703125/1207959552
7-limit
4000/3969, 65625/65536, 245/243, 2401/2400 117649/116640
11-limit
4000/3993, 12005/11979, 16384/16335, 4375/4356, 78125/77616, 896/891, 67228/66825, 1375/1372, 6875/6804, 5632/5625, 385/384, 94325/93312, 15488/15435, 75625/75264, 15488/15309, 3388/3375, 1331/1323, 6655/6561, 65219/64800, 43923/43904, 73205/72576,
13-limit
28672/28561, 86240/85683, 20480/20449, 5600/5577, 16807/16731, 25000/24843, 6125/6084, 86625/86528, 68992/68445, 58080/57967, 96800/95823, 847/845, 41503/41067, 33275/33124, 65219/64896, 29575/29403, 4225/4224, 21632/21609, 676/675, 33124/32805, 9295/9261, 46475/45927, 13013/12960, 28561/28512