298edo

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298 equal division divides the octave into steps of 4.027 cents each.

Theory

Approximation of prime intervals in 298 EDO
Prime number 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59
Error absolute (¢) +0.00 -1.28 +0.26 +1.64 +0.36 +1.08 -0.26 +0.47 -0.09 +1.30 -1.41 -1.68 +1.81 -0.11 -1.08 +0.32 -0.11
relative (%) +0 -32 +7 +41 +9 +27 -6 +12 -2 +32 -35 -42 +45 -3 -27 +8 -3
Steps (reduced) 298 (0) 472 (174) 692 (96) 837 (241) 1031 (137) 1103 (209) 1218 (26) 1266 (74) 1348 (156) 1448 (256) 1476 (284) 1552 (62) 1597 (107) 1617 (127) 1655 (165) 1707 (217) 1753 (263)

298edo has excellent representation of the 2.5.11.17.23.43.53.59 subgroup, with all the harmonics having errors of less than 10 rc. It is a double of 149edo, which is the smallest edo that is uniquely consistent within the 17-odd-limit. It supports a 17-limit extension of Sensi, 111 & 103 & 298. However, compared to 149edo, 298edo's patent val differs on the mapping of 7, 11, and 13th harmonics.

In the patent val, 298edo tempers out 351/350, 561/560, 936/935, and 1156/1155 in the full 17-limit. In the 2.5.11.13.17 subgroup, it tempers out 2200/2197 and 6656/6655.

In the 2.5.11.17.23.43.53.59, 298edo tempers out 3176/3175, 3128/3125, 3128/3127, 32906/32065 and 76585/76582.

The concoctic scale for 298edo is a generator of 105 steps (paraconcoctic).