301edo

The 301 equal division divides the octave into 301 equal parts of 3.98671 cents each. It is a strong 7-limit system, and distinctly consistent through the 17-limit. It tempers out 32805/32768 in the 5-limit, 2401/2400 in the 7-limit, 3025/3024, 5632/5625, 8019/8000 in the 11-limit, 847/845, 729/728, 1001/1000, 1716/1715 in the 13-limit, and 561/560, 833/832, 1089/1088, 1156/1155, 1275/1274 and 1701/1700 in the 17-limit. Because it tempers out both 32805/32768 and 2401/2400, it supports sesquiquartififths temperament.

301 is a composite number, since 301 = 7 * 43. This is related to the proposal of the deaf French mathematician and acoustician Joseph Sauveur to divide the octave in 43 parts called merides, and those into seven more parts called heptamerides. Back in the days of slide rules and log tables, this made sense since by multiplying the log base ten of the interval in question by 1000, one came close to how many heptamerides it constituted.