85edo

The 85 equal temperament divides the octave in 85 equal parts of 14.458 cents each. 85 = {{#rreplace: 5 * 17|/(\d+)(\D+)?/|\1\2}}, and it shares the same 3.9 cent sharp fifth as {{#rreplace: 17, 34, 51, and 68|/(\d+)(\D+)?/|\1\2}}. The patent val tempers out 3125/3072 in the 5-limit and 875/864, 245/243 and 225/224 in the 7-limit, so that it supports magic. It tempers out 100/99 and 245/243 in the 11-limit, supporting 11-limit magic, and 1188/1183, 847/845 and 1575/1573 in the 13-limit. It provides the optimal patent val for the 13-limit temperament tempering out 100/99, 540/539, 847/845 and 1575/1573.