350edo
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The 350 equal division divides the octave into 350 equal parts of 3.429 cents each. It tempers out 1600000/1594323, the amity comma, in the 5-limit, and 4375/4374, 5120/5103 and 6144/6125 in the 7-limit, and it provides the optimal patent val for amity temperament. In the 11-limit it tempers out 3025/3024 and 9801/9800, and provides the optimal patent val for hemiamity temperament.
350 is divisible by 2, 5, 7, 10, 14, 25, 35, 50, 70 and 175.