114edo

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114edo is the equal division of the octave into 114 parts, each of 10.52632 cents. In the 5-limit it tempers out 2048/2025, in the 7-limit 245/243, in the 11-limit 121/120 and 176/175, in the 13-limit 196/195 and 325/324, in the 17-limit 136/135 and 154/153, in the 19-limit 286/285 and 343/342. These commas make for 114edo being an excellent tuning for shrutar temperament; it is in fact the optimal patent val for shrutar in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.

Period of 19-limit Shrutar

Degree Cents
2 21.05263
3 31.57895
5 52.63158
7 73.68421
8 84.21053
10 105.26316
12 126.31579
13 136.842105
15 157.89474
17 178.94737
18 189.47369
20 210.52632
22 231.57895
23 242.10526
25 263.157895
27 284.21053
29 305.26316
30 315.78947
32 336.842105
34 357.89474
35 368.42105
37 389.47368
39 410.52632
40 421.05263
42 442.10526
44 463.157895
45 473.68421
47 494.73684
49 515.78947
50 526.31579
52 547.36842
54 568.42105
55 578.94737