75edo

75edo divides the octave into 75 equal parts of exactly 16 cents each. In the 5-limit, it tempers out the tetracot comma, 20000/19683 and the semicomma 2109375/2097152, and provides a good tuning for tetracot temperament. It provides the optimal patent val for the 12&51 temperament in the 7-limit and the 31&75 temperament in the 13-limit.

Intervals

Step	Size in
	Cents	pions	7mus
0
1	16	16.96	20.48 (14.7B16)
2	32	33.92	40.96 (28.F616)
3	48	50.88	61.44 (3D.7116)
4	64	67.84	81.92 (51.EB816)
5	80	84.8	102.4 (66.6616)
6	96	101.76	122.88 (7A.E116)
7	112	118.72	143.36 (8F.5C16)
8	128	135.68	163.84 (A3.D716)
9	144	152.64	184.32 (B8.5216)
10	160	169.6	204.8 (CC.CD16)
11	176	186.56	225.28 (E1.4816)
12	192	203.52	245.76 (F5.C316)
13	208	220.48	266.24 (10A.3D16)
14	224	237.44	286.72 (11E.B816)
15	240	254.4	307.2 (133.3316)
16	256	271.36	327.68 (147.AE16)
17	272	288.32	348.16 (15C.2916)
18	288	305.28	368.64 (170.A416)
19	304	322.24	389.12 (185.1F16)
20	320	339.2	409.6 (199.9A16)
21	336	356.16	430.08 (1AE.14816)
22	352	373.12	450.56 (1C2.8F16)
23	368	390.08	471.04 (1D7.0A16)
24	384	407.04	491.52 (1E9.8516)
25	400	424	512 (20016)
26	416	440.96	532.48 (214.7B16)
27	432	457.92	552.96 (228.F616)
28	448	474.88	573.44 (23D.7116)
29	464	491.84	593.92 (251.EB816)
30	480	508.8	614.4 (266.6616)
31	496	525.76	634.88 (27A.E116)
32	512	542.72	655.36 (28F.5C16)
33	528	559.68	675.84 (2A3.D716)
34	544	576.64	696.32 (2B8.5216)
35	560	593.6	716.8 (2CC.CD16)
36	576	610.56	737.28 (2E1.4816)
37	592	627.52	757.76 (2F5.C316)
38	608	644.48	778.24 (30A.3D16)
39	624	661.44	798.72 (31E.B816)
40	640	678.4	819.2 (333.3316)
41	656	695.36	839.68 (347.AE16)
42	672	712.32	860.16 (35C.2916)
43	688	729.28	880.64 (370.A416)
44	704	746.24	901.12 (385.1F16)
45	720	763.2	921.6 (399.9A16)
46	736	780.16	942.08 (3AE.14816)
47	752	797.12	962.56 (3C2.8F16)
48	768	814.08	983.04 (3D7.0A16)
49	784	831.04	1003.52 (3E9.8516)
50	800	848	1024 (40016)
51	816	864.96	1044.48 (414.7B16)
52	832	881.92	1064.96 (428.F616)
53	848	898.88	1085.44 (43D.7116)
54	864	915.84	1105.92 (551.EB816)
55	880	932.8	1126.4 (466.6616)
56	896	949.76	1146.88 (47A.E116)
57	912	966.72	1167.36 (48F.5C16)
58	928	983.68	1187.84 (4A3.D716)
59	944	1000.64	1208.32 (4B8.5216)
60	960	1017.6	1228.8 (4CC.CD16)
61	976	1034.56	1249.28 (4E1.4816)
62	992	1051.52	1269.76 (4F5.C316)
63	1008	1068.48	1290.24 (50A.3D16)
64	1024	1085.44	1310.72 (51E.B816)
65	1040	1102.4	1331.2 (533.3316)
66	1056	1119.36	1351.68 (547.AE16)
67	1072	1136.32	1372.16 (55C.2916)
68	1088	1153.28	1392.64 (570.A416)
69	1104	1170.24	1413.12 (585.1F16)
70	1120	1187.2	1433.6 (599.9A16)
71	1136	1204.16	1454.08 (5AE.14816)
72	1152	1221.12	1474.56 (5C2.8F16)
73	1168	1238.08	1495.04 (5D7.0A16)
74	1184	1255.04	1515.52 (5E9.8516)
75	1200	1272	1536 (60016)