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. In the 7-limit, it tenpers 225/224, 1728/1715 and 6144/6125. In the 11-limit, 75e val scores lower in badness than the patent val, tempers 100/99 and 243/242, in the 13-limit, it tempers 325/324 and 512/507, in the 17-limit, it tempers 120/119 and 256/255, in the 19-limit, it tempers 190/189 and 250/247.

It provides the optimal patent val for the 12&51 temperament in the 7-limit and the 31&44 temperament in the 19-limit.

Approximation of odd harmonics in 75edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+2.04	-2.31	+7.17	+4.09	-7.32	+7.47	-0.27	+7.04	+6.49	-6.78	-4.27
	Relative (%)	+12.8	-14.5	+44.8	+25.6	-45.7	+46.7	-1.7	+44.0	+40.5	-42.4	-26.7
Steps (reduced)		119 (44)	174 (24)	211 (61)	238 (13)	259 (34)	278 (53)	293 (68)	307 (7)	319 (19)	329 (29)	339 (39)

Intervals

Step	Cents
0	0
1	16
2	32
3	48
4	64
5	80
6	96
7	112
8	128
9	144
10	160
11	176
12	192
13	208
14	224
15	240
16	256
17	272
18	288
19	304
20	320
21	336
22	352
23	368
24	384
25	400
26	416
27	432
28	448
29	464
30	480
31	496
32	512
33	528
34	544
35	560
36	576
37	592
38	608
39	624
40	640
41	656
42	672
43	688
44	704
45	720
46	736
47	752
48	768
49	784
50	800
51	816
52	832
53	848
54	864
55	880
56	896
57	912
58	928
59	944
60	960
61	976
62	992
63	1008
64	1024
65	1040
66	1056
67	1072
68	1088
69	1104
70	1120
71	1136
72	1152
73	1168
74	1184
75	1200