88edo

In music, 88 equal temperament is the scale derived by dividing the octave into 88 equally large steps, 13.6363 cents in size. Using two different approximations to the perfect fifth (one of 51 steps and one of 52 steps), it is compatible with both meantone temperament and the particular variety of superpyth temperament(s) supported by 22 equal temperament, respectively. The meantone fifth is 0.0384 cents flatter than that of Lucy Tuning and, thus, audibly indistinguishable from it. It also gives the optimal patent val for the 11-limit mothra and euterpe temperaments.

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	3125/3072	126/125	121/120	66/65
2	?	50/49	45/44	45/44
3	?	36/35	33/32	27/26
4	128/125	128/125	77/75	77/75
5	25/24	25/24	25/24	25/24
6	78125/73728	21/20	21/20	21/20
7	?	392/375	132/125	132/125
8	16384/15625	15/14	15/14	15/14
9	16/15	16/15	16/15	14/13
10	625/576	375/343	242/225	130/121
11	?	35/32	12/11	12/11
12	?	49/45	11/10	11/10
13	2048/1875	125/112	125/112	125/112
14	9/8	9/8	9/8	9/8
15	9375/8192	28/25	28/25	28/25
16	?	225/196	25/22	25/22
17	?	8/7	8/7	8/7
18	144/125	144/125	121/105	121/104
19	75/64	75/64	75/64	65/56
20	78125/65536	7/6	7/6	7/6
21	?	147/125	88/75	77/65
22	18432/15625	25/21	25/21	13/11
23	6/5	6/5	6/5	6/5
24	625/512	448/375	121/100	121/100
25	?	60/49	27/22	27/22
26	?	49/40	11/9	11/9
27	768/625	625/504	150/121	150/121
28	5/4	5/4	5/4	5/4
29	15625/12288	56/45	44/35	33/26
30	?	125/98	125/98	125/98
31	98304/78125	9/7	9/7	9/7
32	32/25	32/25	32/25	32/25
33	125/96	125/96	100/77	100/77
34	?	21/16	21/16	13/10
35	?	98/75	33/25	33/25
36	4096/3125	75/56	75/56	65/49
37	4/3	4/3	4/3	4/3
38	3125/2304	168/125	121/90	88/65
39	?	135/98	15/11	15/11
40	?	48/35	11/8	11/8
41	512/375	343/250	242/175	242/175
42	25/18	25/18	25/18	25/18
43	46875/32768	7/5	7/5	7/5
44	?	625/441	125/88	125/88
45	65536/46875	10/7	10/7	10/7
46	36/25	36/25	36/25	36/25
47	375/256	375/256	175/121	175/121
48	?	35/24	16/11	13/9
49	?	147/100	22/15	22/15
50	4608/3125	125/84	125/84	65/44
51	3/2	3/2	3/2	3/2
52	3125/2048	112/75	112/75	98/65
53	?	75/49	50/33	50/33
54	?	32/21	32/21	20/13
55	192/125	192/125	77/50	77/50
56	25/16	25/16	25/16	25/16
57	78125/49152	14/9	11/7	11/7
58	?	196/125	196/125	196/125
59	24576/15625	45/28	35/22	35/22
60	8/5	8/5	8/5	8/5
61	625/384	625/384	121/75	121/75
62	?	80/49	18/11	13/8
63	?	49/30	33/20	33/20
64	1024/625	375/224	200/121	200/121
65	5/3	5/3	5/3	5/3
66	15625/9216	42/25	42/25	22/13
67	?	250/147	75/44	75/44
68	?	12/7	12/7	12/7
69	128/75	128/75	77/45	77/45
70	125/72	125/72	125/72	125/72
71	?	7/4	7/4	7/4
72	?	392/225	44/25	44/25
73	16384/9375	25/14	25/14	25/14
74	9/5	9/5	9/5	9/5
75	1875/1024	224/125	224/125	224/125
76	?	90/49	20/11	20/11
77	?	49/27	11/6	11/6
78	1152/625	625/336	225/121	121/65
79	15/8	15/8	15/8	13/7
80	15625/8192	28/15	28/15	28/15
81	?	375/196	125/66	125/66
82	?	27/14	21/11	21/11
83	48/25	48/25	48/25	48/25
84	125/64	125/64	125/64	125/64
85	?	35/18	35/18	35/18
86	?	49/25	49/25	49/25
87	6144/3125	125/63	125/63	65/33
88	2/1	2/1	2/1	2/1