88edt

← 87edt

88edt

89edt →

Prime factorization	23 × 11
Step size	21.6131¢
Octave	56\88edt (1210.34¢) (→7\11edt)
Consistency limit	2
Distinct consistency limit	2

88EDT is the equal division of the third harmonic into 88 parts of 21.6131 cents each, corresponding to 55.5218 edo (similar to every second step of 111edo). It is consistent to the no-twos 11-limit, tempering out 1331/1323, 16875/16807, and 216513/214375. In the 3.4.5.7.11 subgroup, it tempers out 176/175, 540/539, 1331/1323, and 5120/5103.

88EDT is the 15th no-twos zeta peak EDT.

Harmonics

Approximation of prime harmonics in 88edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+10.34	+0.00	+1.78	+2.82	-1.60	-9.84	+1.22	+3.18	-3.38	+5.97	-1.43
	Relative (%)	+47.8	+0.0	+8.2	+13.1	-7.4	-45.5	+5.7	+14.7	-15.6	+27.6	-6.6
Steps (reduced)		56 (56)	88 (0)	129 (41)	156 (68)	192 (16)	205 (29)	227 (51)	236 (60)	251 (75)	270 (6)	275 (11)

Approximation of prime harmonics in 88edt

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-5.15	-9.96	-5.97	-8.66	-0.53	+8.32	-6.17	+4.32	-9.62	+7.13	+0.06
	Relative (%)	-23.8	-46.1	-27.6	-40.1	-2.5	+38.5	-28.5	+20.0	-44.5	+33.0	+0.3
Steps (reduced)		289 (25)	297 (33)	301 (37)	308 (44)	318 (54)	327 (63)	329 (65)	337 (73)	341 (77)	344 (80)	350 (86)

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	21.6
2	43.2
3	64.8	27/26
4	86.5	41/39
5	108.1	33/31
6	129.7
7	151.3
8	172.9	21/19
9	194.5	19/17
10	216.1	17/15
11	237.7	31/27
12	259.4	29/25
13	281
14	302.6	25/21, 31/26
15	324.2	35/29
16	345.8	11/9
17	367.4	21/17, 26/21
18	389
19	410.6	19/15, 33/26
20	432.3	9/7
21	453.9
22	475.5	25/19, 29/22
23	497.1
24	518.7	31/23
25	540.3	26/19
26	561.9
27	583.6	7/5
28	605.2
29	626.8	33/23
30	648.4
31	670	25/17
32	691.6
33	713.2
34	734.8	26/17, 29/19
35	756.5	17/11
36	778.1
37	799.7	27/17
38	821.3	37/23
39	842.9
40	864.5
41	886.1	5/3
42	907.8
43	929.4
44	951	26/15
45	972.6
46	994.2
47	1015.8	9/5
48	1037.4	31/17
49	1059	35/19
50	1080.7
51	1102.3	17/9
52	1123.9
53	1145.5	33/17
54	1167.1
55	1188.7
56	1210.3
57	1231.9
58	1253.6
59	1275.2	23/11
60	1296.8
61	1318.4	15/7
62	1340
63	1361.6
64	1383.2
65	1404.9
66	1426.5
67	1448.1
68	1469.7	7/3
69	1491.3	26/11
70	1512.9
71	1534.5	17/7
72	1556.1	27/11
73	1577.8
74	1599.4
75	1621
76	1642.6
77	1664.2
78	1685.8
79	1707.4
80	1729.1	19/7
81	1750.7
82	1772.3
83	1793.9	31/11
84	1815.5
85	1837.1	26/9
86	1858.7
87	1880.3
88	1902	3/1