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	21.613
2	43.226
3	64.839	27/26
4	86.453	41/39
5	108.066	33/31
6	129.679
7	151.292
8	172.905	21/19
9	194.518	19/17
10	216.131	17/15
11	237.744	31/27
12	259.358	29/25
13	280.971
14	302.584	25/21, 31/26
15	324.197	35/29
16	345.81	11/9
17	367.423	21/17, 26/21
18	389.036
19	410.649	19/15, 33/26
20	432.263	9/7
21	453.876
22	475.489	25/19, 29/22
23	497.102
24	518.715	31/23
25	540.328	26/19
26	561.941
27	583.554	7/5
28	605.168
29	626.781	33/23
30	648.394
31	670.007	25/17
32	691.62
33	713.233
34	734.846	26/17, 29/19
35	756.459	17/11
36	778.073
37	799.686	27/17
38	821.299	37/23
39	842.912
40	864.525
41	886.138	5/3
42	907.751
43	929.364
44	950.978	26/15
45	972.591
46	994.204
47	1015.817	9/5
48	1037.43	31/17
49	1059.043	35/19
50	1080.656
51	1102.269	17/9
52	1123.883
53	1145.496	33/17
54	1167.109
55	1188.722
56	1210.335
57	1231.948
58	1253.561
59	1275.174	23/11
60	1296.788
61	1318.401	15/7
62	1340.014
63	1361.627
64	1383.24
65	1404.853
66	1426.466
67	1448.079
68	1469.693	7/3
69	1491.306	26/11
70	1512.919
71	1534.532	17/7
72	1556.145	27/11
73	1577.758
74	1599.371
75	1620.984
76	1642.598
77	1664.211
78	1685.824
79	1707.437
80	1729.05	19/7
81	1750.663
82	1772.276
83	1793.889	31/11
84	1815.503
85	1837.116	26/9
86	1858.729
87	1880.342
88	1901.955	3/1