88edt

← 87edt

88edt

89edt →

Prime factorization	23 × 11
Step size	21.6131 ¢
Octave	56\88edt (1210.34 ¢) (→ 7\11edt)
Consistency limit	3
Distinct consistency limit	3

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 largest EDT to not correspond to a val of some EDO that has a diatonic fifth, instead corresponding to both the 55b val, with 5edo's fifth, and the 56b val, with 7edo's fifth. It is also a 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	Hekts	Approximate ratios
0	0	0	1/1
1	21.6	14.8
2	43.2	29.5
3	64.8	44.3	27/26
4	86.5	59.1	41/39
5	108.1	73.9	33/31
6	129.7	88.6
7	151.3	103.4
8	172.9	118.2	21/19
9	194.5	133	19/17
10	216.1	147.7	17/15
11	237.7	162.5	31/27
12	259.4	177.3	29/25
13	281	192
14	302.6	206.8	25/21, 31/26
15	324.2	221.6	35/29
16	345.8	236.4	11/9
17	367.4	251.1	21/17, 26/21
18	389	265.9
19	410.6	280.7	19/15, 33/26
20	432.3	295.5	9/7
21	453.9	310.2
22	475.5	325	25/19, 29/22
23	497.1	339.8
24	518.7	354.5	31/23
25	540.3	369.3	26/19
26	561.9	384.1
27	583.6	398.9	7/5
28	605.2	413.6
29	626.8	428.4	33/23
30	648.4	443.2
31	670	458	25/17
32	691.6	472.7
33	713.2	487.5
34	734.8	502.3	26/17, 29/19
35	756.5	517	17/11
36	778.1	531.8
37	799.7	546.6	27/17
38	821.3	561.4	37/23
39	842.9	576.1
40	864.5	590.9
41	886.1	605.7	5/3
42	907.8	620.5
43	929.4	635.2
44	951	650	26/15
45	972.6	664.8
46	994.2	679.5
47	1015.8	694.3	9/5
48	1037.4	709.1	31/17
49	1059	723.9	35/19
50	1080.7	738.6
51	1102.3	753.4	17/9
52	1123.9	768.2
53	1145.5	783	33/17
54	1167.1	797.7
55	1188.7	812.5
56	1210.3	827.3
57	1231.9	842
58	1253.6	856.8
59	1275.2	871.6	23/11
60	1296.8	886.4
61	1318.4	901.1	15/7
62	1340	915.9
63	1361.6	930.7
64	1383.2	945.5
65	1404.9	960.2
66	1426.5	975
67	1448.1	989.8
68	1469.7	1004.5	7/3
69	1491.3	1019.3	26/11
70	1512.9	1034.1
71	1534.5	1048.9	17/7
72	1556.1	1063.6	27/11
73	1577.8	1078.4
74	1599.4	1093.2
75	1621	1108
76	1642.6	1122.7
77	1664.2	1137.5
78	1685.8	1152.3
79	1707.4	1167
80	1729.1	1181.8	19/7
81	1750.7	1196.6
82	1772.3	1211.4
83	1793.9	1226.1	31/11
84	1815.5	1240.9
85	1837.1	1255.7	26/9
86	1858.7	1270.5
87	1880.3	1285.2
88	1902	1300	3/1