87edt

← 86edt

87edt

88edt →

Prime factorization	3 × 29
Step size	21.8616¢
Octave	55\87edt (1202.39¢)
Consistency limit	4
Distinct consistency limit	4

Division of the third harmonic into 87 equal parts (87EDT) is related to 55 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 2.3853 cents stretched and the step size is about 21.8616 cents. Unlike 55edo, it is only consistent up to the 4-integer-limit, with discrepancy for the 5th harmonic.

Lookalikes: 55edo, 142ed6, 154ed7

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	21.862
2	43.723	38/37, 39/38, 40/39, 41/40
3	65.585	27/26, 28/27
4	87.446	20/19, 41/39
5	109.308	33/31
6	131.169	14/13, 41/38
7	153.031	12/11
8	174.892	21/19, 31/28, 41/37
9	196.754	37/33
10	218.616	17/15
11	240.477	23/20, 31/27
12	262.339
13	284.2	20/17, 33/28
14	306.062	31/26, 37/31
15	327.923	23/19, 29/24
16	349.785	11/9, 38/31
17	371.646	26/21, 36/29
18	393.508
19	415.369	14/11, 33/26
20	437.231	9/7
21	459.093	30/23
22	480.954	29/22, 37/28
23	502.816
24	524.677	23/17
25	546.539	37/27
26	568.4
27	590.262	38/27
28	612.123	37/26
29	633.985	13/9
30	655.847	19/13
31	677.708	34/23, 40/27
32	699.57	3/2
33	721.431	41/27
34	743.293	20/13
35	765.154	14/9
36	787.016	41/26
37	808.877
38	830.739	21/13
39	852.601	18/11
40	874.462
41	896.324
42	918.185	17/10
43	940.047	31/18
44	961.908
45	983.77	30/17
46	1005.631	34/19
47	1027.493	29/16, 38/21
48	1049.354	11/6
49	1071.216	13/7
50	1093.078
51	1114.939	40/21
52	1136.801	27/14
53	1158.662	39/20, 41/21
54	1180.524
55	1202.385	2/1
56	1224.247
57	1246.108	37/18, 39/19
58	1267.97	27/13
59	1289.832	40/19
60	1311.693
61	1333.555	41/19
62	1355.416
63	1377.278	31/14
64	1399.139
65	1421.001
66	1442.862	23/10
67	1464.724	7/3
68	1486.586	26/11, 33/14
69	1508.447
70	1530.309	29/12
71	1552.17	27/11
72	1574.032
73	1595.893
74	1617.755	28/11
75	1639.616
76	1661.478
77	1683.339	37/14
78	1705.201
79	1727.063	19/7
80	1748.924	11/4
81	1770.786	39/14
82	1792.647	31/11
83	1814.509
84	1836.37	26/9
85	1858.232	38/13, 41/14
86	1880.093
87	1901.955	3/1

Harmonics

Approximation of harmonics in 87edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.39	+0.00	+4.77	-9.90	+2.39	-2.15	+7.16	+0.00	-7.51	+2.38	+4.77
	Relative (%)	+10.9	+0.0	+21.8	-45.3	+10.9	-9.8	+32.7	+0.0	-34.4	+10.9	+21.8
Steps (reduced)		55 (55)	87 (0)	110 (23)	127 (40)	142 (55)	154 (67)	165 (78)	174 (0)	182 (8)	190 (16)	197 (23)

Approximation of harmonics in 87edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+0.24	-9.90	+9.54	-7.97	+2.39	-3.77	-5.13	-2.15	+4.76	-6.61
	Relative (%)	-12.0	+1.1	-45.3	+43.6	-36.4	+10.9	-17.3	-23.4	-9.8	+21.8	-30.2
Steps (reduced)		203 (29)	209 (35)	214 (40)	220 (46)	224 (50)	229 (55)	233 (59)	237 (63)	241 (67)	245 (71)	248 (74)