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	21.9
2	43.7	38/37, 39/38, 40/39, 41/40
3	65.6	27/26, 28/27
4	87.4	20/19, 41/39
5	109.3	33/31
6	131.2	14/13, 41/38
7	153	12/11
8	174.9	21/19, 31/28, 41/37
9	196.8	37/33
10	218.6	17/15
11	240.5	23/20, 31/27
12	262.3
13	284.2	20/17, 33/28
14	306.1	31/26, 37/31
15	327.9	23/19, 29/24
16	349.8	11/9, 38/31
17	371.6	26/21, 36/29
18	393.5
19	415.4	14/11, 33/26
20	437.2	9/7
21	459.1	30/23
22	481	29/22, 37/28
23	502.8
24	524.7	23/17
25	546.5	37/27
26	568.4
27	590.3	38/27
28	612.1	37/26
29	634	13/9
30	655.8	19/13
31	677.7	34/23, 40/27
32	699.6	3/2
33	721.4	41/27
34	743.3	20/13
35	765.2	14/9
36	787	41/26
37	808.9
38	830.7	21/13
39	852.6	18/11
40	874.5
41	896.3
42	918.2	17/10
43	940	31/18
44	961.9
45	983.8	30/17
46	1005.6	34/19
47	1027.5	29/16, 38/21
48	1049.4	11/6
49	1071.2	13/7
50	1093.1
51	1114.9	40/21
52	1136.8	27/14
53	1158.7	39/20, 41/21
54	1180.5
55	1202.4	2/1
56	1224.2
57	1246.1	37/18, 39/19
58	1268	27/13
59	1289.8	40/19
60	1311.7
61	1333.6	41/19
62	1355.4
63	1377.3	31/14
64	1399.1
65	1421
66	1442.9	23/10
67	1464.7	7/3
68	1486.6	26/11, 33/14
69	1508.4
70	1530.3	29/12
71	1552.2	27/11
72	1574
73	1595.9
74	1617.8	28/11
75	1639.6
76	1661.5
77	1683.3	37/14
78	1705.2
79	1727.1	19/7
80	1748.9	11/4
81	1770.8	39/14
82	1792.6	31/11
83	1814.5
84	1836.4	26/9
85	1858.2	38/13, 41/14
86	1880.1
87	1902	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)