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	Hekts	Approximate ratios
0	0	0	1/1
1	21.9	14.9
2	43.7	29.9	38/37, 39/38, 40/39, 41/40
3	65.6	44.8	27/26, 28/27
4	87.4	59.8	20/19, 41/39
5	109.3	74.7	33/31
6	131.2	89.7	14/13, 41/38
7	153	104.6	12/11
8	174.9	119.5	21/19, 31/28, 41/37
9	196.8	134.5	37/33
10	218.6	149.4	17/15
11	240.5	164.4	23/20, 31/27
12	262.3	179.3
13	284.2	194.3	20/17, 33/28
14	306.1	209.2	31/26, 37/31
15	327.9	224.1	23/19, 29/24
16	349.8	239.1	11/9, 38/31
17	371.6	254	26/21, 36/29
18	393.5	269
19	415.4	283.9	14/11, 33/26
20	437.2	298.9	9/7
21	459.1	313.8	30/23
22	481	328.7	29/22, 37/28
23	502.8	343.7
24	524.7	358.6	23/17
25	546.5	373.6	37/27
26	568.4	388.5
27	590.3	403.4	38/27
28	612.1	418.4	37/26
29	634	433.3	13/9
30	655.8	448.3	19/13
31	677.7	463.2	34/23, 40/27
32	699.6	478.2	3/2
33	721.4	493.1	41/27
34	743.3	508	20/13
35	765.2	523	14/9
36	787	537.9	41/26
37	808.9	552.9
38	830.7	567.8	21/13
39	852.6	582.8	18/11
40	874.5	597.7
41	896.3	612.6
42	918.2	627.6	17/10
43	940	642.5	31/18
44	961.9	657.5
45	983.8	672.4	30/17
46	1005.6	687.4	34/19
47	1027.5	702.3	29/16, 38/21
48	1049.4	717.2	11/6
49	1071.2	732.2	13/7
50	1093.1	747.1
51	1114.9	762.1	40/21
52	1136.8	777	27/14
53	1158.7	792	39/20, 41/21
54	1180.5	806.9
55	1202.4	821.8	2/1
56	1224.2	836.8
57	1246.1	851.7	37/18, 39/19
58	1268	866.7	27/13
59	1289.8	881.6	40/19
60	1311.7	896.6
61	1333.6	911.5	41/19
62	1355.4	926.4
63	1377.3	941.4	31/14
64	1399.1	956.3
65	1421	971.3
66	1442.9	986.2	23/10
67	1464.7	1001.1	7/3
68	1486.6	1016.1	26/11, 33/14
69	1508.4	1031
70	1530.3	1046	29/12
71	1552.2	1060.9	27/11
72	1574	1075.9
73	1595.9	1090.8
74	1617.8	1105.7	28/11
75	1639.6	1120.7
76	1661.5	1135.6
77	1683.3	1150.6	37/14
78	1705.2	1165.5
79	1727.1	1180.5	19/7
80	1748.9	1195.4	11/4
81	1770.8	1210.3	39/14
82	1792.6	1225.3	31/11
83	1814.5	1240.2
84	1836.4	1255.2	26/9
85	1858.2	1270.1	38/13, 41/14
86	1880.1	1285.1
87	1902	1300	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)