89ed7/3

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Prime factorization	89 (prime)
Step size	16.4817¢
Octave	73\89ed7/3 (1203.16¢)
Twelfth	115\89ed7/3 (1895.39¢)
Consistency limit	2
Distinct consistency limit	2

89 equal divisions of 7/3 (abbreviated 89ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 89 equal parts of about 16.5⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/89, or the 89th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	16.5
2	33
3	49.4	36/35, 37/36
4	65.9	26/25
5	82.4
6	98.9	37/35
7	115.4	31/29
8	131.9	41/38
9	148.3	12/11
10	164.8	11/10
11	181.3
12	197.8	28/25, 37/33
13	214.3	26/23
14	230.7
15	247.2	15/13
16	263.7
17	280.2	20/17
18	296.7
19	313.2	6/5
20	329.6	23/19, 29/24
21	346.1
22	362.6	37/30
23	379.1
24	395.6
25	412	19/15, 33/26
26	428.5
27	445	22/17, 31/24
28	461.5	30/23
29	478	29/22, 33/25
30	494.5
31	510.9
32	527.4	19/14
33	543.9	26/19
34	560.4
35	576.9
36	593.3	31/22
37	609.8	37/26
38	626.3	33/23
39	642.8	29/20
40	659.3	19/13, 41/28
41	675.7
42	692.2
43	708.7
44	725.2	35/23, 38/25
45	741.7	23/15
46	758.2	31/20
47	774.6	36/23
48	791.1	30/19, 41/26
49	807.6
50	824.1	37/23
51	840.6
52	857	23/14, 41/25
53	873.5
54	890
55	906.5
56	923	29/17
57	939.5
58	955.9	33/19
59	972.4
60	988.9	23/13
61	1005.4	25/14
62	1021.9
63	1038.3	31/17
64	1054.8	35/19
65	1071.3	13/7
66	1087.8
67	1104.3	36/19
68	1120.8
69	1137.2
70	1153.7	35/18, 37/19
71	1170.2
72	1186.7
73	1203.2
74	1219.6
75	1236.1
76	1252.6
77	1269.1	25/12
78	1285.6
79	1302.1
80	1318.5	15/7
81	1335
82	1351.5	24/11
83	1368
84	1384.5
85	1400.9
86	1417.4
87	1433.9
88	1450.4	30/13
89	1466.9	7/3

Harmonics

Approximation of harmonics in 89ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.16	-6.56	+6.33	-0.91	-3.40	-6.56	-6.99	+3.36	+2.26	+2.07	-0.23
	Relative (%)	+19.2	-39.8	+38.4	-5.5	-20.6	-39.8	-42.4	+20.4	+13.7	+12.6	-1.4
Steps (reduced)		73 (73)	115 (26)	146 (57)	169 (80)	188 (10)	204 (26)	218 (40)	231 (53)	242 (64)	252 (74)	261 (83)

Approximation of harmonics in 89ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-6.95	-3.40	-7.47	-3.83	+6.59	+6.53	-4.67	+5.42	+3.36	+5.23	-5.80
	Relative (%)	-42.2	-20.6	-45.3	-23.2	+40.0	+39.6	-28.3	+32.9	+20.4	+31.8	-35.2
Steps (reduced)		269 (2)	277 (10)	284 (17)	291 (24)	298 (31)	304 (37)	309 (42)	315 (48)	320 (53)	325 (58)	329 (62)