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	16.482
2	32.963
3	49.445	36/35, 37/36
4	65.927	26/25
5	82.408
6	98.89	37/35
7	115.372	31/29
8	131.854	41/38
9	148.335	12/11
10	164.817	11/10
11	181.299
12	197.78	28/25, 37/33
13	214.262	26/23
14	230.744
15	247.225	15/13
16	263.707
17	280.189	20/17
18	296.671
19	313.152	6/5
20	329.634	23/19, 29/24
21	346.116
22	362.597	37/30
23	379.079
24	395.561
25	412.042	19/15, 33/26
26	428.524
27	445.006	22/17, 31/24
28	461.487	30/23
29	477.969	29/22, 33/25
30	494.451
31	510.933
32	527.414	19/14
33	543.896	26/19
34	560.378
35	576.859
36	593.341	31/22
37	609.823	37/26
38	626.304	33/23
39	642.786	29/20
40	659.268	19/13, 41/28
41	675.75
42	692.231
43	708.713
44	725.195	35/23, 38/25
45	741.676	23/15
46	758.158	31/20
47	774.64	36/23
48	791.121	30/19, 41/26
49	807.603
50	824.085	37/23
51	840.566
52	857.048	23/14, 41/25
53	873.53
54	890.012
55	906.493
56	922.975	29/17
57	939.457
58	955.938	33/19
59	972.42
60	988.902	23/13
61	1005.383	25/14
62	1021.865
63	1038.347	31/17
64	1054.829	35/19
65	1071.31	13/7
66	1087.792
67	1104.274	36/19
68	1120.755
69	1137.237
70	1153.719	35/18, 37/19
71	1170.2
72	1186.682
73	1203.164
74	1219.645
75	1236.127
76	1252.609
77	1269.091	25/12
78	1285.572
79	1302.054
80	1318.536	15/7
81	1335.017
82	1351.499	24/11
83	1367.981
84	1384.462
85	1400.944
86	1417.426
87	1433.908
88	1450.389	30/13
89	1466.871	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)