90ed7/3

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90ed7/3

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Prime factorization	2 × 32 × 5
Step size	16.2986¢
Octave	74\90ed7/3 (1206.09¢) (→37\45ed7/3)
Twelfth	117\90ed7/3 (1906.93¢) (→13\10ed7/3)
Consistency limit	3
Distinct consistency limit	3

90 equal divisions of 7/3 (abbreviated 90ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 90 equal parts of about 16.3 ¢ each. Each step represents a frequency ratio of (7/3)^1/90, or the 90th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	16.299
2	32.597
3	48.896	34/33, 35/34, 38/37
4	65.194	26/25, 28/27
5	81.493	22/21
6	97.791	37/35
7	114.09	31/29
8	130.389
9	146.687	25/23, 37/34
10	162.986	11/10
11	179.284
12	195.583	37/33
13	211.881	26/23, 35/31
14	228.18
15	244.478	38/33
16	260.777
17	277.076	34/29
18	293.374
19	309.673
20	325.971	35/29
21	342.27
22	358.568
23	374.867	31/25
24	391.166
25	407.464	19/15
26	423.763	37/29
27	440.061
28	456.36
29	472.658	25/19
30	488.957
31	505.256
32	521.554	23/17, 27/20
33	537.853	15/11
34	554.151
35	570.45
36	586.748
37	603.047
38	619.345	10/7
39	635.644
40	651.943
41	668.241	25/17
42	684.54
43	700.838	3/2
44	717.137
45	733.435	26/17, 29/19
46	749.734
47	766.033	14/9
48	782.331	11/7
49	798.63
50	814.928
51	831.227
52	847.525	31/19
53	863.824
54	880.123
55	896.421
56	912.72	39/23
57	929.018
58	945.317	19/11
59	961.615
60	977.914	37/21
61	994.213
62	1010.511
63	1026.81	38/21
64	1043.108
65	1059.407	35/19
66	1075.705
67	1092.004
68	1108.302
69	1124.601
70	1140.9	29/15
71	1157.198
72	1173.497
73	1189.795
74	1206.094
75	1222.392
76	1238.691
77	1254.99	31/15
78	1271.288
79	1287.587
80	1303.885
81	1320.184	15/7
82	1336.482
83	1352.781
84	1369.08
85	1385.378
86	1401.677	9/4
87	1417.975	34/15
88	1434.274
89	1450.572
90	1466.871	7/3

Harmonics

Approximation of harmonics in 90ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+6.09	+4.98	-4.11	+0.74	-5.23	+4.98	+1.98	-6.34	+6.83	+4.82	+0.87
	Relative (%)	+37.4	+30.5	-25.2	+4.5	-32.1	+30.5	+12.2	-38.9	+41.9	+29.6	+5.3
Steps (reduced)		74 (74)	117 (27)	147 (57)	171 (81)	190 (10)	207 (27)	221 (41)	233 (53)	245 (65)	255 (75)	264 (84)

Approximation of harmonics in 90ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-7.32	-5.23	+5.72	+8.08	+0.91	-0.25	+3.94	-3.37	-6.34	-5.39	-0.85
	Relative (%)	-44.9	-32.1	+35.1	+49.6	+5.6	-1.5	+24.2	-20.7	-38.9	-33.1	-5.2
Steps (reduced)		272 (2)	280 (10)	288 (18)	295 (25)	301 (31)	307 (37)	313 (43)	318 (48)	323 (53)	328 (58)	333 (63)