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	16.3
2	32.6
3	48.9	34/33, 35/34, 38/37
4	65.2	26/25, 28/27
5	81.5	22/21
6	97.8	37/35
7	114.1	31/29
8	130.4
9	146.7	25/23, 37/34
10	163	11/10
11	179.3
12	195.6	37/33
13	211.9	26/23, 35/31
14	228.2
15	244.5	38/33
16	260.8
17	277.1	34/29
18	293.4
19	309.7
20	326	35/29
21	342.3
22	358.6
23	374.9	31/25
24	391.2
25	407.5	19/15
26	423.8	37/29
27	440.1
28	456.4
29	472.7	25/19
30	489
31	505.3
32	521.6	23/17, 27/20
33	537.9	15/11
34	554.2
35	570.4
36	586.7
37	603
38	619.3	10/7
39	635.6
40	651.9
41	668.2	25/17
42	684.5
43	700.8	3/2
44	717.1
45	733.4	26/17, 29/19
46	749.7
47	766	14/9
48	782.3	11/7
49	798.6
50	814.9
51	831.2
52	847.5	31/19
53	863.8
54	880.1
55	896.4
56	912.7	39/23
57	929
58	945.3	19/11
59	961.6
60	977.9	37/21
61	994.2
62	1010.5
63	1026.8	38/21
64	1043.1
65	1059.4	35/19
66	1075.7
67	1092
68	1108.3
69	1124.6
70	1140.9	29/15
71	1157.2
72	1173.5
73	1189.8
74	1206.1
75	1222.4
76	1238.7
77	1255	31/15
78	1271.3
79	1287.6
80	1303.9
81	1320.2	15/7
82	1336.5
83	1352.8
84	1369.1
85	1385.4
86	1401.7	9/4
87	1418	34/15
88	1434.3
89	1450.6
90	1466.9	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)