90edt

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90edt

91edt →

Prime factorization	2 × 32 × 5
Step size	21.1328¢
Octave	57\90edt (1204.57¢) (→19\30edt)
Consistency limit	5
Distinct consistency limit	5

90 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 90edt or 90ed3), is a nonoctave tuning system that divides the interval of 3/1 into 90 equal parts of about 21.1 ¢ each. Each step represents a frequency ratio of 3^1/90, or the 90th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	21.133
2	42.266	39/38, 42/41
3	63.399	27/26, 28/27, 29/28
4	84.531	41/39
5	105.664	33/31
6	126.797	14/13
7	147.93	37/34
8	169.063
9	190.196	19/17, 29/26
10	211.328	26/23, 35/31
11	232.461
12	253.594	22/19
13	274.727	34/29, 41/35
14	295.86
15	316.993	6/5
16	338.125	17/14, 28/23
17	359.258
18	380.391
19	401.524	29/23, 34/27
20	422.657	23/18, 37/29
21	443.79	22/17
22	464.922	17/13
23	486.055	41/31
24	507.188
25	528.321	19/14, 42/31
26	549.454
27	570.587	25/18
28	591.719	31/22, 38/27
29	612.852	37/26
30	633.985	13/9, 36/25
31	655.118	19/13
32	676.251	31/21, 34/23, 37/25
33	697.384
34	718.516
35	739.649	23/15
36	760.782
37	781.915	11/7
38	803.048	27/17, 35/22
39	824.181	29/18, 37/23
40	845.313	31/19
41	866.446	28/17, 38/23
42	887.579
43	908.712	22/13
44	929.845
45	950.978	26/15
46	972.11
47	993.243	39/22
48	1014.376
49	1035.509
50	1056.642	35/19
51	1077.775	28/15, 41/22
52	1098.907	17/9
53	1120.04	21/11
54	1141.173	29/15
55	1162.306
56	1183.439
57	1204.572
58	1225.704
59	1246.837	37/18, 39/19
60	1267.97	25/12, 27/13
61	1289.103
62	1310.236
63	1331.369	41/19
64	1352.501
65	1373.634	31/14, 42/19
66	1394.767	38/17
67	1415.9	34/15
68	1437.033	39/17
69	1458.166
70	1479.298
71	1500.431
72	1521.564	41/17
73	1542.697
74	1563.83	37/15, 42/17
75	1584.963	5/2
76	1606.095
77	1627.228
78	1648.361
79	1669.494
80	1690.627
81	1711.76
82	1732.892
83	1754.025
84	1775.158	39/14
85	1796.291	31/11
86	1817.424
87	1838.557	26/9
88	1859.689	38/13, 41/14
89	1880.822
90	1901.955	3/1

Harmonics

Approximation of harmonics in 90edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.57	+0.00	+9.14	+3.22	+4.57	-8.71	-7.42	+0.00	+7.79	-9.28	+9.14
	Relative (%)	+21.6	+0.0	+43.3	+15.2	+21.6	-41.2	-35.1	+0.0	+36.9	-43.9	+43.3
Steps (reduced)		57 (57)	90 (0)	114 (24)	132 (42)	147 (57)	159 (69)	170 (80)	180 (0)	189 (9)	196 (16)	204 (24)

Approximation of harmonics in 90edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-4.13	+3.22	-2.85	-2.14	+4.57	-4.50	-8.77	-8.71	-4.71	+2.86
	Relative (%)	-12.5	-19.6	+15.2	-13.5	-10.1	+21.6	-21.3	-41.5	-41.2	-22.3	+13.6
Steps (reduced)		210 (30)	216 (36)	222 (42)	227 (47)	232 (52)	237 (57)	241 (61)	245 (65)	249 (69)	253 (73)	257 (77)