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	21.1
2	42.3	39/38, 42/41
3	63.4	27/26, 28/27, 29/28
4	84.5	41/39
5	105.7	33/31
6	126.8	14/13
7	147.9	37/34
8	169.1
9	190.2	19/17, 29/26
10	211.3	26/23, 35/31
11	232.5
12	253.6	22/19
13	274.7	34/29, 41/35
14	295.9
15	317	6/5
16	338.1	17/14, 28/23
17	359.3
18	380.4
19	401.5	29/23, 34/27
20	422.7	23/18, 37/29
21	443.8	22/17
22	464.9	17/13
23	486.1	41/31
24	507.2
25	528.3	19/14, 42/31
26	549.5
27	570.6	25/18
28	591.7	31/22, 38/27
29	612.9	37/26
30	634	13/9, 36/25
31	655.1	19/13
32	676.3	31/21, 34/23, 37/25
33	697.4
34	718.5
35	739.6	23/15
36	760.8
37	781.9	11/7
38	803	27/17, 35/22
39	824.2	29/18, 37/23
40	845.3	31/19
41	866.4	28/17, 38/23
42	887.6
43	908.7	22/13
44	929.8
45	951	26/15
46	972.1
47	993.2	39/22
48	1014.4
49	1035.5
50	1056.6	35/19
51	1077.8	28/15, 41/22
52	1098.9	17/9
53	1120	21/11
54	1141.2	29/15
55	1162.3
56	1183.4
57	1204.6
58	1225.7
59	1246.8	37/18, 39/19
60	1268	25/12, 27/13
61	1289.1
62	1310.2
63	1331.4	41/19
64	1352.5
65	1373.6	31/14, 42/19
66	1394.8	38/17
67	1415.9	34/15
68	1437	39/17
69	1458.2
70	1479.3
71	1500.4
72	1521.6	41/17
73	1542.7
74	1563.8	37/15, 42/17
75	1585	5/2
76	1606.1
77	1627.2
78	1648.4
79	1669.5
80	1690.6
81	1711.8
82	1732.9
83	1754
84	1775.2	39/14
85	1796.3	31/11
86	1817.4
87	1838.6	26/9
88	1859.7	38/13, 41/14
89	1880.8
90	1902	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)