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	Hekts	Approximate ratios
0	0	0	1/1
1	21.1	14.4
2	42.3	28.9	39/38, 42/41
3	63.4	43.3	27/26, 28/27, 29/28
4	84.5	57.8	41/39
5	105.7	72.2	33/31
6	126.8	86.7	14/13
7	147.9	101.1	37/34
8	169.1	115.6
9	190.2	130	19/17, 29/26
10	211.3	144.4	26/23, 35/31
11	232.5	158.9
12	253.6	173.3	22/19
13	274.7	187.8	34/29, 41/35
14	295.9	202.2
15	317	216.7	6/5
16	338.1	231.1	17/14, 28/23
17	359.3	245.6
18	380.4	260
19	401.5	274.4	29/23, 34/27
20	422.7	288.9	23/18, 37/29
21	443.8	303.3	22/17
22	464.9	317.8	17/13
23	486.1	332.2	41/31
24	507.2	346.7
25	528.3	361.1	19/14, 42/31
26	549.5	375.6
27	570.6	390	25/18
28	591.7	404.4	31/22, 38/27
29	612.9	418.9	37/26
30	634	433.3	13/9, 36/25
31	655.1	447.8	19/13
32	676.3	462.2	31/21, 34/23, 37/25
33	697.4	476.7
34	718.5	491.1
35	739.6	505.6	23/15
36	760.8	520
37	781.9	534.4	11/7
38	803	548.9	27/17, 35/22
39	824.2	563.3	29/18, 37/23
40	845.3	577.8	31/19
41	866.4	592.2	28/17, 38/23
42	887.6	606.7
43	908.7	621.1	22/13
44	929.8	635.6
45	951	650	26/15
46	972.1	664.4
47	993.2	678.9	39/22
48	1014.4	693.3
49	1035.5	707.8
50	1056.6	722.2	35/19
51	1077.8	736.7	28/15, 41/22
52	1098.9	751.1	17/9
53	1120	765.6	21/11
54	1141.2	780	29/15
55	1162.3	794.4
56	1183.4	808.9
57	1204.6	823.3
58	1225.7	837.8
59	1246.8	852.2	37/18, 39/19
60	1268	866.7	25/12, 27/13
61	1289.1	881.1
62	1310.2	895.6
63	1331.4	910	41/19
64	1352.5	924.4
65	1373.6	938.9	31/14, 42/19
66	1394.8	953.3	38/17
67	1415.9	967.8	34/15
68	1437	982.2	39/17
69	1458.2	996.7
70	1479.3	1011.1
71	1500.4	1025.6
72	1521.6	1040	41/17
73	1542.7	1054.4
74	1563.8	1068.9	37/15, 42/17
75	1585	1083.3	5/2
76	1606.1	1097.8
77	1627.2	1112.2
78	1648.4	1126.7
79	1669.5	1141.1
80	1690.6	1155.6
81	1711.8	1170
82	1732.9	1184.4
83	1754	1198.9
84	1775.2	1213.3	39/14
85	1796.3	1227.8	31/11
86	1817.4	1242.2
87	1838.6	1256.7	26/9
88	1859.7	1271.1	38/13, 41/14
89	1880.8	1285.6
90	1902	1300	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)