145edt

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145edt

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Prime factorization	5 × 29
Step size	13.1169¢
Octave	91\145edt (1193.64¢)
Consistency limit	2
Distinct consistency limit	2

145 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 145edt or 145ed3), is a nonoctave tuning system that divides the interval of 3/1 into 145 equal parts of about 13.1 ¢ each. Each step represents a frequency ratio of 3^1/145, or the 145th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	13.117
2	26.234
3	39.351	43/42, 46/45
4	52.468	34/33
5	65.585	27/26
6	78.702	45/43
7	91.819	39/37
8	104.935
9	118.052	15/14, 46/43
10	131.169	41/38
11	144.286
12	157.403	23/21
13	170.52
14	183.637
15	196.754	28/25
16	209.871	35/31
17	222.988	33/29
18	236.105	47/41
19	249.222	52/45
20	262.339
21	275.456	34/29, 41/35
22	288.572
23	301.689
24	314.806	6/5
25	327.923	52/43
26	341.04
27	354.157
28	367.274	21/17, 47/38
29	380.391
30	393.508	54/43
31	406.625	43/34
32	419.742
33	432.859
34	445.976
35	459.093	43/33
36	472.21	46/35
37	485.326	41/31, 45/34, 49/37
38	498.443
39	511.56	47/35
40	524.677	23/17, 42/31
41	537.794	15/11
42	550.911
43	564.028
44	577.145
45	590.262	38/27
46	603.379
47	616.496
48	629.613
49	642.73	42/29
50	655.847	19/13
51	668.963
52	682.08	43/29, 46/31
53	695.197
54	708.314
55	721.431	47/31
56	734.548	26/17, 55/36
57	747.665
58	760.782	45/29
59	773.899
60	787.016	41/26, 52/33
61	800.133	27/17, 46/29
62	813.25
63	826.367	29/18
64	839.484
65	852.601	18/11
66	865.717
67	878.834
68	891.951
69	905.068
70	918.185
71	931.302
72	944.419
73	957.536
74	970.653
75	983.77
76	996.887
77	1010.004	52/29
78	1023.121
79	1036.238
80	1049.354	11/6
81	1062.471
82	1075.588	54/29
83	1088.705
84	1101.822	17/9
85	1114.939
86	1128.056
87	1141.173	29/15
88	1154.29	37/19
89	1167.407	51/26, 55/28
90	1180.524
91	1193.641
92	1206.758
93	1219.875
94	1232.992
95	1246.108	39/19
96	1259.225	29/14
97	1272.342
98	1285.459
99	1298.576
100	1311.693
101	1324.81
102	1337.927
103	1351.044
104	1364.161	11/5
105	1377.278	31/14, 51/23
106	1390.395
107	1403.512
108	1416.629	34/15
109	1429.745
110	1442.862
111	1455.979
112	1469.096
113	1482.213
114	1495.33
115	1508.447	43/18
116	1521.564
117	1534.681	17/7
118	1547.798
119	1560.915
120	1574.032
121	1587.149	5/2
122	1600.266
123	1613.383
124	1626.499
125	1639.616	49/19
126	1652.733
127	1665.85
128	1678.967	29/11
129	1692.084
130	1705.201
131	1718.318
132	1731.435
133	1744.552
134	1757.669
135	1770.786
136	1783.903	14/5
137	1797.02
138	1810.136	37/13
139	1823.253	43/15
140	1836.37	26/9
141	1849.487
142	1862.604
143	1875.721
144	1888.838
145	1901.955	3/1

Harmonics

Approximation of harmonics in 145edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.36	+0.00	+0.40	-5.52	-6.36	+2.23	-5.96	+0.00	+1.23	-6.37	+0.40
	Relative (%)	-48.5	+0.0	+3.0	-42.1	-48.5	+17.0	-45.4	+0.0	+9.4	-48.5	+3.0
Steps (reduced)		91 (91)	145 (0)	183 (38)	212 (67)	236 (91)	257 (112)	274 (129)	290 (0)	304 (14)	316 (26)	328 (38)

Approximation of harmonics in 145edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.11	-4.13	-5.52	+0.80	+0.78	-6.36	+4.97	-5.13	+2.23	+0.39	+2.14
	Relative (%)	+46.6	-31.5	-42.1	+6.1	+5.9	-48.5	+37.9	-39.1	+17.0	+3.0	+16.3
Steps (reduced)		339 (49)	348 (58)	357 (67)	366 (76)	374 (84)	381 (91)	389 (99)	395 (105)	402 (112)	408 (118)	414 (124)