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	13.1
2	26.2
3	39.4	43/42, 46/45
4	52.5	34/33
5	65.6	27/26
6	78.7	45/43
7	91.8	39/37
8	104.9
9	118.1	15/14, 46/43
10	131.2	41/38
11	144.3
12	157.4	23/21
13	170.5
14	183.6
15	196.8	28/25
16	209.9	35/31
17	223	33/29
18	236.1	47/41
19	249.2	52/45
20	262.3
21	275.5	34/29, 41/35
22	288.6
23	301.7
24	314.8	6/5
25	327.9	52/43
26	341
27	354.2
28	367.3	21/17, 47/38
29	380.4
30	393.5	54/43
31	406.6	43/34
32	419.7
33	432.9
34	446
35	459.1	43/33
36	472.2	46/35
37	485.3	41/31, 45/34, 49/37
38	498.4
39	511.6	47/35
40	524.7	23/17, 42/31
41	537.8	15/11
42	550.9
43	564
44	577.1
45	590.3	38/27
46	603.4
47	616.5
48	629.6
49	642.7	42/29
50	655.8	19/13
51	669
52	682.1	43/29, 46/31
53	695.2
54	708.3
55	721.4	47/31
56	734.5	26/17, 55/36
57	747.7
58	760.8	45/29
59	773.9
60	787	41/26, 52/33
61	800.1	27/17, 46/29
62	813.2
63	826.4	29/18
64	839.5
65	852.6	18/11
66	865.7
67	878.8
68	892
69	905.1
70	918.2
71	931.3
72	944.4
73	957.5
74	970.7
75	983.8
76	996.9
77	1010	52/29
78	1023.1
79	1036.2
80	1049.4	11/6
81	1062.5
82	1075.6	54/29
83	1088.7
84	1101.8	17/9
85	1114.9
86	1128.1
87	1141.2	29/15
88	1154.3	37/19
89	1167.4	51/26, 55/28
90	1180.5
91	1193.6
92	1206.8
93	1219.9
94	1233
95	1246.1	39/19
96	1259.2	29/14
97	1272.3
98	1285.5
99	1298.6
100	1311.7
101	1324.8
102	1337.9
103	1351
104	1364.2	11/5
105	1377.3	31/14, 51/23
106	1390.4
107	1403.5
108	1416.6	34/15
109	1429.7
110	1442.9
111	1456
112	1469.1
113	1482.2
114	1495.3
115	1508.4	43/18
116	1521.6
117	1534.7	17/7
118	1547.8
119	1560.9
120	1574
121	1587.1	5/2
122	1600.3
123	1613.4
124	1626.5
125	1639.6	49/19
126	1652.7
127	1665.9
128	1679	29/11
129	1692.1
130	1705.2
131	1718.3
132	1731.4
133	1744.6
134	1757.7
135	1770.8
136	1783.9	14/5
137	1797
138	1810.1	37/13
139	1823.3	43/15
140	1836.4	26/9
141	1849.5
142	1862.6
143	1875.7
144	1888.8
145	1902	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)