146edt

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← 145edt

146edt

147edt →

Prime factorization	2 × 73
Step size	13.0271¢
Octave	92\146edt (1198.49¢) (→46\73edt)
Consistency limit	5
Distinct consistency limit	5

146 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 146edt or 146ed3), is a nonoctave tuning system that divides the interval of 3/1 into 146 equal parts of about 13 ¢ each. Each step represents a frequency ratio of 3^1/146, or the 146th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	13.027
2	26.054
3	39.081	44/43, 45/44, 46/45
4	52.108	34/33
5	65.135	27/26
6	78.163	23/22, 45/43
7	91.19	39/37
8	104.217
9	117.244	46/43
10	130.271	55/51
11	143.298	25/23
12	156.325	23/21
13	169.352	32/29, 43/39
14	182.379	10/9
15	195.406	28/25, 47/42
16	208.433	44/39
17	221.461	25/22
18	234.488
19	247.515	15/13
20	260.542	43/37, 50/43
21	273.569	41/35, 55/47
22	286.596	46/39
23	299.623	44/37
24	312.65
25	325.677	41/34
26	338.704	45/37
27	351.731	38/31
28	364.758	21/17
29	377.786	46/37, 51/41, 56/45
30	390.813
31	403.84	24/19
32	416.867	14/11
33	429.894	50/39
34	442.921	31/24
35	455.948	56/43
36	468.975	38/29
37	482.002	33/25, 37/28
38	495.029
39	508.056	55/41
40	521.084	27/20, 50/37
41	534.111
42	547.138
43	560.165	47/34
44	573.192	39/28
45	586.219
46	599.246
47	612.273	37/26, 47/33
48	625.3	33/23, 56/39
49	638.327
50	651.354	51/35
51	664.382	22/15
52	677.409	34/23, 37/25
53	690.436
54	703.463	3/2
55	716.49	56/37
56	729.517
57	742.544	43/28
58	755.571	48/31
59	768.598	39/25
60	781.625	11/7
61	794.652	19/12
62	807.68
63	820.707	45/28
64	833.734	34/21, 55/34
65	846.761	31/19, 44/27
66	859.788	23/14
67	872.815	48/29
68	885.842	5/3
69	898.869	37/22, 42/25
70	911.896	22/13
71	924.923
72	937.95	43/25
73	950.978	26/15, 45/26
74	964.005
75	977.032
76	990.059	39/22
77	1003.086	25/14
78	1016.113	9/5
79	1029.14	29/16
80	1042.167	42/23
81	1055.194	46/25
82	1068.221	50/27
83	1081.248	28/15
84	1094.275	47/25
85	1107.303	36/19
86	1120.33	21/11
87	1133.357	25/13, 52/27
88	1146.384	31/16
89	1159.411	41/21, 43/22
90	1172.438
91	1185.465
92	1198.492	2/1
93	1211.519
94	1224.546
95	1237.573	45/22, 47/23
96	1250.601	35/17
97	1263.628	56/27
98	1276.655	23/11
99	1289.682	40/19
100	1302.709
101	1315.736	47/22
102	1328.763	28/13
103	1341.79
104	1354.817
105	1367.844
106	1380.871	20/9
107	1393.899	47/21
108	1406.926
109	1419.953	25/11
110	1432.98
111	1446.007
112	1459.034
113	1472.061
114	1485.088	33/14
115	1498.115	19/8
116	1511.142
117	1524.169	41/17
118	1537.197	17/7
119	1550.224
120	1563.251	37/15
121	1576.278
122	1589.305
123	1602.332
124	1615.359
125	1628.386
126	1641.413
127	1654.44	13/5
128	1667.467	55/21
129	1680.494
130	1693.522
131	1706.549
132	1719.576	27/10
133	1732.603
134	1745.63
135	1758.657
136	1771.684
137	1784.711
138	1797.738
139	1810.765	37/13
140	1823.792	43/15
141	1836.82	26/9
142	1849.847
143	1862.874	44/15
144	1875.901
145	1888.928
146	1901.955	3/1

Harmonics

Approximation of harmonics in 146edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.51	+0.00	-3.02	+1.48	-1.51	+5.19	-4.52	+0.00	-0.02	+4.32	-3.02
	Relative (%)	-11.6	+0.0	-23.1	+11.4	-11.6	+39.8	-34.7	+0.0	-0.2	+33.2	-23.1
Steps (reduced)		92 (92)	146 (0)	184 (38)	214 (68)	238 (92)	259 (113)	276 (130)	292 (0)	306 (14)	319 (27)	330 (38)

Approximation of harmonics in 146edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.71	+3.68	+1.48	-6.03	+6.26	-1.51	-3.92	-1.53	+5.19	+2.82	+4.02
	Relative (%)	+13.1	+28.3	+11.4	-46.3	+48.0	-11.6	-30.1	-11.8	+39.8	+21.6	+30.9
Steps (reduced)		341 (49)	351 (59)	360 (68)	368 (76)	377 (85)	384 (92)	391 (99)	398 (106)	405 (113)	411 (119)	417 (125)