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	Hekts	Approximate ratios
0	0	0	1/1
1	13	8.9
2	26.1	17.8
3	39.1	26.7	44/43, 45/44, 46/45
4	52.1	35.6	34/33
5	65.1	44.5	27/26
6	78.2	53.4	23/22, 45/43
7	91.2	62.3	39/37
8	104.2	71.2
9	117.2	80.1	46/43
10	130.3	89	55/51
11	143.3	97.9	25/23
12	156.3	106.8	23/21
13	169.4	115.8	32/29, 43/39
14	182.4	124.7	10/9
15	195.4	133.6	28/25, 47/42
16	208.4	142.5	44/39
17	221.5	151.4	25/22
18	234.5	160.3
19	247.5	169.2	15/13
20	260.5	178.1	43/37, 50/43
21	273.6	187	41/35, 55/47
22	286.6	195.9	46/39
23	299.6	204.8	44/37
24	312.7	213.7
25	325.7	222.6	41/34
26	338.7	231.5	45/37
27	351.7	240.4	38/31
28	364.8	249.3	21/17
29	377.8	258.2	46/37, 51/41, 56/45
30	390.8	267.1
31	403.8	276	24/19
32	416.9	284.9	14/11
33	429.9	293.8	50/39
34	442.9	302.7	31/24
35	455.9	311.6	56/43
36	469	320.5	38/29
37	482	329.5	33/25, 37/28
38	495	338.4
39	508.1	347.3	55/41
40	521.1	356.2	27/20, 50/37
41	534.1	365.1
42	547.1	374
43	560.2	382.9	47/34
44	573.2	391.8	39/28
45	586.2	400.7
46	599.2	409.6
47	612.3	418.5	37/26, 47/33
48	625.3	427.4	33/23, 56/39
49	638.3	436.3
50	651.4	445.2	51/35
51	664.4	454.1	22/15
52	677.4	463	34/23, 37/25
53	690.4	471.9
54	703.5	480.8	3/2
55	716.5	489.7	56/37
56	729.5	498.6
57	742.5	507.5	43/28
58	755.6	516.4	48/31
59	768.6	525.3	39/25
60	781.6	534.2	11/7
61	794.7	543.2	19/12
62	807.7	552.1
63	820.7	561	45/28
64	833.7	569.9	34/21, 55/34
65	846.8	578.8	31/19, 44/27
66	859.8	587.7	23/14
67	872.8	596.6	48/29
68	885.8	605.5	5/3
69	898.9	614.4	37/22, 42/25
70	911.9	623.3	22/13
71	924.9	632.2
72	938	641.1	43/25
73	951	650	26/15, 45/26
74	964	658.9
75	977	667.8
76	990.1	676.7	39/22
77	1003.1	685.6	25/14
78	1016.1	694.5	9/5
79	1029.1	703.4	29/16
80	1042.2	712.3	42/23
81	1055.2	721.2	46/25
82	1068.2	730.1	50/27
83	1081.2	739	28/15
84	1094.3	747.9	47/25
85	1107.3	756.8	36/19
86	1120.3	765.8	21/11
87	1133.4	774.7	25/13, 52/27
88	1146.4	783.6	31/16
89	1159.4	792.5	41/21, 43/22
90	1172.4	801.4
91	1185.5	810.3
92	1198.5	819.2	2/1
93	1211.5	828.1
94	1224.5	837
95	1237.6	845.9	45/22, 47/23
96	1250.6	854.8	35/17
97	1263.6	863.7	56/27
98	1276.7	872.6	23/11
99	1289.7	881.5	40/19
100	1302.7	890.4
101	1315.7	899.3	47/22
102	1328.8	908.2	28/13
103	1341.8	917.1
104	1354.8	926
105	1367.8	934.9
106	1380.9	943.8	20/9
107	1393.9	952.7	47/21
108	1406.9	961.6
109	1420	970.5	25/11
110	1433	979.5
111	1446	988.4
112	1459	997.3
113	1472.1	1006.2
114	1485.1	1015.1	33/14
115	1498.1	1024	19/8
116	1511.1	1032.9
117	1524.2	1041.8	41/17
118	1537.2	1050.7	17/7
119	1550.2	1059.6
120	1563.3	1068.5	37/15
121	1576.3	1077.4
122	1589.3	1086.3
123	1602.3	1095.2
124	1615.4	1104.1
125	1628.4	1113
126	1641.4	1121.9
127	1654.4	1130.8	13/5
128	1667.5	1139.7	55/21
129	1680.5	1148.6
130	1693.5	1157.5
131	1706.5	1166.4
132	1719.6	1175.3	27/10
133	1732.6	1184.2
134	1745.6	1193.2
135	1758.7	1202.1
136	1771.7	1211
137	1784.7	1219.9
138	1797.7	1228.8
139	1810.8	1237.7	37/13
140	1823.8	1246.6	43/15
141	1836.8	1255.5	26/9
142	1849.8	1264.4
143	1862.9	1273.3	44/15
144	1875.9	1282.2
145	1888.9	1291.1
146	1902	1300	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)