147edt

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147edt

148edt →

Prime factorization	3 × 72
Step size	12.9385¢
Octave	93\147edt (1203.28¢) (→31\49edt)
Consistency limit	2
Distinct consistency limit	2

147 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 147edt or 147ed3), is a nonoctave tuning system that divides the interval of 3/1 into 147 equal parts of about 12.9 ¢ each. Each step represents a frequency ratio of 3^1/147, or the 147th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	12.9
2	25.9
3	38.8
4	51.8	34/33
5	64.7	27/26
6	77.6	23/22, 45/43
7	90.6	39/37
8	103.5
9	116.4
10	129.4	14/13, 55/51
11	142.3	51/47
12	155.3	47/43
13	168.2	43/39
14	181.1	10/9
15	194.1	19/17, 47/42
16	207
17	220	42/37
18	232.9
19	245.8
20	258.8	43/37
21	271.7	55/47
22	284.6	33/28
23	297.6
24	310.5
25	323.5	41/34, 47/39
26	336.4	17/14
27	349.3
28	362.3	37/30
29	375.2	36/29, 41/33
30	388.2
31	401.1	29/23
32	414	33/26, 47/37
33	427	55/43
34	439.9
35	452.8	13/10
36	465.8	17/13, 55/42
37	478.7	29/22
38	491.7
39	504.6
40	517.5
41	530.5
42	543.4	26/19
43	556.4	40/29, 51/37
44	569.3
45	582.2	7/5
46	595.2	55/39
47	608.1	27/19
48	621
49	634
50	646.9
51	659.9	41/28
52	672.8	28/19, 31/21
53	685.7	55/37
54	698.7
55	711.6
56	724.6	41/27
57	737.5
58	750.4
59	763.4	14/9
60	776.3	36/23, 47/30
61	789.2	30/19, 41/26
62	802.2	27/17
63	815.1
64	828.1	50/31
65	841
66	853.9	18/11
67	866.9	33/20
68	879.8
69	892.8
70	905.7
71	918.6	17/10
72	931.6
73	944.5
74	957.4	40/23
75	970.4
76	983.3	30/17
77	996.3
78	1009.2
79	1022.1
80	1035.1	20/11
81	1048	11/6
82	1061
83	1073.9
84	1086.8
85	1099.8	17/9
86	1112.7	19/10
87	1125.6	23/12
88	1138.6	27/14, 56/29
89	1151.5
90	1164.5	49/25
91	1177.4
92	1190.3
93	1203.3
94	1216.2
95	1229.2
96	1242.1	41/20, 43/21
97	1255
98	1268
99	1280.9
100	1293.8	19/9
101	1306.8
102	1319.7	15/7
103	1332.7	41/19
104	1345.6	37/17
105	1358.5
106	1371.5
107	1384.4
108	1397.4
109	1410.3
110	1423.2
111	1436.2	39/17
112	1449.1	30/13
113	1462
114	1475
115	1487.9	26/11
116	1500.9	50/21
117	1513.8
118	1526.7	29/12
119	1539.7	56/23
120	1552.6
121	1565.6	42/17
122	1578.5
123	1591.4
124	1604.4
125	1617.3	28/11
126	1630.2
127	1643.2
128	1656.1
129	1669.1
130	1682	37/14
131	1694.9
132	1707.9	51/19
133	1720.8	27/10
134	1733.8
135	1746.7
136	1759.6	47/17
137	1772.6	39/14
138	1785.5
139	1798.4
140	1811.4	37/13
141	1824.3	43/15
142	1837.3	26/9
143	1850.2
144	1863.1
145	1876.1
146	1889
147	1902	3/1

Harmonics

Approximation of harmonics in 147edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.28	+0.00	-6.38	-4.54	+3.28	-4.82	-3.11	+0.00	-1.27	+1.93	-6.38
	Relative (%)	+25.3	+0.0	-49.3	-35.1	+25.3	-37.3	-24.0	+0.0	-9.8	+14.9	-49.3
Steps (reduced)		93 (93)	147 (0)	185 (38)	215 (68)	240 (93)	260 (113)	278 (131)	294 (0)	308 (14)	321 (27)	332 (38)

Approximation of harmonics in 147edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-1.55	-4.54	+0.17	-1.28	+3.28	+0.24	+2.01	-4.82	+5.21	+5.88
	Relative (%)	-20.3	-12.0	-35.1	+1.3	-9.9	+25.3	+1.9	+15.6	-37.3	+40.3	+45.5
Steps (reduced)		343 (49)	353 (59)	362 (68)	371 (77)	379 (85)	387 (93)	394 (100)	401 (107)	407 (113)	414 (120)	420 (126)