147edt

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 146edt

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	12.938
2	25.877
3	38.815
4	51.754	34/33
5	64.692	27/26
6	77.631	23/22, 45/43
7	90.569	39/37
8	103.508
9	116.446
10	129.385	14/13, 55/51
11	142.323	51/47
12	155.262	47/43
13	168.2	43/39
14	181.139	10/9
15	194.077	19/17, 47/42
16	207.016
17	219.954	42/37
18	232.892
19	245.831
20	258.769	43/37
21	271.708	55/47
22	284.646	33/28
23	297.585
24	310.523
25	323.462	41/34, 47/39
26	336.4	17/14
27	349.339
28	362.277	37/30
29	375.216	36/29, 41/33
30	388.154
31	401.093	29/23
32	414.031	33/26, 47/37
33	426.969	55/43
34	439.908
35	452.846	13/10
36	465.785	17/13, 55/42
37	478.723	29/22
38	491.662
39	504.6
40	517.539
41	530.477
42	543.416	26/19
43	556.354	40/29, 51/37
44	569.293
45	582.231	7/5
46	595.17	55/39
47	608.108	27/19
48	621.047
49	633.985
50	646.923
51	659.862	41/28
52	672.8	28/19, 31/21
53	685.739	55/37
54	698.677
55	711.616
56	724.554	41/27
57	737.493
58	750.431
59	763.37	14/9
60	776.308	36/23, 47/30
61	789.247	30/19, 41/26
62	802.185	27/17
63	815.124
64	828.062	50/31
65	841.001
66	853.939	18/11
67	866.877	33/20
68	879.816
69	892.754
70	905.693
71	918.631	17/10
72	931.57
73	944.508
74	957.447	40/23
75	970.385
76	983.324	30/17
77	996.262
78	1009.201
79	1022.139
80	1035.078	20/11
81	1048.016	11/6
82	1060.954
83	1073.893
84	1086.831
85	1099.77	17/9
86	1112.708	19/10
87	1125.647	23/12
88	1138.585	27/14, 56/29
89	1151.524
90	1164.462	49/25
91	1177.401
92	1190.339
93	1203.278
94	1216.216
95	1229.155
96	1242.093	41/20, 43/21
97	1255.032
98	1267.97
99	1280.908
100	1293.847	19/9
101	1306.785
102	1319.724	15/7
103	1332.662	41/19
104	1345.601	37/17
105	1358.539
106	1371.478
107	1384.416
108	1397.355
109	1410.293
110	1423.232
111	1436.17	39/17
112	1449.109	30/13
113	1462.047
114	1474.986
115	1487.924	26/11
116	1500.862	50/21
117	1513.801
118	1526.739	29/12
119	1539.678	56/23
120	1552.616
121	1565.555	42/17
122	1578.493
123	1591.432
124	1604.37
125	1617.309	28/11
126	1630.247
127	1643.186
128	1656.124
129	1669.063
130	1682.001	37/14
131	1694.939
132	1707.878	51/19
133	1720.816	27/10
134	1733.755
135	1746.693
136	1759.632	47/17
137	1772.57	39/14
138	1785.509
139	1798.447
140	1811.386	37/13
141	1824.324	43/15
142	1837.263	26/9
143	1850.201
144	1863.14
145	1876.078
146	1889.017
147	1901.955	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)