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	Hekts	Approximate ratios
0	0	0	1/1
1	12.9	8.8
2	25.9	17.7
3	38.8	26.5
4	51.8	35.4	34/33
5	64.7	44.2	27/26
6	77.6	53.1	23/22, 45/43
7	90.6	61.9	39/37
8	103.5	70.7
9	116.4	79.6
10	129.4	88.4	14/13, 55/51
11	142.3	97.3	51/47
12	155.3	106.1	47/43
13	168.2	115	43/39
14	181.1	123.8	10/9
15	194.1	132.7	19/17, 47/42
16	207	141.5
17	220	150.3	42/37
18	232.9	159.2
19	245.8	168
20	258.8	176.9	43/37
21	271.7	185.7	55/47
22	284.6	194.6	33/28
23	297.6	203.4
24	310.5	212.2
25	323.5	221.1	41/34, 47/39
26	336.4	229.9	17/14
27	349.3	238.8
28	362.3	247.6	37/30
29	375.2	256.5	36/29, 41/33
30	388.2	265.3
31	401.1	274.1	29/23
32	414	283	33/26, 47/37
33	427	291.8	55/43
34	439.9	300.7
35	452.8	309.5	13/10
36	465.8	318.4	17/13, 55/42
37	478.7	327.2	29/22
38	491.7	336.1
39	504.6	344.9
40	517.5	353.7
41	530.5	362.6
42	543.4	371.4	26/19
43	556.4	380.3	40/29, 51/37
44	569.3	389.1
45	582.2	398	7/5
46	595.2	406.8	55/39
47	608.1	415.6	27/19
48	621	424.5
49	634	433.3
50	646.9	442.2
51	659.9	451	41/28
52	672.8	459.9	28/19, 31/21
53	685.7	468.7	55/37
54	698.7	477.6
55	711.6	486.4
56	724.6	495.2	41/27
57	737.5	504.1
58	750.4	512.9
59	763.4	521.8	14/9
60	776.3	530.6	36/23, 47/30
61	789.2	539.5	30/19, 41/26
62	802.2	548.3	27/17
63	815.1	557.1
64	828.1	566	50/31
65	841	574.8
66	853.9	583.7	18/11
67	866.9	592.5	33/20
68	879.8	601.4
69	892.8	610.2
70	905.7	619
71	918.6	627.9	17/10
72	931.6	636.7
73	944.5	645.6
74	957.4	654.4	40/23
75	970.4	663.3
76	983.3	672.1	30/17
77	996.3	681
78	1009.2	689.8
79	1022.1	698.6
80	1035.1	707.5	20/11
81	1048	716.3	11/6
82	1061	725.2
83	1073.9	734
84	1086.8	742.9
85	1099.8	751.7	17/9
86	1112.7	760.5	19/10
87	1125.6	769.4	23/12
88	1138.6	778.2	27/14, 56/29
89	1151.5	787.1
90	1164.5	795.9	49/25
91	1177.4	804.8
92	1190.3	813.6
93	1203.3	822.4
94	1216.2	831.3
95	1229.2	840.1
96	1242.1	849	41/20, 43/21
97	1255	857.8
98	1268	866.7
99	1280.9	875.5
100	1293.8	884.4	19/9
101	1306.8	893.2
102	1319.7	902	15/7
103	1332.7	910.9	41/19
104	1345.6	919.7	37/17
105	1358.5	928.6
106	1371.5	937.4
107	1384.4	946.3
108	1397.4	955.1
109	1410.3	963.9
110	1423.2	972.8
111	1436.2	981.6	39/17
112	1449.1	990.5	30/13
113	1462	999.3
114	1475	1008.2
115	1487.9	1017	26/11
116	1500.9	1025.9	50/21
117	1513.8	1034.7
118	1526.7	1043.5	29/12
119	1539.7	1052.4	56/23
120	1552.6	1061.2
121	1565.6	1070.1	42/17
122	1578.5	1078.9
123	1591.4	1087.8
124	1604.4	1096.6
125	1617.3	1105.4	28/11
126	1630.2	1114.3
127	1643.2	1123.1
128	1656.1	1132
129	1669.1	1140.8
130	1682	1149.7	37/14
131	1694.9	1158.5
132	1707.9	1167.3	51/19
133	1720.8	1176.2	27/10
134	1733.8	1185
135	1746.7	1193.9
136	1759.6	1202.7	47/17
137	1772.6	1211.6	39/14
138	1785.5	1220.4
139	1798.4	1229.3
140	1811.4	1238.1	37/13
141	1824.3	1246.9	43/15
142	1837.3	1255.8	26/9
143	1850.2	1264.6
144	1863.1	1273.5
145	1876.1	1282.3
146	1889	1291.2
147	1902	1300	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)