147ed4

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147ed4

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Prime factorization	3 × 72
Step size	16.3265¢
Octave	74\147ed4 (1208.16¢)
Twelfth	116\147ed4 (1893.88¢)
Consistency limit	1
Distinct consistency limit	1

147 equal divisions of the 4th harmonic (abbreviated 147ed4) is a nonoctave tuning system that divides the interval of 4/1 into 147 equal parts of about 16.3 ¢ each. Each step represents a frequency ratio of 4^1/147, or the 147th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	16.3
2	32.7
3	49	35/34, 36/35, 37/36
4	65.3
5	81.6	43/41
6	98	18/17
7	114.3	31/29
8	130.6	41/38
9	146.9	37/34, 49/45
10	163.3
11	179.6
12	195.9	28/25, 47/42
13	212.2
14	228.6
15	244.9
16	261.2	43/37
17	277.6
18	293.9
19	310.2	55/46
20	326.5	35/29
21	342.9
22	359.2
23	375.5	36/29, 46/37
24	391.8
25	408.2	19/15
26	424.5	23/18
27	440.8
28	457.1
29	473.5	46/35
30	489.8
31	506.1
32	522.4	23/17
33	538.8
34	555.1
35	571.4
36	587.8
37	604.1
38	620.4
39	636.7
40	653.1
41	669.4
42	685.7	49/33, 55/37
43	702
44	718.4
45	734.7	55/36
46	751
47	767.3
48	783.7	11/7
49	800	46/29
50	816.3
51	832.7	55/34
52	849	31/19
53	865.3
54	881.6
55	898
56	914.3	39/23
57	930.6
58	946.9	19/11
59	963.3
60	979.6	44/25
61	995.9
62	1012.2
63	1028.6
64	1044.9
65	1061.2
66	1077.6	41/22
67	1093.9
68	1110.2
69	1126.5
70	1142.9	29/15
71	1159.2	43/22
72	1175.5
73	1191.8
74	1208.2
75	1224.5
76	1240.8
77	1257.1	31/15
78	1273.5
79	1289.8
80	1306.1
81	1322.4
82	1338.8	13/6
83	1355.1
84	1371.4
85	1387.8	29/13
86	1404.1
87	1420.4
88	1436.7	39/17
89	1453.1
90	1469.4
91	1485.7
92	1502
93	1518.4
94	1534.7	17/7
95	1551
96	1567.3	42/17, 47/19
97	1583.7
98	1600
99	1616.3
100	1632.7
101	1649
102	1665.3	34/13
103	1681.6	37/14
104	1698
105	1714.3	35/13
106	1730.6
107	1746.9
108	1763.3	36/13
109	1779.6
110	1795.9
111	1812.2	37/13
112	1828.6
113	1844.9
114	1861.2	41/14
115	1877.6
116	1893.9
117	1910.2
118	1926.5
119	1942.9	43/14
120	1959.2
121	1975.5
122	1991.8
123	2008.2
124	2024.5
125	2040.8
126	2057.1
127	2073.5
128	2089.8
129	2106.1
130	2122.4
131	2138.8
132	2155.1
133	2171.4
134	2187.8	46/13
135	2204.1
136	2220.4
137	2236.7
138	2253.1
139	2269.4
140	2285.7
141	2302
142	2318.4	42/11
143	2334.7
144	2351
145	2367.3	55/14
146	2383.7
147	2400

Harmonics

Approximation of harmonics in 147ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.16	-8.08	+0.00	+5.52	+0.09	-5.56	+8.16	+0.17	-2.64	-4.38	-8.08
	Relative (%)	+50.0	-49.5	+0.0	+33.8	+0.5	-34.1	+50.0	+1.1	-16.2	-26.8	-49.5
Steps (reduced)		74 (74)	116 (116)	147 (0)	171 (24)	190 (43)	206 (59)	221 (74)	233 (86)	244 (97)	254 (107)	263 (116)

Approximation of harmonics in 147ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.29	+2.60	-2.55	+0.00	-7.00	-7.99	-3.64	+5.52	+2.69	+3.78	-7.87
	Relative (%)	+1.8	+15.9	-15.6	+0.0	-42.9	-48.9	-22.3	+33.8	+16.5	+23.2	-48.2
Steps (reduced)		272 (125)	280 (133)	287 (140)	294 (0)	300 (6)	306 (12)	312 (18)	318 (24)	323 (29)	328 (34)	332 (38)