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	16.327
2	32.653
3	48.98	35/34, 36/35, 37/36
4	65.306
5	81.633	43/41
6	97.959	18/17
7	114.286	31/29
8	130.612	41/38
9	146.939	37/34, 49/45
10	163.265
11	179.592
12	195.918	28/25, 47/42
13	212.245
14	228.571
15	244.898
16	261.224	43/37
17	277.551
18	293.878
19	310.204	55/46
20	326.531	35/29
21	342.857
22	359.184
23	375.51	36/29, 46/37
24	391.837
25	408.163	19/15
26	424.49	23/18
27	440.816
28	457.143
29	473.469	46/35
30	489.796
31	506.122
32	522.449	23/17
33	538.776
34	555.102
35	571.429
36	587.755
37	604.082
38	620.408
39	636.735
40	653.061
41	669.388
42	685.714	49/33, 55/37
43	702.041
44	718.367
45	734.694	55/36
46	751.02
47	767.347
48	783.673	11/7
49	800	46/29
50	816.327
51	832.653	55/34
52	848.98	31/19
53	865.306
54	881.633
55	897.959
56	914.286	39/23
57	930.612
58	946.939	19/11
59	963.265
60	979.592	44/25
61	995.918
62	1012.245
63	1028.571
64	1044.898
65	1061.224
66	1077.551	41/22
67	1093.878
68	1110.204
69	1126.531
70	1142.857	29/15
71	1159.184	43/22
72	1175.51
73	1191.837
74	1208.163
75	1224.49
76	1240.816
77	1257.143	31/15
78	1273.469
79	1289.796
80	1306.122
81	1322.449
82	1338.776	13/6
83	1355.102
84	1371.429
85	1387.755	29/13
86	1404.082
87	1420.408
88	1436.735	39/17
89	1453.061
90	1469.388
91	1485.714
92	1502.041
93	1518.367
94	1534.694	17/7
95	1551.02
96	1567.347	42/17, 47/19
97	1583.673
98	1600
99	1616.327
100	1632.653
101	1648.98
102	1665.306	34/13
103	1681.633	37/14
104	1697.959
105	1714.286	35/13
106	1730.612
107	1746.939
108	1763.265	36/13
109	1779.592
110	1795.918
111	1812.245	37/13
112	1828.571
113	1844.898
114	1861.224	41/14
115	1877.551
116	1893.878
117	1910.204
118	1926.531
119	1942.857	43/14
120	1959.184
121	1975.51
122	1991.837
123	2008.163
124	2024.49
125	2040.816
126	2057.143
127	2073.469
128	2089.796
129	2106.122
130	2122.449
131	2138.776
132	2155.102
133	2171.429
134	2187.755	46/13
135	2204.082
136	2220.408
137	2236.735
138	2253.061
139	2269.388
140	2285.714
141	2302.041
142	2318.367	42/11
143	2334.694
144	2351.02
145	2367.347	55/14
146	2383.673
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)