149ed4

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149ed4

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Prime factorization	149 (prime)
Step size	16.1074¢
Octave	75\149ed4 (1208.05¢)
Twelfth	118\149ed4 (1900.67¢)
Consistency limit	1
Distinct consistency limit	1

149 equal divisions of the 4th harmonic (abbreviated 149ed4) is a nonoctave tuning system that divides the interval of 4/1 into 149 equal parts of about 16.1 ¢ each. Each step represents a frequency ratio of 4^1/149, or the 149th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	16.107
2	32.215	55/54
3	48.322
4	64.43
5	80.537
6	96.644	37/35
7	112.752
8	128.859	14/13
9	144.966	25/23
10	161.074	45/41
11	177.181	41/37, 51/46
12	193.289	47/42
13	209.396	35/31
14	225.503	49/43
15	241.611	54/47
16	257.718	29/25
17	273.826	41/35
18	289.933	13/11
19	306.04	37/31
20	322.148	47/39
21	338.255	45/37
22	354.362
23	370.47
24	386.577
25	402.685	29/23
26	418.792	14/11
27	434.899	9/7
28	451.007
29	467.114	38/29, 55/42
30	483.221	41/31
31	499.329
32	515.436	31/23
33	531.544
34	547.651
35	563.758	18/13
36	579.866
37	595.973	55/39
38	612.081	47/33
39	628.188
40	644.295	45/31
41	660.403
42	676.51
43	692.617
44	708.725
45	724.832	38/25
46	740.94	23/15
47	757.047
48	773.154
49	789.262
50	805.369	43/27
51	821.477
52	837.584
53	853.691	18/11
54	869.799	38/23
55	885.906	5/3
56	902.013
57	918.121	17/10
58	934.228
59	950.336
60	966.443
61	982.55	30/17
62	998.658
63	1014.765
64	1030.872	49/27
65	1046.98
66	1063.087
67	1079.195
68	1095.302
69	1111.409
70	1127.517
71	1143.624
72	1159.732	41/21
73	1175.839
74	1191.946
75	1208.054
76	1224.161
77	1240.268	43/21
78	1256.376	31/15
79	1272.483
80	1288.591
81	1304.698
82	1320.805	15/7
83	1336.913
84	1353.02
85	1369.128
86	1385.235
87	1401.342
88	1417.45
89	1433.557
90	1449.664
91	1465.772	7/3
92	1481.879
93	1497.987
94	1514.094
95	1530.201
96	1546.309
97	1562.416	37/15
98	1578.523
99	1594.631
100	1610.738	38/15
101	1626.846
102	1642.953
103	1659.06
104	1675.168
105	1691.275
106	1707.383
107	1723.49	46/17
108	1739.597	41/15
109	1755.705
110	1771.812
111	1787.919
112	1804.027	17/6
113	1820.134
114	1836.242
115	1852.349
116	1868.456	50/17
117	1884.564
118	1900.671	3/1
119	1916.779
120	1932.886	55/18
121	1948.993
122	1965.101
123	1981.208
124	1997.315
125	2013.423
126	2029.53	42/13
127	2045.638
128	2061.745
129	2077.852
130	2093.96
131	2110.067
132	2126.174
133	2142.282	31/9
134	2158.389
135	2174.497
136	2190.604	39/11
137	2206.711
138	2222.819
139	2238.926	51/14
140	2255.034
141	2271.141
142	2287.248
143	2303.356
144	2319.463	42/11
145	2335.57	27/7
146	2351.678	35/9
147	2367.785	51/13, 55/14
148	2383.893
149	2400

Harmonics

Approximation of harmonics in 149ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.05	-1.28	+0.00	+0.26	+6.77	-2.38	+8.05	-2.57	-7.79	+4.39	-1.28
	Relative (%)	+50.0	-8.0	+0.0	+1.6	+42.0	-14.8	+50.0	-15.9	-48.4	+27.2	-8.0
Steps (reduced)		75 (75)	118 (118)	149 (0)	173 (24)	193 (44)	209 (60)	224 (75)	236 (87)	247 (98)	258 (109)	267 (118)

Approximation of harmonics in 149ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.11	+5.67	-1.02	+0.00	+7.80	+5.49	-7.58	+0.26	-3.67	-3.67	-0.09
	Relative (%)	+31.7	+35.2	-6.3	+0.0	+48.4	+34.1	-47.1	+1.6	-22.8	-22.8	-0.5
Steps (reduced)		276 (127)	284 (135)	291 (142)	298 (0)	305 (7)	311 (13)	316 (18)	322 (24)	327 (29)	332 (34)	337 (39)