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	16.1
2	32.2	55/54
3	48.3
4	64.4
5	80.5
6	96.6	37/35
7	112.8
8	128.9	14/13
9	145	25/23
10	161.1	45/41
11	177.2	41/37, 51/46
12	193.3	47/42
13	209.4	35/31
14	225.5	49/43
15	241.6	54/47
16	257.7	29/25
17	273.8	41/35
18	289.9	13/11
19	306	37/31
20	322.1	47/39
21	338.3	45/37
22	354.4
23	370.5
24	386.6
25	402.7	29/23
26	418.8	14/11
27	434.9	9/7
28	451
29	467.1	38/29, 55/42
30	483.2	41/31
31	499.3
32	515.4	31/23
33	531.5
34	547.7
35	563.8	18/13
36	579.9
37	596	55/39
38	612.1	47/33
39	628.2
40	644.3	45/31
41	660.4
42	676.5
43	692.6
44	708.7
45	724.8	38/25
46	740.9	23/15
47	757
48	773.2
49	789.3
50	805.4	43/27
51	821.5
52	837.6
53	853.7	18/11
54	869.8	38/23
55	885.9	5/3
56	902
57	918.1	17/10
58	934.2
59	950.3
60	966.4
61	982.6	30/17
62	998.7
63	1014.8
64	1030.9	49/27
65	1047
66	1063.1
67	1079.2
68	1095.3
69	1111.4
70	1127.5
71	1143.6
72	1159.7	41/21
73	1175.8
74	1191.9
75	1208.1
76	1224.2
77	1240.3	43/21
78	1256.4	31/15
79	1272.5
80	1288.6
81	1304.7
82	1320.8	15/7
83	1336.9
84	1353
85	1369.1
86	1385.2
87	1401.3
88	1417.4
89	1433.6
90	1449.7
91	1465.8	7/3
92	1481.9
93	1498
94	1514.1
95	1530.2
96	1546.3
97	1562.4	37/15
98	1578.5
99	1594.6
100	1610.7	38/15
101	1626.8
102	1643
103	1659.1
104	1675.2
105	1691.3
106	1707.4
107	1723.5	46/17
108	1739.6	41/15
109	1755.7
110	1771.8
111	1787.9
112	1804	17/6
113	1820.1
114	1836.2
115	1852.3
116	1868.5	50/17
117	1884.6
118	1900.7	3/1
119	1916.8
120	1932.9	55/18
121	1949
122	1965.1
123	1981.2
124	1997.3
125	2013.4
126	2029.5	42/13
127	2045.6
128	2061.7
129	2077.9
130	2094
131	2110.1
132	2126.2
133	2142.3	31/9
134	2158.4
135	2174.5
136	2190.6	39/11
137	2206.7
138	2222.8
139	2238.9	51/14
140	2255
141	2271.1
142	2287.2
143	2303.4
144	2319.5	42/11
145	2335.6	27/7
146	2351.7	35/9
147	2367.8	51/13, 55/14
148	2383.9
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)