149edt

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149edt

150edt →

Prime factorization	149 (prime)
Step size	12.7648¢
Octave	94\149edt (1199.89¢) (semiconvergent)
Consistency limit	23
Distinct consistency limit	14

149 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 149edt or 149ed3), is a nonoctave tuning system that divides the interval of 3/1 into 149 equal parts of about 12.8 ¢ each. Each step represents a frequency ratio of 3^1/149, or the 149th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	12.765
2	25.53
3	38.294	44/43, 45/44, 46/45, 47/46
4	51.059	34/33, 35/34
5	63.824	27/26, 28/27
6	76.589	23/22, 47/45
7	89.354	20/19
8	102.118	35/33, 52/49
9	114.883	31/29, 47/44
10	127.648	14/13
11	140.413	51/47
12	153.178	47/43
13	165.942	11/10
14	178.707	41/37, 51/46
15	191.472	19/17, 48/43
16	204.237	9/8
17	217.002	17/15
18	229.766	8/7
19	242.531	23/20
20	255.296	22/19, 51/44
21	268.061	7/6
22	280.826	20/17
23	293.59	32/27, 45/38
24	306.355	37/31, 43/36
25	319.12
26	331.885	23/19, 40/33
27	344.65
28	357.414	43/35
29	370.179	26/21, 57/46
30	382.944
31	395.709	44/35, 49/39, 54/43
32	408.474	19/15
33	421.238	37/29, 51/40
34	434.003	9/7
35	446.768	22/17, 57/44
36	459.533	30/23, 43/33
37	472.298	21/16, 46/35
38	485.062	41/31, 45/34, 49/37
39	497.827	4/3
40	510.592	43/32, 47/35, 51/38
41	523.357	23/17
42	536.122	15/11
43	548.886
44	561.651	47/34
45	574.416	39/28, 46/33
46	587.181
47	599.946	41/29
48	612.71	47/33, 57/40
49	625.475	33/23, 56/39
50	638.24
51	651.005	51/35
52	663.77	22/15
53	676.534	34/23
54	689.299
55	702.064	3/2
56	714.829
57	727.594	35/23
58	740.358	23/15
59	753.123	17/11
60	765.888	14/9
61	778.653	47/30
62	791.418	30/19, 49/31
63	804.182	35/22, 43/27
64	816.947
65	829.712	21/13
66	842.477
67	855.242
68	868.006	33/20, 38/23
69	880.771
70	893.536	57/34
71	906.301	27/16
72	919.066	17/10
73	931.83	12/7
74	944.595
75	957.36	40/23
76	970.125	7/4
77	982.889	30/17
78	995.654	16/9
79	1008.419	34/19, 43/24
80	1021.184
81	1033.949	20/11
82	1046.713
83	1059.478
84	1072.243	13/7
85	1085.008
86	1097.773	49/26
87	1110.537	19/10
88	1123.302	44/23
89	1136.067	27/14, 52/27
90	1148.832	33/17
91	1161.597	43/22, 45/23
92	1174.361
93	1187.126
94	1199.891	2/1
95	1212.656
96	1225.421
97	1238.185	45/22, 47/23
98	1250.95	35/17
99	1263.715	56/27
100	1276.48	23/11
101	1289.245	40/19
102	1302.009
103	1314.774	47/22
104	1327.539	28/13
105	1340.304
106	1353.069
107	1365.833	11/5
108	1378.598	51/23
109	1391.363	38/17
110	1404.128	9/4
111	1416.893	34/15
112	1429.657	16/7
113	1442.422	23/10
114	1455.187	44/19, 51/22
115	1467.952	7/3
116	1480.717	40/17, 47/20
117	1493.481	45/19
118	1506.246	43/18
119	1519.011
120	1531.776	46/19
121	1544.541
122	1557.305
123	1570.07	52/21, 57/23
124	1582.835
125	1595.6
126	1608.365	38/15
127	1621.129	51/20
128	1633.894	18/7
129	1646.659	44/17, 57/22
130	1659.424
131	1672.189	21/8
132	1684.953	45/17
133	1697.718	8/3
134	1710.483	43/16, 51/19
135	1723.248	46/17
136	1736.013	30/11
137	1748.777
138	1761.542	47/17
139	1774.307	39/14
140	1787.072
141	1799.837
142	1812.601	57/20
143	1825.366
144	1838.131	26/9
145	1850.896
146	1863.661	44/15
147	1876.425
148	1889.19
149	1901.955	3/1

Harmonics

Approximation of harmonics in 149edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.11	+0.00	-0.22	-3.59	-0.11	+1.08	-0.33	+0.00	-3.70	-2.76	-0.22
	Relative (%)	-0.9	+0.0	-1.7	-28.1	-0.9	+8.5	-2.6	+0.0	-29.0	-21.6	-1.7
Steps (reduced)		94 (94)	149 (0)	188 (39)	218 (69)	243 (94)	264 (115)	282 (133)	298 (0)	312 (14)	325 (27)	337 (39)

Approximation of harmonics in 149edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.62	+0.97	-3.59	-0.44	-3.27	-0.11	-4.36	-3.81	+1.08	-2.87	-3.23
	Relative (%)	+12.7	+7.6	-28.1	-3.4	-25.6	-0.9	-34.1	-29.8	+8.5	-22.5	-25.3
Steps (reduced)		348 (50)	358 (60)	367 (69)	376 (78)	384 (86)	392 (94)	399 (101)	406 (108)	413 (115)	419 (121)	425 (127)