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	Hekts	Approximate ratios
0	0	0	1/1
1	12.8	8.7
2	25.5	17.4
3	38.3	26.2	44/43, 45/44, 46/45, 47/46
4	51.1	34.9	34/33, 35/34
5	63.8	43.6	27/26, 28/27
6	76.6	52.3	23/22, 47/45
7	89.4	61.1	20/19
8	102.1	69.8	35/33, 52/49
9	114.9	78.5	31/29, 47/44
10	127.6	87.2	14/13
11	140.4	96	51/47
12	153.2	104.7	47/43
13	165.9	113.4	11/10
14	178.7	122.1	41/37, 51/46
15	191.5	130.9	19/17, 48/43
16	204.2	139.6	9/8
17	217	148.3	17/15
18	229.8	157	8/7
19	242.5	165.8	23/20
20	255.3	174.5	22/19, 51/44
21	268.1	183.2	7/6
22	280.8	191.9	20/17
23	293.6	200.7	32/27, 45/38
24	306.4	209.4	37/31, 43/36
25	319.1	218.1
26	331.9	226.8	23/19, 40/33
27	344.6	235.6
28	357.4	244.3	43/35
29	370.2	253	26/21, 57/46
30	382.9	261.7
31	395.7	270.5	44/35, 49/39, 54/43
32	408.5	279.2	19/15
33	421.2	287.9	37/29, 51/40
34	434	296.6	9/7
35	446.8	305.4	22/17, 57/44
36	459.5	314.1	30/23, 43/33
37	472.3	322.8	21/16, 46/35
38	485.1	331.5	41/31, 45/34, 49/37
39	497.8	340.3	4/3
40	510.6	349	43/32, 47/35, 51/38
41	523.4	357.7	23/17
42	536.1	366.4	15/11
43	548.9	375.2
44	561.7	383.9	47/34
45	574.4	392.6	39/28, 46/33
46	587.2	401.3
47	599.9	410.1	41/29
48	612.7	418.8	47/33, 57/40
49	625.5	427.5	33/23, 56/39
50	638.2	436.2
51	651	445	51/35
52	663.8	453.7	22/15
53	676.5	462.4	34/23
54	689.3	471.1
55	702.1	479.9	3/2
56	714.8	488.6
57	727.6	497.3	35/23
58	740.4	506	23/15
59	753.1	514.8	17/11
60	765.9	523.5	14/9
61	778.7	532.2	47/30
62	791.4	540.9	30/19, 49/31
63	804.2	549.7	35/22, 43/27
64	816.9	558.4
65	829.7	567.1	21/13
66	842.5	575.8
67	855.2	584.6
68	868	593.3	33/20, 38/23
69	880.8	602
70	893.5	610.7	57/34
71	906.3	619.5	27/16
72	919.1	628.2	17/10
73	931.8	636.9	12/7
74	944.6	645.6
75	957.4	654.4	40/23
76	970.1	663.1	7/4
77	982.9	671.8	30/17
78	995.7	680.5	16/9
79	1008.4	689.3	34/19, 43/24
80	1021.2	698
81	1033.9	706.7	20/11
82	1046.7	715.4
83	1059.5	724.2
84	1072.2	732.9	13/7
85	1085	741.6
86	1097.8	750.3	49/26
87	1110.5	759.1	19/10
88	1123.3	767.8	44/23
89	1136.1	776.5	27/14, 52/27
90	1148.8	785.2	33/17
91	1161.6	794	43/22, 45/23
92	1174.4	802.7
93	1187.1	811.4
94	1199.9	820.1	2/1
95	1212.7	828.9
96	1225.4	837.6
97	1238.2	846.3	45/22, 47/23
98	1251	855	35/17
99	1263.7	863.8	56/27
100	1276.5	872.5	23/11
101	1289.2	881.2	40/19
102	1302	889.9
103	1314.8	898.7	47/22
104	1327.5	907.4	28/13
105	1340.3	916.1
106	1353.1	924.8
107	1365.8	933.6	11/5
108	1378.6	942.3	51/23
109	1391.4	951	38/17
110	1404.1	959.7	9/4
111	1416.9	968.5	34/15
112	1429.7	977.2	16/7
113	1442.4	985.9	23/10
114	1455.2	994.6	44/19, 51/22
115	1468	1003.4	7/3
116	1480.7	1012.1	40/17, 47/20
117	1493.5	1020.8	45/19
118	1506.2	1029.5	43/18
119	1519	1038.3
120	1531.8	1047	46/19
121	1544.5	1055.7
122	1557.3	1064.4
123	1570.1	1073.2	52/21, 57/23
124	1582.8	1081.9
125	1595.6	1090.6
126	1608.4	1099.3	38/15
127	1621.1	1108.1	51/20
128	1633.9	1116.8	18/7
129	1646.7	1125.5	44/17, 57/22
130	1659.4	1134.2
131	1672.2	1143	21/8
132	1685	1151.7	45/17
133	1697.7	1160.4	8/3
134	1710.5	1169.1	43/16, 51/19
135	1723.2	1177.9	46/17
136	1736	1186.6	30/11
137	1748.8	1195.3
138	1761.5	1204	47/17
139	1774.3	1212.8	39/14
140	1787.1	1221.5
141	1799.8	1230.2
142	1812.6	1238.9	57/20
143	1825.4	1247.7
144	1838.1	1256.4	26/9
145	1850.9	1265.1
146	1863.7	1273.8	44/15
147	1876.4	1282.6
148	1889.2	1291.3
149	1902	1300	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)