151edt

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151edt

152edt →

Prime factorization	151 (prime)
Step size	12.5957 ¢
Octave	95\151edt (1196.59 ¢)
Consistency limit	3
Distinct consistency limit	3

151 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 151edt or 151ed3), is a nonoctave tuning system that divides the interval of 3/1 into 151 equal parts of about 12.6 ¢ each. Each step represents a frequency ratio of 3^1/151, or the 151st root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	12.6	8.6
2	25.2	17.2
3	37.8	25.8	45/44, 46/45, 47/46
4	50.4	34.4	35/34
5	63	43	57/55
6	75.6	51.7	23/22, 47/45
7	88.2	60.3
8	100.8	68.9
9	113.4	77.5	47/44
10	126	86.1
11	138.6	94.7
12	151.1	103.3
13	163.7	111.9
14	176.3	120.5	41/37, 52/47
15	188.9	129.1	29/26
16	201.5	137.7
17	214.1	146.4	43/38
18	226.7	155
19	239.3	163.6	31/27, 54/47
20	251.9	172.2
21	264.5	180.8
22	277.1	189.4	27/23
23	289.7	198	13/11
24	302.3	206.6	25/21
25	314.9	215.2	6/5
26	327.5	223.8	52/43
27	340.1	232.5	45/37
28	352.7	241.1	38/31, 49/40
29	365.3	249.7	21/17
30	377.9	258.3	46/37, 51/41
31	390.5	266.9
32	403.1	275.5
33	415.7	284.1	47/37
34	428.3	292.7
35	440.9	301.3
36	453.4	309.9
37	466	318.5
38	478.6	327.2	29/22
39	491.2	335.8
40	503.8	344.4
41	516.4	353	31/23
42	529	361.6
43	541.6	370.2	26/19, 41/30
44	554.2	378.8	51/37
45	566.8	387.4	43/31
46	579.4	396
47	592	404.6	38/27
48	604.6	413.2
49	617.2	421.9	10/7
50	629.8	430.5	36/25
51	642.4	439.1
52	655	447.7	54/37
53	667.6	456.3	25/17
54	680.2	464.9	37/25
55	692.8	473.5
56	705.4	482.1
57	718	490.7
58	730.6	499.3	29/19
59	743.1	507.9
60	755.7	516.6
61	768.3	525.2
62	780.9	533.8
63	793.5	542.4
64	806.1	551	43/27
65	818.7	559.6
66	831.3	568.2
67	843.9	576.8
68	856.5	585.4	41/25
69	869.1	594	38/23
70	881.7	602.6
71	894.3	611.3	52/31
72	906.9	619.9
73	919.5	628.5	17/10
74	932.1	637.1	12/7
75	944.7	645.7	19/11
76	957.3	654.3	33/19
77	969.9	662.9	7/4
78	982.5	671.5	30/17
79	995.1	680.1
80	1007.7	688.7
81	1020.3	697.4
82	1032.8	706
83	1045.4	714.6
84	1058	723.2
85	1070.6	731.8
86	1083.2	740.4	43/23
87	1095.8	749
88	1108.4	757.6	55/29
89	1121	766.2
90	1133.6	774.8	52/27
91	1146.2	783.4
92	1158.8	792.1	41/21, 43/22
93	1171.4	800.7	57/29
94	1184	809.3
95	1196.6	817.9
96	1209.2	826.5
97	1221.8	835.1
98	1234.4	843.7	49/24, 51/25
99	1247	852.3	37/18
100	1259.6	860.9
101	1272.2	869.5	25/12
102	1284.8	878.1	21/10
103	1297.4	886.8	55/26
104	1310	895.4
105	1322.6	904
106	1335.1	912.6
107	1347.7	921.2	37/17
108	1360.3	929.8	57/26
109	1372.9	938.4
110	1385.5	947
111	1398.1	955.6
112	1410.7	964.2	52/23
113	1423.3	972.8
114	1435.9	981.5
115	1448.5	990.1
116	1461.1	998.7
117	1473.7	1007.3
118	1486.3	1015.9
119	1498.9	1024.5
120	1511.5	1033.1
121	1524.1	1041.7	41/17
122	1536.7	1050.3	17/7
123	1549.3	1058.9
124	1561.9	1067.5	37/15
125	1574.5	1076.2
126	1587.1	1084.8	5/2
127	1599.7	1093.4
128	1612.3	1102	33/13
129	1624.8	1110.6	23/9
130	1637.4	1119.2
131	1650	1127.8
132	1662.6	1136.4	47/18
133	1675.2	1145
134	1687.8	1153.6
135	1700.4	1162.3
136	1713	1170.9
137	1725.6	1179.5
138	1738.2	1188.1
139	1750.8	1196.7
140	1763.4	1205.3
141	1776	1213.9
142	1788.6	1222.5
143	1801.2	1231.1
144	1813.8	1239.7
145	1826.4	1248.3
146	1839	1257	55/19
147	1851.6	1265.6
148	1864.2	1274.2	44/15
149	1876.8	1282.8
150	1889.4	1291.4
151	1902	1300	3/1

Harmonics

Approximation of harmonics in 151edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-3.41	+0.00	+5.78	-2.66	-3.41	-5.77	+2.38	+0.00	-6.06	+5.27	+5.78
	Relative (%)	-27.0	+0.0	+45.9	-21.1	-27.0	-45.8	+18.9	+0.0	-48.1	+41.9	+45.9
Steps (reduced)		95 (95)	151 (0)	191 (40)	221 (70)	246 (95)	267 (116)	286 (135)	302 (0)	316 (14)	330 (28)	342 (40)

Approximation of harmonics in 151edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.76	+3.42	-2.66	-1.03	-5.22	-3.41	+3.76	+3.13	-5.77	+1.87	+0.48
	Relative (%)	+45.8	+27.2	-21.1	-8.2	-41.4	-27.0	+29.8	+24.8	-45.8	+14.8	+3.8
Steps (reduced)		353 (51)	363 (61)	372 (70)	381 (79)	389 (87)	397 (95)	405 (103)	412 (110)	418 (116)	425 (123)	431 (129)