151ed4

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151ed4

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Prime factorization	151 (prime)
Step size	15.894 ¢
Octave	76\151ed4 (1207.95 ¢)
Twelfth	120\151ed4 (1907.28 ¢)
Consistency limit	1
Distinct consistency limit	1

151 equal divisions of the 4th harmonic (abbreviated 151ed4) is a nonoctave tuning system that divides the interval of 4/1 into 151 equal parts of about 15.9 ¢ each. Each step represents a frequency ratio of 4^1/151, or the 151st root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	15.9
2	31.8
3	47.7
4	63.6	28/27
5	79.5	22/21, 45/43
6	95.4	37/35
7	111.3
8	127.2
9	143
10	158.9	23/21, 57/52
11	174.8
12	190.7
13	206.6
14	222.5	33/29
15	238.4
16	254.3	22/19, 51/44
17	270.2
18	286.1
19	302
20	317.9
21	333.8
22	349.7
23	365.6	21/17
24	381.5
25	397.4	39/31
26	413.2	33/26, 47/37
27	429.1	50/39
28	445	22/17
29	460.9	30/23
30	476.8	29/22
31	492.7
32	508.6	51/38, 55/41
33	524.5	23/17
34	540.4
35	556.3
36	572.2
37	588.1
38	604
39	619.9
40	635.8
41	651.7
42	667.5
43	683.4	43/29, 49/33
44	699.3
45	715.2
46	731.1	29/19
47	747
48	762.9
49	778.8
50	794.7
51	810.6
52	826.5	50/31
53	842.4
54	858.3	23/14
55	874.2
56	890.1
57	906
58	921.9	46/27
59	937.7
60	953.6	26/15
61	969.5
62	985.4
63	1001.3
64	1017.2
65	1033.1
66	1049
67	1064.9
68	1080.8
69	1096.7	49/26
70	1112.6	19/10
71	1128.5
72	1144.4
73	1160.3	43/22
74	1176.2
75	1192.1
76	1207.9
77	1223.8
78	1239.7	43/21, 45/22
79	1255.6	31/15
80	1271.5
81	1287.4
82	1303.3
83	1319.2	15/7
84	1335.1
85	1351
86	1366.9
87	1382.8	20/9
88	1398.7
89	1414.6	43/19
90	1430.5
91	1446.4
92	1462.3
93	1478.1
94	1494	45/19
95	1509.9
96	1525.8
97	1541.7
98	1557.6
99	1573.5
100	1589.4
101	1605.3	43/17
102	1621.2	51/20
103	1637.1
104	1653	13/5
105	1668.9
106	1684.8	45/17
107	1700.7
108	1716.6
109	1732.5
110	1748.3
111	1764.2
112	1780.1
113	1796
114	1811.9	37/13, 57/20
115	1827.8
116	1843.7	29/10
117	1859.6
118	1875.5
119	1891.4
120	1907.3
121	1923.2
122	1939.1
123	1955
124	1970.9
125	1986.8
126	2002.6	35/11
127	2018.5
128	2034.4
129	2050.3	49/15
130	2066.2	33/10
131	2082.1
132	2098
133	2113.9
134	2129.8
135	2145.7
136	2161.6
137	2177.5
138	2193.4
139	2209.3
140	2225.2	47/13
141	2241.1
142	2257
143	2272.8	26/7
144	2288.7
145	2304.6
146	2320.5
147	2336.4
148	2352.3
149	2368.2
150	2384.1
151	2400

Harmonics

Approximation of harmonics in 151ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+7.95	+5.33	+0.00	-4.86	-2.62	+0.71	+7.95	-5.23	+3.09	-2.97	+5.33
	Relative (%)	+50.0	+33.5	+0.0	-30.6	-16.5	+4.5	+50.0	-32.9	+19.4	-18.7	+33.5
Steps (reduced)		76 (76)	120 (120)	151 (0)	175 (24)	195 (44)	212 (61)	227 (76)	239 (88)	251 (100)	261 (110)	271 (120)

Approximation of harmonics in 151ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-6.09	-7.24	+0.47	+0.00	+6.30	+2.71	+4.47	-4.86	+6.04	+4.97	+7.49
	Relative (%)	-38.3	-45.5	+3.0	+0.0	+39.7	+17.1	+28.1	-30.6	+38.0	+31.3	+47.1
Steps (reduced)		279 (128)	287 (136)	295 (144)	302 (0)	309 (7)	315 (13)	321 (19)	326 (24)	332 (30)	337 (35)	342 (40)