131ed4

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131ed4

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Prime factorization	131 (prime)
Step size	18.3206 ¢
Octave	66\131ed4 (1209.16 ¢)
Twelfth	104\131ed4 (1905.34 ¢)
Consistency limit	1
Distinct consistency limit	1

131 equal divisions of the 4th harmonic (abbreviated 131ed4) is a nonoctave tuning system that divides the interval of 4/1 into 131 equal parts of about 18.3 ¢ each. Each step represents a frequency ratio of 4^1/131, or the 131st root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	18.3
2	36.6	46/45, 47/46, 50/49
3	55
4	73.3	49/47
5	91.6	39/37
6	109.9	49/46
7	128.2
8	146.6	49/45
9	164.9	11/10
10	183.2	10/9
11	201.5
12	219.8
13	238.2	47/41
14	256.5	29/25
15	274.8	41/35
16	293.1	45/38
17	311.5
18	329.8	23/19
19	348.1	11/9
20	366.4	21/17, 47/38
21	384.7
22	403.1	29/23
23	421.4	37/29
24	439.7	49/38
25	458
26	476.3	25/19
27	494.7
28	513	35/26, 39/29
29	531.3
30	549.6
31	567.9	43/31
32	586.3
33	604.6
34	622.9
35	641.2
36	659.5
37	677.9	37/25
38	696.2
39	714.5
40	732.8	29/19
41	751.1
42	769.5	39/25
43	787.8	41/26, 52/33
44	806.1
45	824.4	37/23
46	842.7
47	861.1
48	879.4
49	897.7
50	916
51	934.4
52	952.7	26/15
53	971
54	989.3	23/13
55	1007.6
56	1026	38/21, 47/26
57	1044.3
58	1062.6
59	1080.9
60	1099.2	17/9
61	1117.6
62	1135.9	27/14, 52/27
63	1154.2	37/19
64	1172.5
65	1190.8
66	1209.2
67	1227.5
68	1245.8	39/19
69	1264.1
70	1282.4
71	1300.8
72	1319.1	15/7
73	1337.4
74	1355.7	46/21
75	1374
76	1392.4	38/17
77	1410.7
78	1429
79	1447.3
80	1465.6	7/3
81	1484	33/14
82	1502.3	50/21
83	1520.6
84	1538.9
85	1557.3
86	1575.6
87	1593.9
88	1612.2
89	1630.5
90	1648.9
91	1667.2
92	1685.5	45/17
93	1703.8
94	1722.1	46/17
95	1740.5	41/15
96	1758.8	47/17
97	1777.1
98	1795.4
99	1813.7
100	1832.1	49/17
101	1850.4
102	1868.7	50/17
103	1887
104	1905.3
105	1923.7
106	1942
107	1960.3
108	1978.6	47/15
109	1996.9
110	2015.3
111	2033.6
112	2051.9
113	2070.2	43/13
114	2088.5
115	2106.9
116	2125.2
117	2143.5
118	2161.8
119	2180.2
120	2198.5
121	2216.8
122	2235.1
123	2253.4
124	2271.8	26/7
125	2290.1
126	2308.4
127	2326.7
128	2345
129	2363.4
130	2381.7
131	2400

Harmonics

Approximation of harmonics in 131ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+9.16	+3.39	+0.00	-1.58	-5.77	+2.17	+9.16	+6.78	+7.58	+7.46	+3.39
	Relative (%)	+50.0	+18.5	+0.0	-8.6	-31.5	+11.8	+50.0	+37.0	+41.4	+40.7	+18.5
Steps (reduced)		66 (66)	104 (104)	131 (0)	152 (21)	169 (38)	184 (53)	197 (66)	208 (77)	218 (87)	227 (96)	235 (104)

Approximation of harmonics in 131ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-6.94	-6.99	+1.81	+0.00	+4.97	-2.38	-4.38	-1.58	+5.55	-1.70	-5.37
	Relative (%)	-37.9	-38.2	+9.9	+0.0	+27.1	-13.0	-23.9	-8.6	+30.3	-9.3	-29.3
Steps (reduced)		242 (111)	249 (118)	256 (125)	262 (0)	268 (6)	273 (11)	278 (16)	283 (21)	288 (26)	292 (30)	296 (34)