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	18.321
2	36.641	46/45, 47/46, 50/49
3	54.962
4	73.282	49/47
5	91.603	39/37
6	109.924	49/46
7	128.244
8	146.565	49/45
9	164.885	11/10
10	183.206	10/9
11	201.527
12	219.847
13	238.168	47/41
14	256.489	29/25
15	274.809	41/35
16	293.13	45/38
17	311.45
18	329.771	23/19
19	348.092	11/9
20	366.412	21/17, 47/38
21	384.733
22	403.053	29/23
23	421.374	37/29
24	439.695	49/38
25	458.015
26	476.336	25/19
27	494.656
28	512.977	35/26, 39/29
29	531.298
30	549.618
31	567.939	43/31
32	586.26
33	604.58
34	622.901
35	641.221
36	659.542
37	677.863	37/25
38	696.183
39	714.504
40	732.824	29/19
41	751.145
42	769.466	39/25
43	787.786	41/26, 52/33
44	806.107
45	824.427	37/23
46	842.748
47	861.069
48	879.389
49	897.71
50	916.031
51	934.351
52	952.672	26/15
53	970.992
54	989.313	23/13
55	1007.634
56	1025.954	38/21, 47/26
57	1044.275
58	1062.595
59	1080.916
60	1099.237	17/9
61	1117.557
62	1135.878	27/14, 52/27
63	1154.198	37/19
64	1172.519
65	1190.84
66	1209.16
67	1227.481
68	1245.802	39/19
69	1264.122
70	1282.443
71	1300.763
72	1319.084	15/7
73	1337.405
74	1355.725	46/21
75	1374.046
76	1392.366	38/17
77	1410.687
78	1429.008
79	1447.328
80	1465.649	7/3
81	1483.969	33/14
82	1502.29	50/21
83	1520.611
84	1538.931
85	1557.252
86	1575.573
87	1593.893
88	1612.214
89	1630.534
90	1648.855
91	1667.176
92	1685.496	45/17
93	1703.817
94	1722.137	46/17
95	1740.458	41/15
96	1758.779	47/17
97	1777.099
98	1795.42
99	1813.74
100	1832.061	49/17
101	1850.382
102	1868.702	50/17
103	1887.023
104	1905.344
105	1923.664
106	1941.985
107	1960.305
108	1978.626	47/15
109	1996.947
110	2015.267
111	2033.588
112	2051.908
113	2070.229	43/13
114	2088.55
115	2106.87
116	2125.191
117	2143.511
118	2161.832
119	2180.153
120	2198.473
121	2216.794
122	2235.115
123	2253.435
124	2271.756	26/7
125	2290.076
126	2308.397
127	2326.718
128	2345.038
129	2363.359
130	2381.679
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)