137ed4

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137ed4

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Prime factorization	137 (prime)
Step size	17.5182¢
Octave	69\137ed4 (1208.76¢)
Twelfth	109\137ed4 (1909.49¢)
Consistency limit	1
Distinct consistency limit	1

137 equal divisions of the 4th harmonic (abbreviated 137ed4) is a nonoctave tuning system that divides the interval of 4/1 into 137 equal parts of about 17.5 ¢ each. Each step represents a frequency ratio of 4^1/137, or the 137th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	17.518
2	35.036	51/50, 52/51
3	52.555	34/33
4	70.073
5	87.591	41/39
6	105.109
7	122.628
8	140.146
9	157.664	23/21
10	175.182
11	192.701	19/17
12	210.219	35/31
13	227.737
14	245.255	38/33
15	262.774	50/43
16	280.292
17	297.81
18	315.328
19	332.847
20	350.365
21	367.883
22	385.401
23	402.92	29/23
24	420.438	37/29
25	437.956
26	455.474
27	472.993
28	490.511
29	508.029	51/38
30	525.547
31	543.066	26/19
32	560.584
33	578.102
34	595.62
35	613.139
36	630.657
37	648.175
38	665.693
39	683.212	43/29
40	700.73	3/2
41	718.248	50/33
42	735.766	26/17
43	753.285	17/11
44	770.803	39/25
45	788.321	41/26, 52/33
46	805.839
47	823.358	37/23
48	840.876
49	858.394	23/14
50	875.912
51	893.431
52	910.949
53	928.467
54	945.985	19/11
55	963.504
56	981.022	37/21
57	998.54
58	1016.058
59	1033.577
60	1051.095
61	1068.613
62	1086.131
63	1103.65
64	1121.168	21/11
65	1138.686
66	1156.204
67	1173.723
68	1191.241
69	1208.759
70	1226.277
71	1243.796	39/19
72	1261.314	29/14
73	1278.832
74	1296.35
75	1313.869
76	1331.387	41/19
77	1348.905
78	1366.423	11/5
79	1383.942	20/9
80	1401.46
81	1418.978
82	1436.496	39/17
83	1454.015	51/22
84	1471.533
85	1489.051	26/11
86	1506.569
87	1524.088	41/17
88	1541.606
89	1559.124
90	1576.642
91	1594.161
92	1611.679
93	1629.197
94	1646.715
95	1664.234
96	1681.752	37/14
97	1699.27
98	1716.788
99	1734.307
100	1751.825
101	1769.343
102	1786.861
103	1804.38
104	1821.898	43/15
105	1839.416
106	1856.934
107	1874.453
108	1891.971
109	1909.489
110	1927.007
111	1944.526
112	1962.044
113	1979.562
114	1997.08
115	2014.599
116	2032.117
117	2049.635
118	2067.153	33/10
119	2084.672	10/3
120	2102.19
121	2119.708	17/5
122	2137.226
123	2154.745
124	2172.263
125	2189.781	39/11
126	2207.299
127	2224.818	47/13
128	2242.336
129	2259.854
130	2277.372	41/11
131	2294.891
132	2312.409	19/5
133	2329.927
134	2347.445
135	2364.964
136	2382.482
137	2400

Harmonics

Approximation of harmonics in 137ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.76	+7.53	+0.00	-0.91	-1.23	-5.32	+8.76	-2.45	+7.85	+0.51	+7.53
	Relative (%)	+50.0	+43.0	+0.0	-5.2	-7.0	-30.4	+50.0	-14.0	+44.8	+2.9	+43.0
Steps (reduced)		69 (69)	109 (109)	137 (0)	159 (22)	177 (40)	192 (55)	206 (69)	217 (80)	228 (91)	237 (100)	246 (109)

Approximation of harmonics in 137ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-8.41	+3.44	+6.62	+0.00	+0.15	+6.31	+0.30	-0.91	+2.21	-8.25	+2.38
	Relative (%)	-48.0	+19.6	+37.8	+0.0	+0.9	+36.0	+1.7	-5.2	+12.6	-47.1	+13.6
Steps (reduced)		253 (116)	261 (124)	268 (131)	274 (0)	280 (6)	286 (12)	291 (17)	296 (22)	301 (27)	305 (31)	310 (36)