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	17.5
2	35	51/50, 52/51
3	52.6	34/33
4	70.1
5	87.6	41/39
6	105.1
7	122.6
8	140.1
9	157.7	23/21
10	175.2
11	192.7	19/17
12	210.2	35/31
13	227.7
14	245.3	38/33
15	262.8	50/43
16	280.3
17	297.8
18	315.3
19	332.8
20	350.4
21	367.9
22	385.4
23	402.9	29/23
24	420.4	37/29
25	438
26	455.5
27	473
28	490.5
29	508	51/38
30	525.5
31	543.1	26/19
32	560.6
33	578.1
34	595.6
35	613.1
36	630.7
37	648.2
38	665.7
39	683.2	43/29
40	700.7	3/2
41	718.2	50/33
42	735.8	26/17
43	753.3	17/11
44	770.8	39/25
45	788.3	41/26, 52/33
46	805.8
47	823.4	37/23
48	840.9
49	858.4	23/14
50	875.9
51	893.4
52	910.9
53	928.5
54	946	19/11
55	963.5
56	981	37/21
57	998.5
58	1016.1
59	1033.6
60	1051.1
61	1068.6
62	1086.1
63	1103.6
64	1121.2	21/11
65	1138.7
66	1156.2
67	1173.7
68	1191.2
69	1208.8
70	1226.3
71	1243.8	39/19
72	1261.3	29/14
73	1278.8
74	1296.4
75	1313.9
76	1331.4	41/19
77	1348.9
78	1366.4	11/5
79	1383.9	20/9
80	1401.5
81	1419
82	1436.5	39/17
83	1454	51/22
84	1471.5
85	1489.1	26/11
86	1506.6
87	1524.1	41/17
88	1541.6
89	1559.1
90	1576.6
91	1594.2
92	1611.7
93	1629.2
94	1646.7
95	1664.2
96	1681.8	37/14
97	1699.3
98	1716.8
99	1734.3
100	1751.8
101	1769.3
102	1786.9
103	1804.4
104	1821.9	43/15
105	1839.4
106	1856.9
107	1874.5
108	1892
109	1909.5
110	1927
111	1944.5
112	1962
113	1979.6
114	1997.1
115	2014.6
116	2032.1
117	2049.6
118	2067.2	33/10
119	2084.7	10/3
120	2102.2
121	2119.7	17/5
122	2137.2
123	2154.7
124	2172.3
125	2189.8	39/11
126	2207.3
127	2224.8	47/13
128	2242.3
129	2259.9
130	2277.4	41/11
131	2294.9
132	2312.4	19/5
133	2329.9
134	2347.4
135	2365
136	2382.5
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)