137edt

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137edt

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Prime factorization	137 (prime)
Step size	13.8829¢
Octave	86\137edt (1193.93¢)
Consistency limit	2
Distinct consistency limit	2

137 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 137edt or 137ed3), is a nonoctave tuning system that divides the interval of 3/1 into 137 equal parts of about 13.9 ¢ each. Each step represents a frequency ratio of 3^1/137, or the 137th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	13.883
2	27.766
3	41.649	42/41, 43/42
4	55.532	31/30
5	69.414
6	83.297	43/41
7	97.18
8	111.063
9	124.946	29/27
10	138.829
11	152.712	47/43
12	166.595	11/10
13	180.477
14	194.36	47/42
15	208.243
16	222.126	33/29
17	236.009	47/41
18	249.892
19	263.775
20	277.658	27/23
21	291.541
22	305.423	31/26, 37/31
23	319.306
24	333.189
25	347.072	11/9
26	360.955
27	374.838	41/33
28	388.721
29	402.604	29/23
30	416.486	14/11
31	430.369	50/39
32	444.252
33	458.135	43/33
34	472.018
35	485.901
36	499.784
37	513.667	39/29
38	527.55	19/14
39	541.432	26/19, 41/30
40	555.315	51/37
41	569.198
42	583.081	7/5
43	596.964
44	610.847	37/26, 47/33
45	624.73	33/23, 43/30
46	638.613
47	652.496
48	666.378
49	680.261	43/29
50	694.144
51	708.027
52	721.91	41/27, 47/31
53	735.793	26/17
54	749.676
55	763.559	14/9
56	777.441	47/30
57	791.324	30/19
58	805.207	43/27
59	819.09
60	832.973
61	846.856	31/19
62	860.739	23/14, 51/31
63	874.622
64	888.505
65	902.387
66	916.27
67	930.153
68	944.036	50/29
69	957.919
70	971.802
71	985.685
72	999.568	41/23
73	1013.45
74	1027.333
75	1041.216	31/17, 42/23
76	1055.099
77	1068.982
78	1082.865	43/23
79	1096.748
80	1110.631	19/10
81	1124.514
82	1138.396	27/14
83	1152.279	37/19
84	1166.162	49/25, 51/26
85	1180.045
86	1193.928
87	1207.811
88	1221.694
89	1235.577	47/23
90	1249.459
91	1263.342
92	1277.225	23/11
93	1291.108
94	1304.991
95	1318.874	15/7
96	1332.757	41/19
97	1346.64	37/17
98	1360.523
99	1374.405	42/19
100	1388.288	29/13
101	1402.171
102	1416.054
103	1429.937
104	1443.82
105	1457.703
106	1471.586
107	1485.469	33/14
108	1499.351
109	1513.234
110	1527.117
111	1541
112	1554.883	27/11
113	1568.766	47/19
114	1582.649
115	1596.532
116	1610.414
117	1624.297	23/9
118	1638.18
119	1652.063
120	1665.946
121	1679.829	29/11
122	1693.712
123	1707.595
124	1721.478
125	1735.36	30/11
126	1749.243
127	1763.126
128	1777.009
129	1790.892
130	1804.775
131	1818.658
132	1832.541
133	1846.423
134	1860.306	41/14
135	1874.189
136	1888.072
137	1901.955	3/1

Harmonics

Approximation of harmonics in 137edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.07	+0.00	+1.74	+4.15	-6.07	+4.71	-4.33	+0.00	-1.93	-0.34	+1.74
	Relative (%)	-43.7	+0.0	+12.5	+29.9	-43.7	+34.0	-31.2	+0.0	-13.9	-2.4	+12.5
Steps (reduced)		86 (86)	137 (0)	173 (36)	201 (64)	223 (86)	243 (106)	259 (122)	274 (0)	287 (13)	299 (25)	310 (36)

Approximation of harmonics in 137edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.99	-1.36	+4.15	+3.48	-4.30	-6.07	-2.49	+5.88	+4.71	-6.41	-0.07
	Relative (%)	+14.4	-9.8	+29.9	+25.0	-31.0	-43.7	-18.0	+42.4	+34.0	-46.2	-0.5
Steps (reduced)		320 (46)	329 (55)	338 (64)	346 (72)	353 (79)	360 (86)	367 (93)	374 (100)	380 (106)	385 (111)	391 (117)