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	Hekts	Approximate ratios
0	0	0	1/1
1	13.9	9.5
2	27.8	19
3	41.6	28.5	42/41, 43/42
4	55.5	38	31/30
5	69.4	47.4
6	83.3	56.9	43/41
7	97.2	66.4
8	111.1	75.9
9	124.9	85.4	29/27
10	138.8	94.9
11	152.7	104.4	47/43
12	166.6	113.9	11/10
13	180.5	123.4
14	194.4	132.8	47/42
15	208.2	142.3
16	222.1	151.8	33/29
17	236	161.3	47/41
18	249.9	170.8
19	263.8	180.3
20	277.7	189.8	27/23
21	291.5	199.3
22	305.4	208.8	31/26, 37/31
23	319.3	218.2
24	333.2	227.7
25	347.1	237.2	11/9
26	361	246.7
27	374.8	256.2	41/33
28	388.7	265.7
29	402.6	275.2	29/23
30	416.5	284.7	14/11
31	430.4	294.2	50/39
32	444.3	303.6
33	458.1	313.1	43/33
34	472	322.6
35	485.9	332.1
36	499.8	341.6
37	513.7	351.1	39/29
38	527.5	360.6	19/14
39	541.4	370.1	26/19, 41/30
40	555.3	379.6	51/37
41	569.2	389.1
42	583.1	398.5	7/5
43	597	408
44	610.8	417.5	37/26, 47/33
45	624.7	427	33/23, 43/30
46	638.6	436.5
47	652.5	446
48	666.4	455.5
49	680.3	465	43/29
50	694.1	474.5
51	708	483.9
52	721.9	493.4	41/27, 47/31
53	735.8	502.9	26/17
54	749.7	512.4
55	763.6	521.9	14/9
56	777.4	531.4	47/30
57	791.3	540.9	30/19
58	805.2	550.4	43/27
59	819.1	559.9
60	833	569.3
61	846.9	578.8	31/19
62	860.7	588.3	23/14, 51/31
63	874.6	597.8
64	888.5	607.3
65	902.4	616.8
66	916.3	626.3
67	930.2	635.8
68	944	645.3	50/29
69	957.9	654.7
70	971.8	664.2
71	985.7	673.7
72	999.6	683.2	41/23
73	1013.5	692.7
74	1027.3	702.2
75	1041.2	711.7	31/17, 42/23
76	1055.1	721.2
77	1069	730.7
78	1082.9	740.1	43/23
79	1096.7	749.6
80	1110.6	759.1	19/10
81	1124.5	768.6
82	1138.4	778.1	27/14
83	1152.3	787.6	37/19
84	1166.2	797.1	49/25, 51/26
85	1180	806.6
86	1193.9	816.1
87	1207.8	825.5
88	1221.7	835
89	1235.6	844.5	47/23
90	1249.5	854
91	1263.3	863.5
92	1277.2	873	23/11
93	1291.1	882.5
94	1305	892
95	1318.9	901.5	15/7
96	1332.8	910.9	41/19
97	1346.6	920.4	37/17
98	1360.5	929.9
99	1374.4	939.4	42/19
100	1388.3	948.9	29/13
101	1402.2	958.4
102	1416.1	967.9
103	1429.9	977.4
104	1443.8	986.9
105	1457.7	996.4
106	1471.6	1005.8
107	1485.5	1015.3	33/14
108	1499.4	1024.8
109	1513.2	1034.3
110	1527.1	1043.8
111	1541	1053.3
112	1554.9	1062.8	27/11
113	1568.8	1072.3	47/19
114	1582.6	1081.8
115	1596.5	1091.2
116	1610.4	1100.7
117	1624.3	1110.2	23/9
118	1638.2	1119.7
119	1652.1	1129.2
120	1665.9	1138.7
121	1679.8	1148.2	29/11
122	1693.7	1157.7
123	1707.6	1167.2
124	1721.5	1176.6
125	1735.4	1186.1	30/11
126	1749.2	1195.6
127	1763.1	1205.1
128	1777	1214.6
129	1790.9	1224.1
130	1804.8	1233.6
131	1818.7	1243.1
132	1832.5	1252.6
133	1846.4	1262
134	1860.3	1271.5	41/14
135	1874.2	1281
136	1888.1	1290.5
137	1902	1300	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)