136edt

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136edt

137edt →

Prime factorization	23 × 17
Step size	13.985¢
Octave	86\136edt (1202.71¢) (→43\68edt)
Consistency limit	4
Distinct consistency limit	4

136 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 136edt or 136ed3), is a nonoctave tuning system that divides the interval of 3/1 into 136 equal parts of about 14 ¢ each. Each step represents a frequency ratio of 3^1/136, or the 136th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	13.985
2	27.97
3	41.955	41/40, 42/41, 43/42
4	55.94	31/30
5	69.925	51/49
6	83.91	21/20, 43/41
7	97.895	18/17, 37/35
8	111.88
9	125.865	43/40
10	139.85	13/12, 51/47
11	153.835	47/43
12	167.82	43/39, 54/49
13	181.805	10/9
14	195.789	47/42
15	209.774	35/31, 44/39
16	223.759	33/29, 41/36
17	237.744	31/27, 39/34, 47/41
18	251.729
19	265.714	7/6
20	279.699	20/17, 47/40
21	293.684	45/38, 51/43
22	307.669	37/31, 43/36, 49/41
23	321.654	47/39
24	335.639	17/14
25	349.624	49/40
26	363.609	37/30
27	377.594	46/37, 51/41
28	391.579
29	405.564	43/34
30	419.549	51/40
31	433.534	9/7
32	447.519	22/17
33	461.504	30/23, 47/36
34	475.489	25/19, 54/41
35	489.474
36	503.459
37	517.444	31/23
38	531.429
39	545.414	37/27
40	559.399	29/21, 47/34
41	573.383	39/28, 46/33
42	587.368
43	601.353	17/12
44	615.338
45	629.323
46	643.308	29/20
47	657.293
48	671.278
49	685.263	49/33
50	699.248
51	713.233
52	727.218	35/23
53	741.203	23/15, 43/28
54	755.188	17/11
55	769.173
56	783.158	11/7
57	797.143	46/29
58	811.128
59	825.113	29/18
60	839.098	13/8
61	853.083	18/11
62	867.068	33/20
63	881.053
64	895.038	47/28
65	909.023	49/29
66	923.008	29/17, 46/27
67	936.993
68	950.978
69	964.962
70	978.947	37/21, 51/29
71	992.932
72	1006.917
73	1020.902
74	1034.887	20/11
75	1048.872	11/6
76	1062.857	24/13
77	1076.842	41/22, 54/29
78	1090.827
79	1104.812
80	1118.797	21/11
81	1132.782
82	1146.767	33/17
83	1160.752	43/22, 45/23
84	1174.737
85	1188.722
86	1202.707
87	1216.692
88	1230.677
89	1244.662
90	1258.647
91	1272.632
92	1286.617
93	1300.602	36/17
94	1314.587	47/22
95	1328.572	28/13
96	1342.556
97	1356.541	46/21
98	1370.526
99	1384.511
100	1398.496
101	1412.481
102	1426.466	41/18
103	1440.451	23/10
104	1454.436	51/22
105	1468.421	7/3
106	1482.406	40/17
107	1496.391
108	1510.376
109	1524.361	41/17
110	1538.346
111	1552.331	49/20
112	1566.316	42/17
113	1580.301
114	1594.286
115	1608.271	38/15, 43/17
116	1622.256	51/20
117	1636.241	18/7
118	1650.226
119	1664.211	34/13
120	1678.196	29/11
121	1692.181
122	1706.166
123	1720.15	27/10
124	1734.135	49/18
125	1748.12
126	1762.105	36/13, 47/17
127	1776.09
128	1790.075
129	1804.06	17/6
130	1818.045	20/7
131	1832.03	49/17
132	1846.015
133	1860	41/14
134	1873.985
135	1887.97
136	1901.955	3/1

Harmonics

Approximation of harmonics in 136edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.71	+0.00	+5.41	-3.31	+2.71	+1.55	-5.86	+0.00	-0.60	+2.22	+5.41
	Relative (%)	+19.4	+0.0	+38.7	-23.6	+19.4	+11.1	-41.9	+0.0	-4.3	+15.8	+38.7
Steps (reduced)		86 (86)	136 (0)	172 (36)	199 (63)	222 (86)	241 (105)	257 (121)	272 (0)	285 (13)	297 (25)	308 (36)

Approximation of harmonics in 136edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.69	+4.26	-3.31	-3.16	+3.77	+2.71	-6.99	+2.11	+1.55	+4.92	-2.11
	Relative (%)	+47.8	+30.4	-23.6	-22.6	+26.9	+19.4	-50.0	+15.1	+11.1	+35.2	-15.1
Steps (reduced)		318 (46)	327 (55)	335 (63)	343 (71)	351 (79)	358 (86)	364 (92)	371 (99)	377 (105)	383 (111)	388 (116)