136edt

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← 135edt

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	14
2	28
3	42	41/40, 42/41, 43/42
4	55.9	31/30
5	69.9	51/49
6	83.9	21/20, 43/41
7	97.9	18/17, 37/35
8	111.9
9	125.9	43/40
10	139.8	13/12, 51/47
11	153.8	47/43
12	167.8	43/39, 54/49
13	181.8	10/9
14	195.8	47/42
15	209.8	35/31, 44/39
16	223.8	33/29, 41/36
17	237.7	31/27, 39/34, 47/41
18	251.7
19	265.7	7/6
20	279.7	20/17, 47/40
21	293.7	45/38, 51/43
22	307.7	37/31, 43/36, 49/41
23	321.7	47/39
24	335.6	17/14
25	349.6	49/40
26	363.6	37/30
27	377.6	46/37, 51/41
28	391.6
29	405.6	43/34
30	419.5	51/40
31	433.5	9/7
32	447.5	22/17
33	461.5	30/23, 47/36
34	475.5	25/19, 54/41
35	489.5
36	503.5
37	517.4	31/23
38	531.4
39	545.4	37/27
40	559.4	29/21, 47/34
41	573.4	39/28, 46/33
42	587.4
43	601.4	17/12
44	615.3
45	629.3
46	643.3	29/20
47	657.3
48	671.3
49	685.3	49/33
50	699.2
51	713.2
52	727.2	35/23
53	741.2	23/15, 43/28
54	755.2	17/11
55	769.2
56	783.2	11/7
57	797.1	46/29
58	811.1
59	825.1	29/18
60	839.1	13/8
61	853.1	18/11
62	867.1	33/20
63	881.1
64	895	47/28
65	909	49/29
66	923	29/17, 46/27
67	937
68	951
69	965
70	978.9	37/21, 51/29
71	992.9
72	1006.9
73	1020.9
74	1034.9	20/11
75	1048.9	11/6
76	1062.9	24/13
77	1076.8	41/22, 54/29
78	1090.8
79	1104.8
80	1118.8	21/11
81	1132.8
82	1146.8	33/17
83	1160.8	43/22, 45/23
84	1174.7
85	1188.7
86	1202.7
87	1216.7
88	1230.7
89	1244.7
90	1258.6
91	1272.6
92	1286.6
93	1300.6	36/17
94	1314.6	47/22
95	1328.6	28/13
96	1342.6
97	1356.5	46/21
98	1370.5
99	1384.5
100	1398.5
101	1412.5
102	1426.5	41/18
103	1440.5	23/10
104	1454.4	51/22
105	1468.4	7/3
106	1482.4	40/17
107	1496.4
108	1510.4
109	1524.4	41/17
110	1538.3
111	1552.3	49/20
112	1566.3	42/17
113	1580.3
114	1594.3
115	1608.3	38/15, 43/17
116	1622.3	51/20
117	1636.2	18/7
118	1650.2
119	1664.2	34/13
120	1678.2	29/11
121	1692.2
122	1706.2
123	1720.2	27/10
124	1734.1	49/18
125	1748.1
126	1762.1	36/13, 47/17
127	1776.1
128	1790.1
129	1804.1	17/6
130	1818	20/7
131	1832	49/17
132	1846
133	1860	41/14
134	1874
135	1888
136	1902	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)