135edt

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← 134edt

135edt

136edt →

Prime factorization	33 × 5
Step size	14.0886¢
Octave	85\135edt (1197.53¢) (→17\27edt)
Consistency limit	4
Distinct consistency limit	4

135 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 135edt or 135ed3), is a nonoctave tuning system that divides the interval of 3/1 into 135 equal parts of about 14.1 ¢ each. Each step represents a frequency ratio of 3^1/135, or the 135th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	14.089
2	28.177
3	42.266	40/39, 41/40, 42/41, 43/42
4	56.354	31/30
5	70.443	49/47, 51/49
6	84.531	21/20
7	98.62	18/17
8	112.708	47/44
9	126.797	14/13, 43/40
10	140.886	38/35, 51/47
11	154.974	47/43
12	169.063	43/39
13	183.151	10/9
14	197.24	37/33
15	211.328	26/23, 35/31
16	225.417	33/29, 41/36, 49/43
17	239.505	31/27
18	253.594	22/19
19	267.683	7/6
20	281.771	20/17
21	295.86	51/43
22	309.948	49/41
23	324.037	35/29, 41/34, 47/39
24	338.125	45/37
25	352.214	38/31, 49/40
26	366.302	21/17, 47/38
27	380.391
28	394.48	44/35, 49/39
29	408.568	19/15
30	422.657	23/18, 37/29
31	436.745	9/7
32	450.834	35/27
33	464.922	17/13
34	479.011	29/22, 33/25
35	493.099
36	507.188
37	521.277	27/20, 50/37
38	535.365	15/11, 49/36
39	549.454
40	563.542	18/13
41	577.631
42	591.719	38/27
43	605.808	44/31
44	619.896
45	633.985	49/34
46	648.074
47	662.162	22/15
48	676.251	34/23
49	690.339
50	704.428
51	718.516	50/33
52	732.605	29/19
53	746.693	20/13
54	760.782	45/29
55	774.871	36/23
56	788.959	41/26
57	803.048	35/22
58	817.136
59	831.225	21/13
60	845.313	44/27
61	859.402	23/14
62	873.49
63	887.579
64	901.668	37/22
65	915.756	39/23
66	929.845
67	943.933	50/29
68	958.022	40/23, 47/27
69	972.11
70	986.199	23/13
71	1000.287	41/23
72	1014.376
73	1028.465	38/21
74	1042.553	42/23
75	1056.642	35/19
76	1070.73	13/7
77	1084.819	43/23
78	1098.907
79	1112.996
80	1127.084	23/12
81	1141.173	29/15
82	1155.262	37/19, 39/20
83	1169.35
84	1183.439
85	1197.527
86	1211.616
87	1225.704
88	1239.793	43/21, 45/22
89	1253.881
90	1267.97
91	1282.059	44/21
92	1296.147
93	1310.236	49/23
94	1324.324	43/20
95	1338.413	13/6
96	1352.501
97	1366.59	11/5
98	1380.678	20/9
99	1394.767	47/21
100	1408.856
101	1422.944	25/11
102	1437.033	39/17
103	1451.121
104	1465.21	7/3
105	1479.298	47/20
106	1493.387	45/19
107	1507.475	43/18
108	1521.564
109	1535.653	17/7
110	1549.741	49/20
111	1563.83	37/15
112	1577.918
113	1592.007
114	1606.095	43/17
115	1620.184	51/20
116	1634.272	18/7
117	1648.361
118	1662.45	47/18
119	1676.538	29/11, 50/19
120	1690.627
121	1704.715
122	1718.804	27/10
123	1732.892	49/18
124	1746.981
125	1761.069	47/17
126	1775.158	39/14
127	1789.247
128	1803.335	17/6
129	1817.424	20/7
130	1831.512	49/17
131	1845.601
132	1859.689	41/14
133	1873.778
134	1887.866
135	1901.955	3/1

Harmonics

Approximation of harmonics in 135edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.47	+0.00	-4.95	+3.22	-2.47	-1.66	+6.67	+0.00	+0.75	+4.81	-4.95
	Relative (%)	-17.6	+0.0	-35.1	+22.9	-17.6	-11.8	+47.3	+0.0	+5.3	+34.1	-35.1
Steps (reduced)		85 (85)	135 (0)	170 (35)	198 (63)	220 (85)	239 (104)	256 (121)	270 (0)	283 (13)	295 (25)	305 (35)

Approximation of harmonics in 135edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-4.13	+3.22	+4.20	-2.14	-2.47	+2.54	-1.73	-1.66	+2.33	-4.18
	Relative (%)	-18.7	-29.3	+22.9	+29.8	-15.2	-17.6	+18.1	-12.2	-11.8	+16.6	-29.7
Steps (reduced)		315 (45)	324 (54)	333 (63)	341 (71)	348 (78)	355 (85)	362 (92)	368 (98)	374 (104)	380 (110)	385 (115)