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	Hekts	Approximate ratios
0	0	0	1/1
1	14.1	9.6
2	28.2	19.3
3	42.3	28.9	40/39, 41/40, 42/41, 43/42
4	56.4	38.5	31/30
5	70.4	48.1	49/47, 51/49
6	84.5	57.8	21/20
7	98.6	67.4	18/17
8	112.7	77	47/44
9	126.8	86.7	14/13, 43/40
10	140.9	96.3	38/35, 51/47
11	155	105.9	47/43
12	169.1	115.6	43/39
13	183.2	125.2	10/9
14	197.2	134.8	37/33
15	211.3	144.4	26/23, 35/31
16	225.4	154.1	33/29, 41/36, 49/43
17	239.5	163.7	31/27
18	253.6	173.3	22/19
19	267.7	183	7/6
20	281.8	192.6	20/17
21	295.9	202.2	51/43
22	309.9	211.9	49/41
23	324	221.5	35/29, 41/34, 47/39
24	338.1	231.1	45/37
25	352.2	240.7	38/31, 49/40
26	366.3	250.4	21/17, 47/38
27	380.4	260
28	394.5	269.6	44/35, 49/39
29	408.6	279.3	19/15
30	422.7	288.9	23/18, 37/29
31	436.7	298.5	9/7
32	450.8	308.1	35/27
33	464.9	317.8	17/13
34	479	327.4	29/22, 33/25
35	493.1	337
36	507.2	346.7
37	521.3	356.3	27/20, 50/37
38	535.4	365.9	15/11, 49/36
39	549.5	375.6
40	563.5	385.2	18/13
41	577.6	394.8
42	591.7	404.4	38/27
43	605.8	414.1	44/31
44	619.9	423.7
45	634	433.3	49/34
46	648.1	443
47	662.2	452.6	22/15
48	676.3	462.2	34/23
49	690.3	471.9
50	704.4	481.5
51	718.5	491.1	50/33
52	732.6	500.7	29/19
53	746.7	510.4	20/13
54	760.8	520	45/29
55	774.9	529.6	36/23
56	789	539.3	41/26
57	803	548.9	35/22
58	817.1	558.5
59	831.2	568.1	21/13
60	845.3	577.8	44/27
61	859.4	587.4	23/14
62	873.5	597
63	887.6	606.7
64	901.7	616.3	37/22
65	915.8	625.9	39/23
66	929.8	635.6
67	943.9	645.2	50/29
68	958	654.8	40/23, 47/27
69	972.1	664.4
70	986.2	674.1	23/13
71	1000.3	683.7	41/23
72	1014.4	693.3
73	1028.5	703	38/21
74	1042.6	712.6	42/23
75	1056.6	722.2	35/19
76	1070.7	731.9	13/7
77	1084.8	741.5	43/23
78	1098.9	751.1
79	1113	760.7
80	1127.1	770.4	23/12
81	1141.2	780	29/15
82	1155.3	789.6	37/19, 39/20
83	1169.4	799.3
84	1183.4	808.9
85	1197.5	818.5
86	1211.6	828.1
87	1225.7	837.8
88	1239.8	847.4	43/21, 45/22
89	1253.9	857
90	1268	866.7
91	1282.1	876.3	44/21
92	1296.1	885.9
93	1310.2	895.6	49/23
94	1324.3	905.2	43/20
95	1338.4	914.8	13/6
96	1352.5	924.4
97	1366.6	934.1	11/5
98	1380.7	943.7	20/9
99	1394.8	953.3	47/21
100	1408.9	963
101	1422.9	972.6	25/11
102	1437	982.2	39/17
103	1451.1	991.9
104	1465.2	1001.5	7/3
105	1479.3	1011.1	47/20
106	1493.4	1020.7	45/19
107	1507.5	1030.4	43/18
108	1521.6	1040
109	1535.7	1049.6	17/7
110	1549.7	1059.3	49/20
111	1563.8	1068.9	37/15
112	1577.9	1078.5
113	1592	1088.1
114	1606.1	1097.8	43/17
115	1620.2	1107.4	51/20
116	1634.3	1117	18/7
117	1648.4	1126.7
118	1662.4	1136.3	47/18
119	1676.5	1145.9	29/11, 50/19
120	1690.6	1155.6
121	1704.7	1165.2
122	1718.8	1174.8	27/10
123	1732.9	1184.4	49/18
124	1747	1194.1
125	1761.1	1203.7	47/17
126	1775.2	1213.3	39/14
127	1789.2	1223
128	1803.3	1232.6	17/6
129	1817.4	1242.2	20/7
130	1831.5	1251.9	49/17
131	1845.6	1261.5
132	1859.7	1271.1	41/14
133	1873.8	1280.7
134	1887.9	1290.4
135	1902	1300	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)