135edt

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 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	14.1
2	28.2
3	42.3	40/39, 41/40, 42/41, 43/42
4	56.4	31/30
5	70.4	49/47, 51/49
6	84.5	21/20
7	98.6	18/17
8	112.7	47/44
9	126.8	14/13, 43/40
10	140.9	38/35, 51/47
11	155	47/43
12	169.1	43/39
13	183.2	10/9
14	197.2	37/33
15	211.3	26/23, 35/31
16	225.4	33/29, 41/36, 49/43
17	239.5	31/27
18	253.6	22/19
19	267.7	7/6
20	281.8	20/17
21	295.9	51/43
22	309.9	49/41
23	324	35/29, 41/34, 47/39
24	338.1	45/37
25	352.2	38/31, 49/40
26	366.3	21/17, 47/38
27	380.4
28	394.5	44/35, 49/39
29	408.6	19/15
30	422.7	23/18, 37/29
31	436.7	9/7
32	450.8	35/27
33	464.9	17/13
34	479	29/22, 33/25
35	493.1
36	507.2
37	521.3	27/20, 50/37
38	535.4	15/11, 49/36
39	549.5
40	563.5	18/13
41	577.6
42	591.7	38/27
43	605.8	44/31
44	619.9
45	634	49/34
46	648.1
47	662.2	22/15
48	676.3	34/23
49	690.3
50	704.4
51	718.5	50/33
52	732.6	29/19
53	746.7	20/13
54	760.8	45/29
55	774.9	36/23
56	789	41/26
57	803	35/22
58	817.1
59	831.2	21/13
60	845.3	44/27
61	859.4	23/14
62	873.5
63	887.6
64	901.7	37/22
65	915.8	39/23
66	929.8
67	943.9	50/29
68	958	40/23, 47/27
69	972.1
70	986.2	23/13
71	1000.3	41/23
72	1014.4
73	1028.5	38/21
74	1042.6	42/23
75	1056.6	35/19
76	1070.7	13/7
77	1084.8	43/23
78	1098.9
79	1113
80	1127.1	23/12
81	1141.2	29/15
82	1155.3	37/19, 39/20
83	1169.4
84	1183.4
85	1197.5
86	1211.6
87	1225.7
88	1239.8	43/21, 45/22
89	1253.9
90	1268
91	1282.1	44/21
92	1296.1
93	1310.2	49/23
94	1324.3	43/20
95	1338.4	13/6
96	1352.5
97	1366.6	11/5
98	1380.7	20/9
99	1394.8	47/21
100	1408.9
101	1422.9	25/11
102	1437	39/17
103	1451.1
104	1465.2	7/3
105	1479.3	47/20
106	1493.4	45/19
107	1507.5	43/18
108	1521.6
109	1535.7	17/7
110	1549.7	49/20
111	1563.8	37/15
112	1577.9
113	1592
114	1606.1	43/17
115	1620.2	51/20
116	1634.3	18/7
117	1648.4
118	1662.4	47/18
119	1676.5	29/11, 50/19
120	1690.6
121	1704.7
122	1718.8	27/10
123	1732.9	49/18
124	1747
125	1761.1	47/17
126	1775.2	39/14
127	1789.2
128	1803.3	17/6
129	1817.4	20/7
130	1831.5	49/17
131	1845.6
132	1859.7	41/14
133	1873.8
134	1887.9
135	1902	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)