129edt

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129edt

130edt →

Prime factorization	3 × 43
Step size	14.7438¢
Octave	81\129edt (1194.25¢) (→27\43edt)
Consistency limit	2
Distinct consistency limit	2

129 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 129edt or 129ed3), is a nonoctave tuning system that divides the interval of 3/1 into 129 equal parts of about 14.7 ¢ each. Each step represents a frequency ratio of 3^1/129, or the 129th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	14.744
2	29.488
3	44.232	39/38
4	58.975	30/29
5	73.719	47/45
6	88.463
7	103.207	52/49
8	117.951
9	132.695	27/25, 41/38
10	147.438	37/34
11	162.182	45/41
12	176.926	41/37
13	191.67	19/17
14	206.414
15	221.158	25/22
16	235.901	39/34, 47/41
17	250.645
18	265.389	7/6
19	280.133
20	294.877	51/43
21	309.621
22	324.364	35/29, 41/34, 47/39
23	339.108	45/37
24	353.852	27/22, 38/31
25	368.596	26/21, 47/38
26	383.34
27	398.084	34/27, 39/31
28	412.827	47/37
29	427.571
30	442.315
31	457.059	43/33
32	471.803	46/35
33	486.547	45/34
34	501.29
35	516.034	31/23, 35/26
36	530.778	34/25
37	545.522	37/27
38	560.266	29/21, 47/34
39	575.01
40	589.753
41	604.497	44/31
42	619.241	10/7
43	633.985
44	648.729
45	663.473	22/15
46	678.217	34/23, 37/25
47	692.96
48	707.704
49	722.448	41/27, 44/29
50	737.192
51	751.936	17/11
52	766.68
53	781.423
54	796.167
55	810.911
56	825.655	29/18
57	840.399
58	855.143	41/25
59	869.886	38/23
60	884.63	5/3
61	899.374	37/22
62	914.118	39/23
63	928.862
64	943.606	50/29
65	958.349	47/27
66	973.093
67	987.837	23/13
68	1002.581	41/23
69	1017.325	9/5
70	1032.069
71	1046.812
72	1061.556
73	1076.3	41/22
74	1091.044	47/25
75	1105.788
76	1120.532
77	1135.275
78	1150.019	33/17, 35/18
79	1164.763
80	1179.507
81	1194.251
82	1208.995
83	1223.738
84	1238.482	45/22, 47/23
85	1253.226
86	1267.97
87	1282.714	21/10
88	1297.458
89	1312.202
90	1326.945
91	1341.689
92	1356.433	46/21
93	1371.177
94	1385.921
95	1400.665
96	1415.408	34/15, 43/19
97	1430.152
98	1444.896
99	1459.64
100	1474.384
101	1489.128
102	1503.871	31/13
103	1518.615
104	1533.359
105	1548.103	22/9
106	1562.847	37/15
107	1577.591
108	1592.334
109	1607.078	43/17
110	1621.822
111	1636.566	18/7
112	1651.31
113	1666.054	34/13
114	1680.797
115	1695.541
116	1710.285	51/19
117	1725.029
118	1739.773	41/15
119	1754.517
120	1769.26	25/9
121	1784.004
122	1798.748
123	1813.492
124	1828.236
125	1842.98	29/10
126	1857.723	38/13
127	1872.467
128	1887.211
129	1901.955	3/1

Harmonics

Approximation of harmonics in 129edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.75	+0.00	+3.25	+0.27	-5.75	-7.23	-2.50	+0.00	-5.48	+6.44	+3.25
	Relative (%)	-39.0	+0.0	+22.0	+1.8	-39.0	-49.0	-17.0	+0.0	-37.2	+43.7	+22.0
Steps (reduced)		81 (81)	129 (0)	163 (34)	189 (60)	210 (81)	228 (99)	244 (115)	258 (0)	270 (12)	282 (24)	292 (34)

Approximation of harmonics in 129edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+1.76	+0.27	+6.49	+4.74	-5.75	+3.85	+3.52	-7.23	+0.69	-2.54
	Relative (%)	-17.9	+12.0	+1.8	+44.0	+32.2	-39.0	+26.1	+23.9	-49.0	+4.7	-17.2
Steps (reduced)		301 (43)	310 (52)	318 (60)	326 (68)	333 (75)	339 (81)	346 (88)	352 (94)	357 (99)	363 (105)	368 (110)