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	Hekts	Approximate ratios
0	0	0	1/1
1	14.7	10.1
2	29.5	20.2
3	44.2	30.2	39/38
4	59	40.3	30/29
5	73.7	50.4	47/45
6	88.5	60.5
7	103.2	70.5	52/49
8	118	80.6
9	132.7	90.7	27/25, 41/38
10	147.4	100.8	37/34
11	162.2	110.9	45/41
12	176.9	120.9	41/37
13	191.7	131	19/17
14	206.4	141.1
15	221.2	151.2	25/22
16	235.9	161.2	39/34, 47/41
17	250.6	171.3
18	265.4	181.4	7/6
19	280.1	191.5
20	294.9	201.6	51/43
21	309.6	211.6
22	324.4	221.7	35/29, 41/34, 47/39
23	339.1	231.8	45/37
24	353.9	241.9	27/22, 38/31
25	368.6	251.9	26/21, 47/38
26	383.3	262
27	398.1	272.1	34/27, 39/31
28	412.8	282.2	47/37
29	427.6	292.2
30	442.3	302.3
31	457.1	312.4	43/33
32	471.8	322.5	46/35
33	486.5	332.6	45/34
34	501.3	342.6
35	516	352.7	31/23, 35/26
36	530.8	362.8	34/25
37	545.5	372.9	37/27
38	560.3	382.9	29/21, 47/34
39	575	393
40	589.8	403.1
41	604.5	413.2	44/31
42	619.2	423.3	10/7
43	634	433.3
44	648.7	443.4
45	663.5	453.5	22/15
46	678.2	463.6	34/23, 37/25
47	693	473.6
48	707.7	483.7
49	722.4	493.8	41/27, 44/29
50	737.2	503.9
51	751.9	514	17/11
52	766.7	524
53	781.4	534.1
54	796.2	544.2
55	810.9	554.3
56	825.7	564.3	29/18
57	840.4	574.4
58	855.1	584.5	41/25
59	869.9	594.6	38/23
60	884.6	604.7	5/3
61	899.4	614.7	37/22
62	914.1	624.8	39/23
63	928.9	634.9
64	943.6	645	50/29
65	958.3	655	47/27
66	973.1	665.1
67	987.8	675.2	23/13
68	1002.6	685.3	41/23
69	1017.3	695.3	9/5
70	1032.1	705.4
71	1046.8	715.5
72	1061.6	725.6
73	1076.3	735.7	41/22
74	1091	745.7	47/25
75	1105.8	755.8
76	1120.5	765.9
77	1135.3	776
78	1150	786	33/17, 35/18
79	1164.8	796.1
80	1179.5	806.2
81	1194.3	816.3
82	1209	826.4
83	1223.7	836.4
84	1238.5	846.5	45/22, 47/23
85	1253.2	856.6
86	1268	866.7
87	1282.7	876.7	21/10
88	1297.5	886.8
89	1312.2	896.9
90	1326.9	907
91	1341.7	917.1
92	1356.4	927.1	46/21
93	1371.2	937.2
94	1385.9	947.3
95	1400.7	957.4
96	1415.4	967.4	34/15, 43/19
97	1430.2	977.5
98	1444.9	987.6
99	1459.6	997.7
100	1474.4	1007.8
101	1489.1	1017.8
102	1503.9	1027.9	31/13
103	1518.6	1038
104	1533.4	1048.1
105	1548.1	1058.1	22/9
106	1562.8	1068.2	37/15
107	1577.6	1078.3
108	1592.3	1088.4
109	1607.1	1098.4	43/17
110	1621.8	1108.5
111	1636.6	1118.6	18/7
112	1651.3	1128.7
113	1666.1	1138.8	34/13
114	1680.8	1148.8
115	1695.5	1158.9
116	1710.3	1169	51/19
117	1725	1179.1
118	1739.8	1189.1	41/15
119	1754.5	1199.2
120	1769.3	1209.3	25/9
121	1784	1219.4
122	1798.7	1229.5
123	1813.5	1239.5
124	1828.2	1249.6
125	1843	1259.7	29/10
126	1857.7	1269.8	38/13
127	1872.5	1279.8
128	1887.2	1289.9
129	1902	1300	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)