129ed4

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129ed4

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Prime factorization	3 × 43
Step size	18.6047¢
Octave	65\129ed4 (1209.3¢)
Twelfth	102\129ed4 (1897.67¢) (→34\43ed4)
Consistency limit	1
Distinct consistency limit	1

129 equal divisions of the 4th harmonic (abbreviated 129ed4) is a nonoctave tuning system that divides the interval of 4/1 into 129 equal parts of about 18.6 ¢ each. Each step represents a frequency ratio of 4^1/129, or the 129th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	18.6
2	37.2
3	55.8	31/30
4	74.4	47/45
5	93	19/18
6	111.6
7	130.2	41/38
8	148.8	49/45
9	167.4	43/39
10	186	39/35
11	204.7
12	223.3	33/29
13	241.9
14	260.5	36/31, 43/37
15	279.1
16	297.7
17	316.3	6/5
18	334.9	17/14
19	353.5	38/31
20	372.1	31/25
21	390.7
22	409.3	19/15
23	427.9
24	446.5	22/17
25	465.1	17/13
26	483.7	41/31
27	502.3
28	520.9
29	539.5	41/30
30	558.1	29/21
31	576.7
32	595.3	31/22
33	614	47/33
34	632.6	36/25
35	651.2	51/35
36	669.8
37	688.4
38	707
39	725.6	35/23, 38/25
40	744.2
41	762.8
42	781.4	11/7
43	800
44	818.6
45	837.2	47/29
46	855.8	41/25
47	874.4
48	893
49	911.6	22/13
50	930.2
51	948.8
52	967.4
53	986	23/13
54	1004.7	25/14
55	1023.3
56	1041.9	31/17, 42/23
57	1060.5
58	1079.1	41/22
59	1097.7
60	1116.3
61	1134.9
62	1153.5	37/19
63	1172.1
64	1190.7
65	1209.3
66	1227.9
67	1246.5	37/18, 39/19
68	1265.1
69	1283.7
70	1302.3
71	1320.9	15/7
72	1339.5	13/6
73	1358.1
74	1376.7	31/14
75	1395.3	47/21
76	1414	43/19
77	1432.6
78	1451.2
79	1469.8
80	1488.4
81	1507	43/18
82	1525.6	41/17
83	1544.2
84	1562.8	37/15
85	1581.4
86	1600
87	1618.6
88	1637.2
89	1655.8	13/5
90	1674.4
91	1693
92	1711.6
93	1730.2	19/7
94	1748.8
95	1767.4
96	1786
97	1804.7	17/6
98	1823.3	43/15
99	1841.9
100	1860.5	41/14
101	1879.1
102	1897.7
103	1916.3
104	1934.9
105	1953.5
106	1972.1
107	1990.7
108	2009.3
109	2027.9
110	2046.5
111	2065.1
112	2083.7
113	2102.3
114	2120.9
115	2139.5
116	2158.1
117	2176.7
118	2195.3
119	2214
120	2232.6
121	2251.2	11/3
122	2269.8
123	2288.4
124	2307
125	2325.6	23/6
126	2344.2
127	2362.8
128	2381.4
129	2400

Harmonics

Approximation of harmonics in 129ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+9.30	-4.28	+0.00	+4.38	+5.02	-1.38	+9.30	-8.56	-4.92	-2.48	-4.28
	Relative (%)	+50.0	-23.0	+0.0	+23.6	+27.0	-7.4	+50.0	-46.0	-26.4	-13.3	-23.0
Steps (reduced)		65 (65)	102 (102)	129 (0)	150 (21)	167 (38)	181 (52)	194 (65)	204 (75)	214 (85)	223 (94)	231 (102)

Approximation of harmonics in 129ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.98	+7.92	+0.10	+0.00	+6.67	+0.74	+0.16	+4.38	-5.66	+6.82	+4.28
	Relative (%)	+32.2	+42.6	+0.6	+0.0	+35.9	+4.0	+0.9	+23.6	-30.4	+36.7	+23.0
Steps (reduced)		239 (110)	246 (117)	252 (123)	258 (0)	264 (6)	269 (11)	274 (16)	279 (21)	283 (25)	288 (30)	292 (34)