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	18.605
2	37.209
3	55.814	31/30
4	74.419	47/45
5	93.023	19/18
6	111.628
7	130.233	41/38
8	148.837	49/45
9	167.442	43/39
10	186.047	39/35
11	204.651
12	223.256	33/29
13	241.86
14	260.465	36/31, 43/37
15	279.07
16	297.674
17	316.279	6/5
18	334.884	17/14
19	353.488	38/31
20	372.093	31/25
21	390.698
22	409.302	19/15
23	427.907
24	446.512	22/17
25	465.116	17/13
26	483.721	41/31
27	502.326
28	520.93
29	539.535	41/30
30	558.14	29/21
31	576.744
32	595.349	31/22
33	613.953	47/33
34	632.558	36/25
35	651.163	51/35
36	669.767
37	688.372
38	706.977
39	725.581	35/23, 38/25
40	744.186
41	762.791
42	781.395	11/7
43	800
44	818.605
45	837.209	47/29
46	855.814	41/25
47	874.419
48	893.023
49	911.628	22/13
50	930.233
51	948.837
52	967.442
53	986.047	23/13
54	1004.651	25/14
55	1023.256
56	1041.86	31/17, 42/23
57	1060.465
58	1079.07	41/22
59	1097.674
60	1116.279
61	1134.884
62	1153.488	37/19
63	1172.093
64	1190.698
65	1209.302
66	1227.907
67	1246.512	37/18, 39/19
68	1265.116
69	1283.721
70	1302.326
71	1320.93	15/7
72	1339.535	13/6
73	1358.14
74	1376.744	31/14
75	1395.349	47/21
76	1413.953	43/19
77	1432.558
78	1451.163
79	1469.767
80	1488.372
81	1506.977	43/18
82	1525.581	41/17
83	1544.186
84	1562.791	37/15
85	1581.395
86	1600
87	1618.605
88	1637.209
89	1655.814	13/5
90	1674.419
91	1693.023
92	1711.628
93	1730.233	19/7
94	1748.837
95	1767.442
96	1786.047
97	1804.651	17/6
98	1823.256	43/15
99	1841.86
100	1860.465	41/14
101	1879.07
102	1897.674
103	1916.279
104	1934.884
105	1953.488
106	1972.093
107	1990.698
108	2009.302
109	2027.907
110	2046.512
111	2065.116
112	2083.721
113	2102.326
114	2120.93
115	2139.535
116	2158.14
117	2176.744
118	2195.349
119	2213.953
120	2232.558
121	2251.163	11/3
122	2269.767
123	2288.372
124	2306.977
125	2325.581	23/6
126	2344.186
127	2362.791
128	2381.395
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)