143ed4

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

← 141ed4

143ed4

145ed4 →

Prime factorization	11 × 13
Step size	16.7832¢
Octave	72\143ed4 (1208.39¢)
Twelfth	113\143ed4 (1896.5¢)
Consistency limit	1
Distinct consistency limit	1

143 equal divisions of the 4th harmonic (abbreviated 143ed4) is a nonoctave tuning system that divides the interval of 4/1 into 143 equal parts of about 16.8 ¢ each. Each step represents a frequency ratio of 4^1/143, or the 143rd root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	16.783
2	33.566	50/49
3	50.35	35/34, 36/35
4	67.133
5	83.916	43/41
6	100.699
7	117.483	46/43
8	134.266
9	151.049
10	167.832	43/39
11	184.615
12	201.399
13	218.182	17/15
14	234.965	47/41
15	251.748
16	268.531
17	285.315	46/39
18	302.098	25/21
19	318.881
20	335.664
21	352.448
22	369.231
23	386.014
24	402.797	29/23
25	419.58
26	436.364
27	453.147	13/10
28	469.93
29	486.713
30	503.497
31	520.28
32	537.063	15/11
33	553.846
34	570.629
35	587.413
36	604.196
37	620.979
38	637.762
39	654.545	54/37
40	671.329
41	688.112
42	704.895
43	721.678	47/31
44	738.462	23/15
45	755.245	17/11
46	772.028
47	788.811
48	805.594
49	822.378	37/23
50	839.161
51	855.944	41/25
52	872.727
53	889.51
54	906.294
55	923.077	29/17
56	939.86	31/18, 43/25
57	956.643
58	973.427
59	990.21	39/22
60	1006.993	34/19
61	1023.776
62	1040.559	31/17
63	1057.343	35/19
64	1074.126
65	1090.909
66	1107.692	36/19, 55/29
67	1124.476
68	1141.259	29/15
69	1158.042	41/21
70	1174.825
71	1191.608
72	1208.392
73	1225.175
74	1241.958	43/21
75	1258.741
76	1275.524	23/11
77	1292.308
78	1309.091
79	1325.874
80	1342.657
81	1359.441
82	1376.224
83	1393.007
84	1409.79
85	1426.573	41/18
86	1443.357
87	1460.14
88	1476.923	54/23
89	1493.706
90	1510.49	55/23
91	1527.273
92	1544.056
93	1560.839
94	1577.622
95	1594.406
96	1611.189
97	1627.972
98	1644.755
99	1661.538	47/18
100	1678.322	29/11
101	1695.105
102	1711.888
103	1728.671	19/7
104	1745.455
105	1762.238	36/13
106	1779.021
107	1795.804
108	1812.587
109	1829.371
110	1846.154
111	1862.937
112	1879.72
113	1896.503
114	1913.287
115	1930.07
116	1946.853
117	1963.636
118	1980.42
119	1997.203
120	2013.986
121	2030.769	42/13
122	2047.552
123	2064.336
124	2081.119
125	2097.902
126	2114.685
127	2131.469
128	2148.252
129	2165.035
130	2181.818
131	2198.601
132	2215.385
133	2232.168
134	2248.951	11/3
135	2265.734
136	2282.517
137	2299.301
138	2316.084
139	2332.867	50/13
140	2349.65
141	2366.434
142	2383.217
143	2400

Harmonics

Approximation of harmonics in 143ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.39	-5.45	+0.00	-0.30	+2.94	+4.60	+8.39	+5.88	+8.09	-5.86	-5.45
	Relative (%)	+50.0	-32.5	+0.0	-1.8	+17.5	+27.4	+50.0	+35.0	+48.2	-34.9	-32.5
Steps (reduced)		72 (72)	113 (113)	143 (0)	166 (23)	185 (42)	201 (58)	215 (72)	227 (84)	238 (95)	247 (104)	256 (113)

Approximation of harmonics in 143ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+7.02	-3.79	-5.75	+0.00	-4.26	-2.51	+4.58	-0.30	-0.85	+2.53	-7.30
	Relative (%)	+41.9	-22.6	-34.3	+0.0	-25.4	-15.0	+27.3	-1.8	-5.1	+15.1	-43.5
Steps (reduced)		265 (122)	272 (129)	279 (136)	286 (0)	292 (6)	298 (12)	304 (18)	309 (23)	314 (28)	319 (33)	323 (37)