143ed4

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143ed4

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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	16.8
2	33.6	50/49
3	50.3	35/34, 36/35
4	67.1
5	83.9	43/41
6	100.7
7	117.5	46/43
8	134.3
9	151
10	167.8	43/39
11	184.6
12	201.4
13	218.2	17/15
14	235	47/41
15	251.7
16	268.5
17	285.3	46/39
18	302.1	25/21
19	318.9
20	335.7
21	352.4
22	369.2
23	386
24	402.8	29/23
25	419.6
26	436.4
27	453.1	13/10
28	469.9
29	486.7
30	503.5
31	520.3
32	537.1	15/11
33	553.8
34	570.6
35	587.4
36	604.2
37	621
38	637.8
39	654.5	54/37
40	671.3
41	688.1
42	704.9
43	721.7	47/31
44	738.5	23/15
45	755.2	17/11
46	772
47	788.8
48	805.6
49	822.4	37/23
50	839.2
51	855.9	41/25
52	872.7
53	889.5
54	906.3
55	923.1	29/17
56	939.9	31/18, 43/25
57	956.6
58	973.4
59	990.2	39/22
60	1007	34/19
61	1023.8
62	1040.6	31/17
63	1057.3	35/19
64	1074.1
65	1090.9
66	1107.7	36/19, 55/29
67	1124.5
68	1141.3	29/15
69	1158	41/21
70	1174.8
71	1191.6
72	1208.4
73	1225.2
74	1242	43/21
75	1258.7
76	1275.5	23/11
77	1292.3
78	1309.1
79	1325.9
80	1342.7
81	1359.4
82	1376.2
83	1393
84	1409.8
85	1426.6	41/18
86	1443.4
87	1460.1
88	1476.9	54/23
89	1493.7
90	1510.5	55/23
91	1527.3
92	1544.1
93	1560.8
94	1577.6
95	1594.4
96	1611.2
97	1628
98	1644.8
99	1661.5	47/18
100	1678.3	29/11
101	1695.1
102	1711.9
103	1728.7	19/7
104	1745.5
105	1762.2	36/13
106	1779
107	1795.8
108	1812.6
109	1829.4
110	1846.2
111	1862.9
112	1879.7
113	1896.5
114	1913.3
115	1930.1
116	1946.9
117	1963.6
118	1980.4
119	1997.2
120	2014
121	2030.8	42/13
122	2047.6
123	2064.3
124	2081.1
125	2097.9
126	2114.7
127	2131.5
128	2148.3
129	2165
130	2181.8
131	2198.6
132	2215.4
133	2232.2
134	2249	11/3
135	2265.7
136	2282.5
137	2299.3
138	2316.1
139	2332.9	50/13
140	2349.7
141	2366.4
142	2383.2
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)