143edt

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143edt

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Prime factorization	11 × 13
Step size	13.3004¢
Octave	90\143edt (1197.03¢)
Consistency limit	7
Distinct consistency limit	7

143 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 143edt or 143ed3), is a nonoctave tuning system that divides the interval of 3/1 into 143 equal parts of about 13.3 ¢ each. Each step represents a frequency ratio of 3^1/143, or the 143rd root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	13.3
2	26.601
3	39.901	45/44
4	53.202	34/33
5	66.502	27/26
6	79.802	22/21
7	93.103	19/18
8	106.403
9	119.703	15/14
10	133.004	41/38
11	146.304	37/34, 49/45
12	159.605	34/31, 45/41
13	172.905	21/19
14	186.205	49/44
15	199.506	37/33, 46/41, 55/49
16	212.806	26/23
17	226.107	41/36
18	239.407	31/27, 54/47
19	252.707	22/19
20	266.008	7/6
21	279.308
22	292.608	45/38
23	305.909	31/26, 37/31
24	319.209
25	332.51
26	345.81	11/9
27	359.11
28	372.411
29	385.711	5/4
30	399.012	34/27, 39/31
31	412.312	33/26, 52/41
32	425.612	23/18
33	438.913	49/38
34	452.213
35	465.513	17/13, 55/42
36	478.814	29/22
37	492.114
38	505.415
39	518.715
40	532.015
41	545.316	37/27, 48/35
42	558.616	29/21
43	571.917
44	585.217
45	598.517	41/29
46	611.818	37/26, 47/33
47	625.118	33/23
48	638.418
49	651.719	35/24
50	665.019
51	678.32
52	691.62
53	704.92
54	718.221
55	731.521	29/19
56	744.822
57	758.122
58	771.422	25/16
59	784.723
60	798.023	46/29
61	811.323
62	824.624	29/18, 37/23
63	837.924
64	851.225	18/11
65	864.525
66	877.825
67	891.126
68	904.426
69	917.727
70	931.027
71	944.327
72	957.628
73	970.928
74	984.228
75	997.529
76	1010.829	52/29
77	1024.13	47/26
78	1037.43
79	1050.73	11/6
80	1064.031
81	1077.331	41/22, 54/29
82	1090.632
83	1103.932
84	1117.232
85	1130.533	48/25
86	1143.833
87	1157.133	41/21
88	1170.434	55/28
89	1183.734
90	1197.035
91	1210.335
92	1223.635
93	1236.936	47/23, 49/24
94	1250.236
95	1263.537
96	1276.837	23/11
97	1290.137
98	1303.438
99	1316.738
100	1330.038	41/19
101	1343.339
102	1356.639	35/16, 46/21
103	1369.94
104	1383.24
105	1396.54
106	1409.841
107	1423.141
108	1436.442	39/17, 55/24
109	1449.742
110	1463.042
111	1476.343	54/23
112	1489.643	26/11
113	1502.943	31/13
114	1516.244	12/5
115	1529.544	46/19
116	1542.845
117	1556.145	27/11
118	1569.445	47/19, 52/21
119	1582.746
120	1596.046
121	1609.347	38/15
122	1622.647
123	1635.947	18/7
124	1649.248
125	1662.548	47/18
126	1675.848
127	1689.149
128	1702.449
129	1715.75
130	1729.05	19/7
131	1742.35	41/15, 52/19
132	1755.651
133	1768.951
134	1782.252	14/5
135	1795.552
136	1808.852	54/19
137	1822.153
138	1835.453	26/9
139	1848.753
140	1862.054	44/15
141	1875.354
142	1888.655
143	1901.955	3/1

Harmonics

Approximation of harmonics in 143edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.97	+0.00	-5.93	-6.53	-2.97	-3.83	+4.40	+0.00	+3.80	-1.60	-5.93
	Relative (%)	-22.3	+0.0	-44.6	-49.1	-22.3	-28.8	+33.1	+0.0	+28.6	-12.0	-44.6
Steps (reduced)		90 (90)	143 (0)	180 (37)	209 (66)	233 (90)	253 (110)	271 (128)	286 (0)	300 (14)	312 (26)	323 (37)

Approximation of harmonics in 143edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.80	+6.51	-6.53	+1.44	+2.89	-2.97	-3.47	+0.84	-3.83	-4.56	-1.72
	Relative (%)	+13.5	+48.9	-49.1	+10.8	+21.7	-22.3	-26.1	+6.3	-28.8	-34.3	-12.9
Steps (reduced)		334 (48)	344 (58)	352 (66)	361 (75)	369 (83)	376 (90)	383 (97)	390 (104)	396 (110)	402 (116)	408 (122)