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	26.6
3	39.9	45/44
4	53.2	34/33
5	66.5	27/26
6	79.8	22/21
7	93.1	19/18
8	106.4
9	119.7	15/14
10	133	41/38
11	146.3	37/34, 49/45
12	159.6	34/31, 45/41
13	172.9	21/19
14	186.2	49/44
15	199.5	37/33, 46/41, 55/49
16	212.8	26/23
17	226.1	41/36
18	239.4	31/27, 54/47
19	252.7	22/19
20	266	7/6
21	279.3
22	292.6	45/38
23	305.9	31/26, 37/31
24	319.2
25	332.5
26	345.8	11/9
27	359.1
28	372.4
29	385.7	5/4
30	399	34/27, 39/31
31	412.3	33/26, 52/41
32	425.6	23/18
33	438.9	49/38
34	452.2
35	465.5	17/13, 55/42
36	478.8	29/22
37	492.1
38	505.4
39	518.7
40	532
41	545.3	37/27, 48/35
42	558.6	29/21
43	571.9
44	585.2
45	598.5	41/29
46	611.8	37/26, 47/33
47	625.1	33/23
48	638.4
49	651.7	35/24
50	665
51	678.3
52	691.6
53	704.9
54	718.2
55	731.5	29/19
56	744.8
57	758.1
58	771.4	25/16
59	784.7
60	798	46/29
61	811.3
62	824.6	29/18, 37/23
63	837.9
64	851.2	18/11
65	864.5
66	877.8
67	891.1
68	904.4
69	917.7
70	931
71	944.3
72	957.6
73	970.9
74	984.2
75	997.5
76	1010.8	52/29
77	1024.1	47/26
78	1037.4
79	1050.7	11/6
80	1064
81	1077.3	41/22, 54/29
82	1090.6
83	1103.9
84	1117.2
85	1130.5	48/25
86	1143.8
87	1157.1	41/21
88	1170.4	55/28
89	1183.7
90	1197
91	1210.3
92	1223.6
93	1236.9	47/23, 49/24
94	1250.2
95	1263.5
96	1276.8	23/11
97	1290.1
98	1303.4
99	1316.7
100	1330	41/19
101	1343.3
102	1356.6	35/16, 46/21
103	1369.9
104	1383.2
105	1396.5
106	1409.8
107	1423.1
108	1436.4	39/17, 55/24
109	1449.7
110	1463
111	1476.3	54/23
112	1489.6	26/11
113	1502.9	31/13
114	1516.2	12/5
115	1529.5	46/19
116	1542.8
117	1556.1	27/11
118	1569.4	47/19, 52/21
119	1582.7
120	1596
121	1609.3	38/15
122	1622.6
123	1635.9	18/7
124	1649.2
125	1662.5	47/18
126	1675.8
127	1689.1
128	1702.4
129	1715.7
130	1729.1	19/7
131	1742.4	41/15, 52/19
132	1755.7
133	1769
134	1782.3	14/5
135	1795.6
136	1808.9	54/19
137	1822.2
138	1835.5	26/9
139	1848.8
140	1862.1	44/15
141	1875.4
142	1888.7
143	1902	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)