141edt

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

← 140edt

141edt

142edt →

Prime factorization	3 × 47
Step size	13.489¢
Octave	89\141edt (1200.52¢)
Consistency limit	11
Distinct consistency limit	11

141 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 141edt or 141ed3), is a nonoctave tuning system that divides the interval of 3/1 into 141 equal parts of about 13.5 ¢ each. Each step represents a frequency ratio of 3^1/141, or the 141st root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	13.489
2	26.978
3	40.467	42/41, 43/42, 44/43, 45/44
4	53.956	32/31, 33/32
5	67.445
6	80.934	22/21, 43/41
7	94.423	19/18
8	107.912	33/31
9	121.401	44/41
10	134.89
11	148.379	49/45
12	161.869	45/41
13	175.358	31/28, 52/47
14	188.847	29/26, 48/43
15	202.336	9/8
16	215.825	17/15
17	229.314
18	242.803	38/33
19	256.292	51/44
20	269.781
21	283.27	33/28
22	296.759	19/16, 51/43
23	310.248	49/41
24	323.737	41/34, 47/39
25	337.226	17/14
26	350.715	49/40
27	364.204	21/17
28	377.693	46/37, 51/41
29	391.182
30	404.671	24/19
31	418.16	14/11
32	431.649
33	445.138	22/17
34	458.627	43/33
35	472.116	21/16
36	485.606	41/31, 45/34
37	499.095	4/3
38	512.584	39/29, 43/32
39	526.073	42/31
40	539.562	41/30
41	553.051
42	566.54	43/31
43	580.029
44	593.518	31/22
45	607.007	27/19, 44/31
46	620.496
47	633.985	49/34
48	647.474	16/11
49	660.963	41/28
50	674.452	31/21
51	687.941
52	701.43	3/2
53	714.919
54	728.408	32/21
55	741.897	43/28
56	755.386	48/31
57	768.875
58	782.364	11/7
59	795.854	19/12
60	809.343
61	822.832	37/23, 45/28
62	836.321	47/29
63	849.81	49/30
64	863.299	28/17, 51/31
65	876.788
66	890.277
67	903.766	32/19
68	917.255	17/10
69	930.744
70	944.233
71	957.722
72	971.211
73	984.7	30/17
74	998.189
75	1011.678	52/29
76	1025.167	38/21, 47/26
77	1038.656	31/17, 51/28
78	1052.145
79	1065.634
80	1079.123	28/15, 41/22
81	1092.612
82	1106.101	36/19
83	1119.591	21/11
84	1133.08	52/27
85	1146.569	31/16
86	1160.058	43/22
87	1173.547
88	1187.036
89	1200.525	2/1
90	1214.014
91	1227.503
92	1240.992	43/21
93	1254.481	33/16
94	1267.97
95	1281.459	44/21
96	1294.948	19/9
97	1308.437
98	1321.926
99	1335.415
100	1348.904
101	1362.393
102	1375.882	31/14
103	1389.371	29/13
104	1402.86	9/4
105	1416.349	34/15
106	1429.839	16/7
107	1443.328
108	1456.817	51/22
109	1470.306
110	1483.795	33/14
111	1497.284	19/8
112	1510.773
113	1524.262	41/17
114	1537.751	17/7
115	1551.24	49/20
116	1564.729	42/17
117	1578.218
118	1591.707
119	1605.196	43/17, 48/19
120	1618.685	28/11
121	1632.174
122	1645.663	44/17
123	1659.152
124	1672.641
125	1686.13	45/17
126	1699.619	8/3
127	1713.108	43/16
128	1726.597
129	1740.086	41/15
130	1753.576
131	1767.065
132	1780.554
133	1794.043	31/11
134	1807.532	54/19
135	1821.021
136	1834.51
137	1847.999	32/11
138	1861.488	41/14, 44/15
139	1874.977
140	1888.466
141	1901.955	3/1

Harmonics

Approximation of harmonics in 141edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.52	+0.00	+1.05	+5.92	+0.52	+3.43	+1.57	+0.00	+6.44	+3.31	+1.05
	Relative (%)	+3.9	+0.0	+7.8	+43.9	+3.9	+25.5	+11.7	+0.0	+47.8	+24.5	+7.8
Steps (reduced)		89 (89)	141 (0)	178 (37)	207 (66)	230 (89)	250 (109)	267 (126)	282 (0)	296 (14)	308 (26)	319 (37)

Approximation of harmonics in 141edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+3.96	+5.92	+2.10	+5.06	+0.52	+1.35	-6.52	+3.43	+3.83	-5.68
	Relative (%)	-19.5	+29.4	+43.9	+15.6	+37.5	+3.9	+10.0	-48.3	+25.5	+28.4	-42.1
Steps (reduced)		329 (47)	339 (57)	348 (66)	356 (74)	364 (82)	371 (89)	378 (96)	384 (102)	391 (109)	397 (115)	402 (120)