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	13.5
2	27
3	40.5	42/41, 43/42, 44/43, 45/44
4	54	32/31, 33/32
5	67.4
6	80.9	22/21, 43/41
7	94.4	19/18
8	107.9	33/31
9	121.4	44/41
10	134.9
11	148.4	49/45
12	161.9	45/41
13	175.4	31/28, 52/47
14	188.8	29/26, 48/43
15	202.3	9/8
16	215.8	17/15
17	229.3
18	242.8	38/33
19	256.3	51/44
20	269.8
21	283.3	33/28
22	296.8	19/16, 51/43
23	310.2	49/41
24	323.7	41/34, 47/39
25	337.2	17/14
26	350.7	49/40
27	364.2	21/17
28	377.7	46/37, 51/41
29	391.2
30	404.7	24/19
31	418.2	14/11
32	431.6
33	445.1	22/17
34	458.6	43/33
35	472.1	21/16
36	485.6	41/31, 45/34
37	499.1	4/3
38	512.6	39/29, 43/32
39	526.1	42/31
40	539.6	41/30
41	553.1
42	566.5	43/31
43	580
44	593.5	31/22
45	607	27/19, 44/31
46	620.5
47	634	49/34
48	647.5	16/11
49	661	41/28
50	674.5	31/21
51	687.9
52	701.4	3/2
53	714.9
54	728.4	32/21
55	741.9	43/28
56	755.4	48/31
57	768.9
58	782.4	11/7
59	795.9	19/12
60	809.3
61	822.8	37/23, 45/28
62	836.3	47/29
63	849.8	49/30
64	863.3	28/17, 51/31
65	876.8
66	890.3
67	903.8	32/19
68	917.3	17/10
69	930.7
70	944.2
71	957.7
72	971.2
73	984.7	30/17
74	998.2
75	1011.7	52/29
76	1025.2	38/21, 47/26
77	1038.7	31/17, 51/28
78	1052.1
79	1065.6
80	1079.1	28/15, 41/22
81	1092.6
82	1106.1	36/19
83	1119.6	21/11
84	1133.1	52/27
85	1146.6	31/16
86	1160.1	43/22
87	1173.5
88	1187
89	1200.5	2/1
90	1214
91	1227.5
92	1241	43/21
93	1254.5	33/16
94	1268
95	1281.5	44/21
96	1294.9	19/9
97	1308.4
98	1321.9
99	1335.4
100	1348.9
101	1362.4
102	1375.9	31/14
103	1389.4	29/13
104	1402.9	9/4
105	1416.3	34/15
106	1429.8	16/7
107	1443.3
108	1456.8	51/22
109	1470.3
110	1483.8	33/14
111	1497.3	19/8
112	1510.8
113	1524.3	41/17
114	1537.8	17/7
115	1551.2	49/20
116	1564.7	42/17
117	1578.2
118	1591.7
119	1605.2	43/17, 48/19
120	1618.7	28/11
121	1632.2
122	1645.7	44/17
123	1659.2
124	1672.6
125	1686.1	45/17
126	1699.6	8/3
127	1713.1	43/16
128	1726.6
129	1740.1	41/15
130	1753.6
131	1767.1
132	1780.6
133	1794	31/11
134	1807.5	54/19
135	1821
136	1834.5
137	1848	32/11
138	1861.5	41/14, 44/15
139	1875
140	1888.5
141	1902	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)