141edt

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141edt

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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	Hekts	Approximate ratios
0	0	0	1/1
1	13.5	9.2
2	27	18.4
3	40.5	27.7	42/41, 43/42, 44/43, 45/44
4	54	36.9	32/31, 33/32
5	67.4	46.1
6	80.9	55.3	22/21, 43/41
7	94.4	64.5	19/18
8	107.9	73.8	33/31
9	121.4	83	44/41
10	134.9	92.2
11	148.4	101.4	49/45
12	161.9	110.6	45/41
13	175.4	119.9	31/28, 52/47
14	188.8	129.1	29/26, 48/43
15	202.3	138.3	9/8
16	215.8	147.5	17/15
17	229.3	156.7
18	242.8	166	38/33
19	256.3	175.2	51/44
20	269.8	184.4
21	283.3	193.6	33/28
22	296.8	202.8	19/16, 51/43
23	310.2	212.1	49/41
24	323.7	221.3	41/34, 47/39
25	337.2	230.5	17/14
26	350.7	239.7	49/40
27	364.2	248.9	21/17
28	377.7	258.2	46/37, 51/41
29	391.2	267.4
30	404.7	276.6	24/19
31	418.2	285.8	14/11
32	431.6	295
33	445.1	304.3	22/17
34	458.6	313.5	43/33
35	472.1	322.7	21/16
36	485.6	331.9	41/31, 45/34
37	499.1	341.1	4/3
38	512.6	350.4	39/29, 43/32
39	526.1	359.6	42/31
40	539.6	368.8	41/30
41	553.1	378
42	566.5	387.2	43/31
43	580	396.5
44	593.5	405.7	31/22
45	607	414.9	27/19, 44/31
46	620.5	424.1
47	634	433.3	49/34
48	647.5	442.6	16/11
49	661	451.8	41/28
50	674.5	461	31/21
51	687.9	470.2
52	701.4	479.4	3/2
53	714.9	488.7
54	728.4	497.9	32/21
55	741.9	507.1	43/28
56	755.4	516.3	48/31
57	768.9	525.5
58	782.4	534.8	11/7
59	795.9	544	19/12
60	809.3	553.2
61	822.8	562.4	37/23, 45/28
62	836.3	571.6	47/29
63	849.8	580.9	49/30
64	863.3	590.1	28/17, 51/31
65	876.8	599.3
66	890.3	608.5
67	903.8	617.7	32/19
68	917.3	627	17/10
69	930.7	636.2
70	944.2	645.4
71	957.7	654.6
72	971.2	663.8
73	984.7	673	30/17
74	998.2	682.3
75	1011.7	691.5	52/29
76	1025.2	700.7	38/21, 47/26
77	1038.7	709.9	31/17, 51/28
78	1052.1	719.1
79	1065.6	728.4
80	1079.1	737.6	28/15, 41/22
81	1092.6	746.8
82	1106.1	756	36/19
83	1119.6	765.2	21/11
84	1133.1	774.5	52/27
85	1146.6	783.7	31/16
86	1160.1	792.9	43/22
87	1173.5	802.1
88	1187	811.3
89	1200.5	820.6	2/1
90	1214	829.8
91	1227.5	839
92	1241	848.2	43/21
93	1254.5	857.4	33/16
94	1268	866.7
95	1281.5	875.9	44/21
96	1294.9	885.1	19/9
97	1308.4	894.3
98	1321.9	903.5
99	1335.4	912.8
100	1348.9	922
101	1362.4	931.2
102	1375.9	940.4	31/14
103	1389.4	949.6	29/13
104	1402.9	958.9	9/4
105	1416.3	968.1	34/15
106	1429.8	977.3	16/7
107	1443.3	986.5
108	1456.8	995.7	51/22
109	1470.3	1005
110	1483.8	1014.2	33/14
111	1497.3	1023.4	19/8
112	1510.8	1032.6
113	1524.3	1041.8	41/17
114	1537.8	1051.1	17/7
115	1551.2	1060.3	49/20
116	1564.7	1069.5	42/17
117	1578.2	1078.7
118	1591.7	1087.9
119	1605.2	1097.2	43/17, 48/19
120	1618.7	1106.4	28/11
121	1632.2	1115.6
122	1645.7	1124.8	44/17
123	1659.2	1134
124	1672.6	1143.3
125	1686.1	1152.5	45/17
126	1699.6	1161.7	8/3
127	1713.1	1170.9	43/16
128	1726.6	1180.1
129	1740.1	1189.4	41/15
130	1753.6	1198.6
131	1767.1	1207.8
132	1780.6	1217
133	1794	1226.2	31/11
134	1807.5	1235.5	54/19
135	1821	1244.7
136	1834.5	1253.9
137	1848	1263.1	32/11
138	1861.5	1272.3	41/14, 44/15
139	1875	1281.6
140	1888.5	1290.8
141	1902	1300	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)