141ed4

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141ed4

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Prime factorization	3 × 47
Step size	17.0213 ¢
Octave	71\141ed4 (1208.51 ¢)
Twelfth	112\141ed4 (1906.38 ¢)
Consistency limit	1
Distinct consistency limit	1

141 equal divisions of the 4th harmonic (abbreviated 141ed4) is a nonoctave tuning system that divides the interval of 4/1 into 141 equal parts of about 17 ¢ each. Each step represents a frequency ratio of 4^1/141, or the 141st root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17
2	34
3	51.1	34/33, 35/34
4	68.1	26/25, 51/49
5	85.1	41/39
6	102.1	35/33
7	119.1	15/14
8	136.2
9	153.2	47/43
10	170.2	43/39
11	187.2	39/35
12	204.3
13	221.3	25/22
14	238.3	39/34
15	255.3
16	272.3	41/35, 55/47
17	289.4	13/11
18	306.4	37/31
19	323.4	41/34, 47/39
20	340.4
21	357.4	43/35
22	374.5	41/33
23	391.5
24	408.5
25	425.5	55/43
26	442.6
27	459.6	43/33
28	476.6
29	493.6
30	510.6	47/35, 51/38
31	527.7
32	544.7
33	561.7	47/34
34	578.7
35	595.7	55/39
36	612.8	47/33
37	629.8
38	646.8
39	663.8	22/15
40	680.9
41	697.9
42	714.9
43	731.9	29/19
44	748.9
45	766	14/9
46	783	11/7
47	800
48	817
49	834	34/21, 55/34
50	851.1
51	868.1	38/23
52	885.1	5/3
53	902.1
54	919.1
55	936.2
56	953.2	26/15
57	970.2
58	987.2	23/13
59	1004.3	25/14
60	1021.3
61	1038.3
62	1055.3	46/25
63	1072.3	13/7
64	1089.4
65	1106.4
66	1123.4
67	1140.4
68	1157.4	41/21
69	1174.5
70	1191.5
71	1208.5
72	1225.5
73	1242.6
74	1259.6
75	1276.6	23/11
76	1293.6
77	1310.6	49/23
78	1327.7
79	1344.7
80	1361.7
81	1378.7	51/23
82	1395.7	47/21
83	1412.8
84	1429.8
85	1446.8
86	1463.8
87	1480.9
88	1497.9
89	1514.9
90	1531.9
91	1548.9	22/9
92	1566
93	1583
94	1600
95	1617
96	1634
97	1651.1
98	1668.1	55/21
99	1685.1
100	1702.1
101	1719.1	27/10
102	1736.2
103	1753.2
104	1770.2	25/9
105	1787.2
106	1804.3
107	1821.3
108	1838.3
109	1855.3
110	1872.3
111	1889.4
112	1906.4
113	1923.4
114	1940.4	46/15
115	1957.4
116	1974.5
117	1991.5
118	2008.5
119	2025.5
120	2042.6
121	2059.6	23/7
122	2076.6
123	2093.6
124	2110.6
125	2127.7
126	2144.7	38/11
127	2161.7
128	2178.7
129	2195.7
130	2212.8
131	2229.8
132	2246.8
133	2263.8
134	2280.9
135	2297.9	49/13
136	2314.9
137	2331.9
138	2348.9
139	2366	51/13
140	2383
141	2400

Harmonics

Approximation of harmonics in 141ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.51	+4.43	+0.00	+5.18	-4.08	+1.39	+8.51	-8.17	-3.33	+1.87	+4.43
	Relative (%)	+50.0	+26.0	+0.0	+30.4	-24.0	+8.1	+50.0	-48.0	-19.6	+11.0	+26.0
Steps (reduced)		71 (71)	112 (112)	141 (0)	164 (23)	182 (41)	198 (57)	212 (71)	223 (82)	234 (93)	244 (103)	253 (112)

Approximation of harmonics in 141ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.03	-7.12	-7.42	+0.00	-2.83	+0.35	-8.15	+5.18	+5.81	-6.64	+1.51
	Relative (%)	+11.9	-41.9	-43.6	+0.0	-16.6	+2.0	-47.9	+30.4	+34.2	-39.0	+8.9
Steps (reduced)		261 (120)	268 (127)	275 (134)	282 (0)	288 (6)	294 (12)	299 (17)	305 (23)	310 (28)	314 (32)	319 (37)