141ed4

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

← 139ed4

141ed4

143ed4 →

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	17.021
2	34.043
3	51.064	34/33, 35/34
4	68.085	26/25, 51/49
5	85.106	41/39
6	102.128	35/33
7	119.149	15/14
8	136.17
9	153.191	47/43
10	170.213	43/39
11	187.234	39/35
12	204.255
13	221.277	25/22
14	238.298	39/34
15	255.319
16	272.34	41/35, 55/47
17	289.362	13/11
18	306.383	37/31
19	323.404	41/34, 47/39
20	340.426
21	357.447	43/35
22	374.468	41/33
23	391.489
24	408.511
25	425.532	55/43
26	442.553
27	459.574	43/33
28	476.596
29	493.617
30	510.638	47/35, 51/38
31	527.66
32	544.681
33	561.702	47/34
34	578.723
35	595.745	55/39
36	612.766	47/33
37	629.787
38	646.809
39	663.83	22/15
40	680.851
41	697.872
42	714.894
43	731.915	29/19
44	748.936
45	765.957	14/9
46	782.979	11/7
47	800
48	817.021
49	834.043	34/21, 55/34
50	851.064
51	868.085	38/23
52	885.106	5/3
53	902.128
54	919.149
55	936.17
56	953.191	26/15
57	970.213
58	987.234	23/13
59	1004.255	25/14
60	1021.277
61	1038.298
62	1055.319	46/25
63	1072.34	13/7
64	1089.362
65	1106.383
66	1123.404
67	1140.426
68	1157.447	41/21
69	1174.468
70	1191.489
71	1208.511
72	1225.532
73	1242.553
74	1259.574
75	1276.596	23/11
76	1293.617
77	1310.638	49/23
78	1327.66
79	1344.681
80	1361.702
81	1378.723	51/23
82	1395.745	47/21
83	1412.766
84	1429.787
85	1446.809
86	1463.83
87	1480.851
88	1497.872
89	1514.894
90	1531.915
91	1548.936	22/9
92	1565.957
93	1582.979
94	1600
95	1617.021
96	1634.043
97	1651.064
98	1668.085	55/21
99	1685.106
100	1702.128
101	1719.149	27/10
102	1736.17
103	1753.191
104	1770.213	25/9
105	1787.234
106	1804.255
107	1821.277
108	1838.298
109	1855.319
110	1872.34
111	1889.362
112	1906.383
113	1923.404
114	1940.426	46/15
115	1957.447
116	1974.468
117	1991.489
118	2008.511
119	2025.532
120	2042.553
121	2059.574	23/7
122	2076.596
123	2093.617
124	2110.638
125	2127.66
126	2144.681	38/11
127	2161.702
128	2178.723
129	2195.745
130	2212.766
131	2229.787
132	2246.809
133	2263.83
134	2280.851
135	2297.872	49/13
136	2314.894
137	2331.915
138	2348.936
139	2365.957	51/13
140	2382.979
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)