119ed4

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

← 117ed4

119ed4

121ed4 →

Prime factorization	7 × 17
Step size	20.1681¢
Octave	60\119ed4 (1210.08¢)
Twelfth	94\119ed4 (1895.8¢)
Consistency limit	1
Distinct consistency limit	1

119 equal divisions of the 4th harmonic (abbreviated 119ed4) is a nonoctave tuning system that divides the interval of 4/1 into 119 equal parts of about 20.2 ¢ each. Each step represents a frequency ratio of 4^1/119, or the 119th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	20.168
2	40.336	42/41, 43/42
3	60.504	30/29
4	80.672	43/41
5	100.84	18/17, 35/33
6	121.008
7	141.176
8	161.345	34/31
9	181.513
10	201.681
11	221.849	33/29
12	242.017
13	262.185	43/37
14	282.353
15	302.521	25/21, 31/26
16	322.689	41/34, 47/39
17	342.857
18	363.025	37/30
19	383.193
20	403.361
21	423.529	23/18, 37/29
22	443.697
23	463.866	17/13
24	484.034	41/31
25	504.202
26	524.37	23/17, 42/31
27	544.538	26/19
28	564.706	18/13, 43/31
29	584.874
30	605.042
31	625.21	33/23, 43/30
32	645.378
33	665.546
34	685.714	49/33
35	705.882
36	726.05	35/23
37	746.218
38	766.387
39	786.555	41/26
40	806.723
41	826.891	29/18
42	847.059	31/19
43	867.227
44	887.395
45	907.563	49/29
46	927.731
47	947.899	19/11
48	968.067
49	988.235	23/13
50	1008.403	34/19
51	1028.571
52	1048.739	11/6
53	1068.908
54	1089.076
55	1109.244	19/10
56	1129.412
57	1149.58	33/17, 35/18
58	1169.748
59	1189.916
60	1210.084
61	1230.252
62	1250.42	35/17
63	1270.588
64	1290.756
65	1310.924	49/23
66	1331.092	41/19
67	1351.261
68	1371.429	42/19
69	1391.597
70	1411.765
71	1431.933
72	1452.101
73	1472.269
74	1492.437
75	1512.605
76	1532.773	46/19
77	1552.941
78	1573.109
79	1593.277
80	1613.445	33/13
81	1633.613	18/7
82	1653.782	13/5
83	1673.95
84	1694.118
85	1714.286	35/13
86	1734.454	49/18
87	1754.622
88	1774.79
89	1794.958	31/11
90	1815.126
91	1835.294
92	1855.462
93	1875.63
94	1895.798
95	1915.966
96	1936.134
97	1956.303
98	1976.471	47/15
99	1996.639	19/6
100	2016.807
101	2036.975
102	2057.143
103	2077.311
104	2097.479
105	2117.647	17/5
106	2137.815
107	2157.983
108	2178.151
109	2198.319
110	2218.487	18/5
111	2238.655
112	2258.824
113	2278.992	41/11
114	2299.16
115	2319.328	42/11
116	2339.496
117	2359.664	43/11
118	2379.832
119	2400

Harmonics

Approximation of harmonics in 119ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+10.08	-6.16	+0.00	-3.12	+3.93	-0.76	+10.08	+7.85	+6.96	+3.30	-6.16
	Relative (%)	+50.0	-30.5	+0.0	-15.5	+19.5	-3.8	+50.0	+38.9	+34.5	+16.4	-30.5
Steps (reduced)		60 (60)	94 (94)	119 (0)	138 (19)	154 (35)	167 (48)	179 (60)	189 (70)	198 (79)	206 (87)	213 (94)

Approximation of harmonics in 119ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-3.55	+9.33	-9.28	+0.00	-4.12	-2.23	+5.01	-3.12	-6.92	-6.78	-3.06
	Relative (%)	-17.6	+46.2	-46.0	+0.0	-20.4	-11.1	+24.8	-15.5	-34.3	-33.6	-15.2
Steps (reduced)		220 (101)	227 (108)	232 (113)	238 (0)	243 (5)	248 (10)	253 (15)	257 (19)	261 (23)	265 (27)	269 (31)