119ed4

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119ed4

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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	20.2
2	40.3	42/41, 43/42
3	60.5	30/29
4	80.7	43/41
5	100.8	18/17, 35/33
6	121
7	141.2
8	161.3	34/31
9	181.5
10	201.7
11	221.8	33/29
12	242
13	262.2	43/37
14	282.4
15	302.5	25/21, 31/26
16	322.7	41/34, 47/39
17	342.9
18	363	37/30
19	383.2
20	403.4
21	423.5	23/18, 37/29
22	443.7
23	463.9	17/13
24	484	41/31
25	504.2
26	524.4	23/17, 42/31
27	544.5	26/19
28	564.7	18/13, 43/31
29	584.9
30	605
31	625.2	33/23, 43/30
32	645.4
33	665.5
34	685.7	49/33
35	705.9
36	726.1	35/23
37	746.2
38	766.4
39	786.6	41/26
40	806.7
41	826.9	29/18
42	847.1	31/19
43	867.2
44	887.4
45	907.6	49/29
46	927.7
47	947.9	19/11
48	968.1
49	988.2	23/13
50	1008.4	34/19
51	1028.6
52	1048.7	11/6
53	1068.9
54	1089.1
55	1109.2	19/10
56	1129.4
57	1149.6	33/17, 35/18
58	1169.7
59	1189.9
60	1210.1
61	1230.3
62	1250.4	35/17
63	1270.6
64	1290.8
65	1310.9	49/23
66	1331.1	41/19
67	1351.3
68	1371.4	42/19
69	1391.6
70	1411.8
71	1431.9
72	1452.1
73	1472.3
74	1492.4
75	1512.6
76	1532.8	46/19
77	1552.9
78	1573.1
79	1593.3
80	1613.4	33/13
81	1633.6	18/7
82	1653.8	13/5
83	1673.9
84	1694.1
85	1714.3	35/13
86	1734.5	49/18
87	1754.6
88	1774.8
89	1795	31/11
90	1815.1
91	1835.3
92	1855.5
93	1875.6
94	1895.8
95	1916
96	1936.1
97	1956.3
98	1976.5	47/15
99	1996.6	19/6
100	2016.8
101	2037
102	2057.1
103	2077.3
104	2097.5
105	2117.6	17/5
106	2137.8
107	2158
108	2178.2
109	2198.3
110	2218.5	18/5
111	2238.7
112	2258.8
113	2279	41/11
114	2299.2
115	2319.3	42/11
116	2339.5
117	2359.7	43/11
118	2379.8
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)