119edt

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119edt

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Prime factorization	7 × 17
Step size	15.9828¢
Octave	75\119edt (1198.71¢)
Consistency limit	5
Distinct consistency limit	5

119 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 119edt or 119ed3), is a nonoctave tuning system that divides the interval of 3/1 into 119 equal parts of about 16⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/119, or the 119th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	16
2	32
3	47.9	36/35, 37/36, 38/37
4	63.9	27/26, 28/27
5	79.9	22/21, 45/43
6	95.9	37/35
7	111.9	16/15
8	127.9	14/13
9	143.8	38/35
10	159.8	34/31, 45/41
11	175.8	31/28, 41/37
12	191.8	19/17, 48/43
13	207.8	44/39
14	223.8	33/29, 41/36
15	239.7	31/27
16	255.7	22/19
17	271.7	48/41
18	287.7	13/11, 46/39
19	303.7	31/26
20	319.7
21	335.6	17/14
22	351.6	38/31
23	367.6	21/17, 47/38
24	383.6
25	399.6	29/23, 34/27
26	415.6	14/11, 47/37
27	431.5
28	447.5	22/17, 35/27
29	463.5	17/13, 47/36
30	479.5	29/22
31	495.5
32	511.5	39/29, 43/32, 47/35
33	527.4	19/14, 42/31
34	543.4	26/19
35	559.4	29/21, 47/34
36	575.4	39/28, 46/33
37	591.4	38/27, 45/32
38	607.3	27/19, 44/31
39	623.3	33/23, 43/30
40	639.3	42/29
41	655.3	19/13
42	671.3	28/19
43	687.3
44	703.2	3/2
45	719.2	47/31
46	735.2	26/17
47	751.2	37/24
48	767.2
49	783.2	11/7
50	799.1	27/17, 46/29
51	815.1	8/5
52	831.1	21/13
53	847.1	31/19, 44/27
54	863.1	28/17
55	879.1
56	895	47/28
57	911	22/13
58	927	41/24
59	943	31/18
60	959	47/27
61	975
62	990.9	39/22
63	1006.9	34/19
64	1022.9
65	1038.9	31/17
66	1054.9
67	1070.8	13/7
68	1086.8	15/8
69	1102.8	17/9
70	1118.8	21/11
71	1134.8
72	1150.8	35/18
73	1166.7
74	1182.7
75	1198.7	2/1
76	1214.7
77	1230.7
78	1246.7	37/18, 39/19
79	1262.6	29/14
80	1278.6	23/11, 44/21
81	1294.6	19/9
82	1310.6	32/15, 49/23
83	1326.6	28/13, 43/20
84	1342.6
85	1358.5	46/21
86	1374.5	31/14, 42/19
87	1390.5	29/13
88	1406.5
89	1422.5
90	1438.5	39/17
91	1454.4	44/19
92	1470.4
93	1486.4	33/14
94	1502.4
95	1518.4
96	1534.4	17/7
97	1550.3
98	1566.3	42/17, 47/19
99	1582.3
100	1598.3
101	1614.3	33/13
102	1630.2	41/16
103	1646.2	44/17
104	1662.2	47/18
105	1678.2	29/11
106	1694.2
107	1710.2	43/16
108	1726.1
109	1742.1	41/15
110	1758.1
111	1774.1	39/14
112	1790.1	45/16
113	1806.1
114	1822	43/15
115	1838	26/9
116	1854	35/12
117	1870
118	1886
119	1902	3/1

Harmonics

Approximation of harmonics in 119edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.29	+0.00	-2.58	-5.30	-1.29	+3.55	-3.87	+0.00	-6.59	+4.21	-2.58
	Relative (%)	-8.1	+0.0	-16.1	-33.2	-8.1	+22.2	-24.2	+0.0	-41.2	+26.4	-16.1
Steps (reduced)		75 (75)	119 (0)	150 (31)	174 (55)	194 (75)	211 (92)	225 (106)	238 (0)	249 (11)	260 (22)	269 (31)

Approximation of harmonics in 119edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.69	+2.26	-5.30	-5.16	+1.77	-1.29	+1.01	-7.88	+3.55	+2.93	+5.88
	Relative (%)	+16.9	+14.1	-33.2	-32.3	+11.1	-8.1	+6.3	-49.3	+22.2	+18.3	+36.8
Steps (reduced)		278 (40)	286 (48)	293 (55)	300 (62)	307 (69)	313 (75)	319 (81)	324 (86)	330 (92)	335 (97)	340 (102)