119edt

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119edt

120edt →

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	15.983
2	31.966
3	47.948	36/35, 37/36, 38/37
4	63.931	27/26, 28/27
5	79.914	22/21, 45/43
6	95.897	37/35
7	111.88	16/15
8	127.863	14/13
9	143.845	38/35
10	159.828	34/31, 45/41
11	175.811	31/28, 41/37
12	191.794	19/17, 48/43
13	207.777	44/39
14	223.759	33/29, 41/36
15	239.742	31/27
16	255.725	22/19
17	271.708	48/41
18	287.691	13/11, 46/39
19	303.673	31/26
20	319.656
21	335.639	17/14
22	351.622	38/31
23	367.605	21/17, 47/38
24	383.588
25	399.57	29/23, 34/27
26	415.553	14/11, 47/37
27	431.536
28	447.519	22/17, 35/27
29	463.502	17/13, 47/36
30	479.484	29/22
31	495.467
32	511.45	39/29, 43/32, 47/35
33	527.433	19/14, 42/31
34	543.416	26/19
35	559.399	29/21, 47/34
36	575.381	39/28, 46/33
37	591.364	38/27, 45/32
38	607.347	27/19, 44/31
39	623.33	33/23, 43/30
40	639.313	42/29
41	655.295	19/13
42	671.278	28/19
43	687.261
44	703.244	3/2
45	719.227	47/31
46	735.209	26/17
47	751.192	37/24
48	767.175
49	783.158	11/7
50	799.141	27/17, 46/29
51	815.124	8/5
52	831.106	21/13
53	847.089	31/19, 44/27
54	863.072	28/17
55	879.055
56	895.038	47/28
57	911.02	22/13
58	927.003	41/24
59	942.986	31/18
60	958.969	47/27
61	974.952
62	990.935	39/22
63	1006.917	34/19
64	1022.9
65	1038.883	31/17
66	1054.866
67	1070.849	13/7
68	1086.831	15/8
69	1102.814	17/9
70	1118.797	21/11
71	1134.78
72	1150.763	35/18
73	1166.746
74	1182.728
75	1198.711	2/1
76	1214.694
77	1230.677
78	1246.66	37/18, 39/19
79	1262.642	29/14
80	1278.625	23/11, 44/21
81	1294.608	19/9
82	1310.591	32/15, 49/23
83	1326.574	28/13, 43/20
84	1342.556
85	1358.539	46/21
86	1374.522	31/14, 42/19
87	1390.505	29/13
88	1406.488
89	1422.471
90	1438.453	39/17
91	1454.436	44/19
92	1470.419
93	1486.402	33/14
94	1502.385
95	1518.367
96	1534.35	17/7
97	1550.333
98	1566.316	42/17, 47/19
99	1582.299
100	1598.282
101	1614.264	33/13
102	1630.247	41/16
103	1646.23	44/17
104	1662.213	47/18
105	1678.196	29/11
106	1694.178
107	1710.161	43/16
108	1726.144
109	1742.127	41/15
110	1758.11
111	1774.092	39/14
112	1790.075	45/16
113	1806.058
114	1822.041	43/15
115	1838.024	26/9
116	1854.007	35/12
117	1869.989
118	1885.972
119	1901.955	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)