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	Hekts	Approximate ratios
0	0	0	1/1
1	16	10.9
2	32	21.8
3	47.9	32.8	36/35, 37/36, 38/37
4	63.9	43.7	27/26, 28/27
5	79.9	54.6	22/21, 45/43
6	95.9	65.5	37/35
7	111.9	76.5	16/15
8	127.9	87.4	14/13
9	143.8	98.3	38/35
10	159.8	109.2	34/31, 45/41
11	175.8	120.2	31/28, 41/37
12	191.8	131.1	19/17, 48/43
13	207.8	142	44/39
14	223.8	152.9	33/29, 41/36
15	239.7	163.9	31/27
16	255.7	174.8	22/19
17	271.7	185.7	48/41
18	287.7	196.6	13/11, 46/39
19	303.7	207.6	31/26
20	319.7	218.5
21	335.6	229.4	17/14
22	351.6	240.3	38/31
23	367.6	251.3	21/17, 47/38
24	383.6	262.2
25	399.6	273.1	29/23, 34/27
26	415.6	284	14/11, 47/37
27	431.5	295
28	447.5	305.9	22/17, 35/27
29	463.5	316.8	17/13, 47/36
30	479.5	327.7	29/22
31	495.5	338.7
32	511.5	349.6	39/29, 43/32, 47/35
33	527.4	360.5	19/14, 42/31
34	543.4	371.4	26/19
35	559.4	382.4	29/21, 47/34
36	575.4	393.3	39/28, 46/33
37	591.4	404.2	38/27, 45/32
38	607.3	415.1	27/19, 44/31
39	623.3	426.1	33/23, 43/30
40	639.3	437	42/29
41	655.3	447.9	19/13
42	671.3	458.8	28/19
43	687.3	469.7
44	703.2	480.7	3/2
45	719.2	491.6	47/31
46	735.2	502.5	26/17
47	751.2	513.4	37/24
48	767.2	524.4
49	783.2	535.3	11/7
50	799.1	546.2	27/17, 46/29
51	815.1	557.1	8/5
52	831.1	568.1	21/13
53	847.1	579	31/19, 44/27
54	863.1	589.9	28/17
55	879.1	600.8
56	895	611.8	47/28
57	911	622.7	22/13
58	927	633.6	41/24
59	943	644.5	31/18
60	959	655.5	47/27
61	975	666.4
62	990.9	677.3	39/22
63	1006.9	688.2	34/19
64	1022.9	699.2
65	1038.9	710.1	31/17
66	1054.9	721
67	1070.8	731.9	13/7
68	1086.8	742.9	15/8
69	1102.8	753.8	17/9
70	1118.8	764.7	21/11
71	1134.8	775.6
72	1150.8	786.6	35/18
73	1166.7	797.5
74	1182.7	808.4
75	1198.7	819.3	2/1
76	1214.7	830.3
77	1230.7	841.2
78	1246.7	852.1	37/18, 39/19
79	1262.6	863	29/14
80	1278.6	873.9	23/11, 44/21
81	1294.6	884.9	19/9
82	1310.6	895.8	32/15, 49/23
83	1326.6	906.7	28/13, 43/20
84	1342.6	917.6
85	1358.5	928.6	46/21
86	1374.5	939.5	31/14, 42/19
87	1390.5	950.4	29/13
88	1406.5	961.3
89	1422.5	972.3
90	1438.5	983.2	39/17
91	1454.4	994.1	44/19
92	1470.4	1005
93	1486.4	1016	33/14
94	1502.4	1026.9
95	1518.4	1037.8
96	1534.4	1048.7	17/7
97	1550.3	1059.7
98	1566.3	1070.6	42/17, 47/19
99	1582.3	1081.5
100	1598.3	1092.4
101	1614.3	1103.4	33/13
102	1630.2	1114.3	41/16
103	1646.2	1125.2	44/17
104	1662.2	1136.1	47/18
105	1678.2	1147.1	29/11
106	1694.2	1158
107	1710.2	1168.9	43/16
108	1726.1	1179.8
109	1742.1	1190.8	41/15
110	1758.1	1201.7
111	1774.1	1212.6	39/14
112	1790.1	1223.5	45/16
113	1806.1	1234.5
114	1822	1245.4	43/15
115	1838	1256.3	26/9
116	1854	1267.2	35/12
117	1870	1278.2
118	1886	1289.1
119	1902	1300	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)