119edt

From Xenharmonic Wiki
Jump to navigation Jump to search
Icon-Stub.png This page is a stub. You can help the Xenharmonic Wiki by expanding it.
← 118edt 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 31/119, 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)