117edt

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← 116edt 117edt 118edt →
Prime factorization 32 × 13
Step size 16.256¢ 
Octave 74\117edt (1202.95¢)
Consistency limit 4
Distinct consistency limit 4

117 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 117edt or 117ed3), is a nonoctave tuning system that divides the interval of 3/1 into 117 equal parts of about 16.3⁠ ⁠¢ each. Each step represents a frequency ratio of 31/117, or the 117th root of 3.

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 16.3 11.1
2 32.5 22.2
3 48.8 33.3 37/36
4 65 44.4 27/26, 28/27
5 81.3 55.6 22/21
6 97.5 66.7 18/17
7 113.8 77.8 31/29, 47/44
8 130 88.9 14/13
9 146.3 100 37/34, 49/45
10 162.6 111.1 45/41
11 178.8 122.2
12 195.1 133.3 47/42
13 211.3 144.4 26/23
14 227.6 155.6
15 243.8 166.7 23/20
16 260.1 177.8 36/31, 43/37
17 276.4 188.9 27/23, 34/29
18 292.6 200
19 308.9 211.1 43/36, 49/41
20 325.1 222.2
21 341.4 233.3 28/23
22 357.6 244.4
23 373.9 255.6 36/29, 41/33
24 390.1 266.7
25 406.4 277.8 24/19, 43/34
26 422.7 288.9 23/18, 37/29
27 438.9 300
28 455.2 311.1 13/10
29 471.4 322.2
30 487.7 333.3
31 503.9 344.4
32 520.2 355.6 27/20
33 536.4 366.7 15/11
34 552.7 377.8
35 569 388.9
36 585.2 400
37 601.5 411.1 17/12
38 617.7 422.2 10/7
39 634 433.3
40 650.2 444.4
41 666.5 455.6
42 682.8 466.7 43/29, 46/31, 49/33
43 699 477.8
44 715.3 488.9
45 731.5 500 29/19
46 747.8 511.1 20/13, 37/24
47 764 522.2 14/9
48 780.3 533.3
49 796.5 544.4 19/12
50 812.8 555.6
51 829.1 566.7 21/13
52 845.3 577.8 44/27
53 861.6 588.9
54 877.8 600
55 894.1 611.1
56 910.3 622.2 22/13
57 926.6 633.3 29/17
58 942.8 644.4 31/18
59 959.1 655.6 40/23, 47/27
60 975.4 666.7
61 991.6 677.8 39/22
62 1007.9 688.9 34/19, 43/24
63 1024.1 700 47/26
64 1040.4 711.1 31/17
65 1056.6 722.2
66 1072.9 733.3 13/7
67 1089.2 744.4
68 1105.4 755.6 36/19
69 1121.7 766.7 44/23
70 1137.9 777.8 27/14
71 1154.2 788.9 37/19, 39/20
72 1170.4 800
73 1186.7 811.1
74 1202.9 822.2
75 1219.2 833.3
76 1235.5 844.4 47/23
77 1251.7 855.6
78 1268 866.7
79 1284.2 877.8 21/10
80 1300.5 888.9 36/17
81 1316.7 900
82 1333 911.1
83 1349.3 922.2
84 1365.5 933.3 11/5
85 1381.8 944.4 20/9
86 1398 955.6
87 1414.3 966.7 43/19
88 1430.5 977.8
89 1446.8 988.9 30/13
90 1463 1000
91 1479.3 1011.1 40/17, 47/20
92 1495.6 1022.2 19/8
93 1511.8 1033.3
94 1528.1 1044.4 29/12
95 1544.3 1055.6
96 1560.6 1066.7
97 1576.8 1077.8
98 1593.1 1088.9
99 1609.3 1100
100 1625.6 1111.1 23/9
101 1641.9 1122.2 31/12
102 1658.1 1133.3
103 1674.4 1144.4
104 1690.6 1155.6
105 1706.9 1166.7
106 1723.1 1177.8 46/17
107 1739.4 1188.9 41/15
108 1755.7 1200
109 1771.9 1211.1 39/14
110 1788.2 1222.2
111 1804.4 1233.3 17/6
112 1820.7 1244.4
113 1836.9 1255.6 26/9
114 1853.2 1266.7
115 1869.4 1277.8
116 1885.7 1288.9
117 1902 1300 3/1

Harmonics

Approximation of harmonics in 117edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +2.95 +0.00 +5.89 -6.53 +2.95 -3.83 -7.42 +0.00 -3.59 -6.03 +5.89
Relative (%) +18.1 +0.0 +36.2 -40.2 +18.1 -23.6 -45.6 +0.0 -22.1 -37.1 +36.2
Steps
(reduced)
74
(74)
117
(0)
148
(31)
171
(54)
191
(74)
207
(90)
221
(104)
234
(0)
245
(11)
255
(21)
265
(31)
Approximation of harmonics in 117edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -2.63 -0.88 -6.53 -4.47 +4.36 +2.95 +6.88 -0.64 -3.83 -3.09 +1.24
Relative (%) -16.2 -5.4 -40.2 -27.5 +26.8 +18.1 +42.3 -3.9 -23.6 -19.0 +7.6
Steps
(reduced)
273
(39)
281
(47)
288
(54)
295
(61)
302
(68)
308
(74)
314
(80)
319
(85)
324
(90)
329
(95)
334
(100)