132edt

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← 131edt 132edt 133edt →
Prime factorization 22 × 3 × 11
Step size 14.4088¢ 
Octave 83\132edt (1195.93¢)
Consistency limit 2
Distinct consistency limit 2

132 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 132edt or 132ed3), is a nonoctave tuning system that divides the interval of 3/1 into 132 equal parts of about 14.4⁠ ⁠¢ each. Each step represents a frequency ratio of 31/132, or the 132nd root of 3.

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 14.4 9.8
2 28.8 19.7
3 43.2 29.5 39/38, 42/41
4 57.6 39.4
5 72 49.2 25/24, 49/47
6 86.5 59.1 41/39
7 100.9 68.9 35/33
8 115.3 78.8 31/29, 46/43
9 129.7 88.6 14/13
10 144.1 98.5 38/35
11 158.5 108.3 23/21
12 172.9 118.2 21/19
13 187.3 128 39/35
14 201.7 137.9
15 216.1 147.7 17/15
16 230.5 157.6
17 244.9 167.4 38/33
18 259.4 177.3 43/37
19 273.8 187.1 41/35
20 288.2 197 13/11
21 302.6 206.8
22 317 216.7 6/5
23 331.4 226.5 23/19
24 345.8 236.4 11/9
25 360.2 246.2
26 374.6 256.1 41/33
27 389 265.9
28 403.4 275.8
29 417.9 285.6 14/11
30 432.3 295.5
31 446.7 305.3 22/17
32 461.1 315.2
33 475.5 325
34 489.9 334.8
35 504.3 344.7
36 518.7 354.5
37 533.1 364.4 34/25
38 547.5 374.2
39 561.9 384.1 18/13
40 576.4 393.9 46/33
41 590.8 403.8 38/27
42 605.2 413.6
43 619.6 423.5
44 634 433.3
45 648.4 443.2
46 662.8 453 22/15
47 677.2 462.9
48 691.6 472.7
49 706 482.6
50 720.4 492.4 47/31
51 734.8 502.3 26/17
52 749.3 512.1
53 763.7 522 14/9
54 778.1 531.8
55 792.5 541.7 49/31
56 806.9 551.5 43/27
57 821.3 561.4 37/23, 45/28
58 835.7 571.2 47/29
59 850.1 581.1
60 864.5 590.9 28/17
61 878.9 600.8
62 893.3 610.6
63 907.8 620.5 49/29
64 922.2 630.3 46/27
65 936.6 640.2
66 951 650 26/15, 45/26
67 965.4 659.8
68 979.8 669.7 37/21, 44/25
69 994.2 679.5
70 1008.6 689.4
71 1023 699.2
72 1037.4 709.1 51/28
73 1051.8 718.9
74 1066.2 728.8
75 1080.7 738.6 28/15
76 1095.1 748.5
77 1109.5 758.3
78 1123.9 768.2
79 1138.3 778 27/14
80 1152.7 787.9 35/18, 37/19
81 1167.1 797.7 51/26
82 1181.5 807.6
83 1195.9 817.4
84 1210.3 827.3
85 1224.7 837.1
86 1239.2 847 43/21, 45/22
87 1253.6 856.8
88 1268 866.7 52/25
89 1282.4 876.5
90 1296.8 886.4
91 1311.2 896.2
92 1325.6 906.1
93 1340 915.9 13/6
94 1354.4 925.8
95 1368.8 935.6
96 1383.2 945.5
97 1397.6 955.3
98 1412.1 965.2
99 1426.5 975 41/18
100 1440.9 984.8
101 1455.3 994.7 51/22
102 1469.7 1004.5
103 1484.1 1014.4 33/14
104 1498.5 1024.2
105 1512.9 1034.1
106 1527.3 1043.9
107 1541.7 1053.8
108 1556.1 1063.6 27/11
109 1570.6 1073.5
110 1585 1083.3 5/2
111 1599.4 1093.2
112 1613.8 1103 33/13
113 1628.2 1112.9
114 1642.6 1122.7
115 1657 1132.6
116 1671.4 1142.4
117 1685.8 1152.3 45/17
118 1700.2 1162.1
119 1714.6 1172 35/13
120 1729.1 1181.8 19/7
121 1743.5 1191.7
122 1757.9 1201.5
123 1772.3 1211.4 39/14
124 1786.7 1221.2
125 1801.1 1231.1
126 1815.5 1240.9
127 1829.9 1250.8
128 1844.3 1260.6
129 1858.7 1270.5 38/13, 41/14
130 1873.1 1280.3
131 1887.5 1290.2
132 1902 1300 3/1

Harmonics

Approximation of harmonics in 132edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -4.07 +0.00 +6.26 -5.42 -4.07 +2.82 +2.19 +0.00 +4.91 -1.60 +6.26
Relative (%) -28.3 +0.0 +43.5 -37.7 -28.3 +19.6 +15.2 +0.0 +34.1 -11.1 +43.5
Steps
(reduced)
83
(83)
132
(0)
167
(35)
193
(61)
215
(83)
234
(102)
250
(118)
264
(0)
277
(13)
288
(24)
299
(35)
Approximation of harmonics in 132edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -2.63 -1.25 -5.42 -1.89 -5.98 -4.07 +3.18 +0.84 +2.82 -5.67 +3.82
Relative (%) -18.3 -8.7 -37.7 -13.1 -41.5 -28.3 +22.1 +5.8 +19.6 -39.4 +26.5
Steps
(reduced)
308
(44)
317
(53)
325
(61)
333
(69)
340
(76)
347
(83)
354
(90)
360
(96)
366
(102)
371
(107)
377
(113)