101edt

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← 100edt 101edt 102edt →
Prime factorization 101 (prime)
Step size 18.8312¢ 
Octave 64\101edt (1205.2¢)
Consistency limit 2
Distinct consistency limit 2

101 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 101edt or 101ed3), is a nonoctave tuning system that divides the interval of 3/1 into 101 equal parts of about 18.8⁠ ⁠¢ each. Each step represents a frequency ratio of 31/101, or the 101st root of 3. It corresponds to 63.7240edo.

Theory

101edt is strong in the 3.5.7.13 subgroup, tempering out 16875/16807, 2205/2197 and 767637/765625. It supports canopus.

Harmonics

Approximation of harmonics in 101edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +5.20 +0.00 -8.43 +0.71 +5.20 +1.97 -3.23 +0.00 +5.91 -8.45 -8.43
Relative (%) +27.6 +0.0 -44.8 +3.8 +27.6 +10.4 -17.2 +0.0 +31.4 -44.8 -44.8
Steps
(reduced)
64
(64)
101
(0)
127
(26)
148
(47)
165
(64)
179
(78)
191
(90)
202
(0)
212
(10)
220
(18)
228
(26)
Approximation of harmonics in 101edt (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +3.64 +7.16 +0.71 +1.97 -8.83 +5.20 +5.75 -7.72 +1.97 -3.25 -4.88 -3.23
Relative (%) +19.4 +38.0 +3.8 +10.4 -46.9 +27.6 +30.5 -41.0 +10.4 -17.2 -25.9 -17.2
Steps
(reduced)
236
(34)
243
(41)
249
(47)
255
(53)
260
(58)
266
(64)
271
(69)
275
(73)
280
(78)
284
(82)
288
(86)
292
(90)

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 18.8 12.9
2 37.7 25.7 44/43, 45/44
3 56.5 38.6 30/29, 31/30
4 75.3 51.5 23/22
5 94.2 64.4 19/18, 37/35
6 113 77.2
7 131.8 90.1 27/25
8 150.6 103
9 169.5 115.8 43/39
10 188.3 128.7 29/26, 39/35
11 207.1 141.6 44/39
12 226 154.5
13 244.8 167.3
14 263.6 180.2
15 282.5 193.1
16 301.3 205.9 25/21, 44/37
17 320.1 218.8
18 339 231.7 45/37
19 357.8 244.6 43/35
20 376.6 257.4 36/29, 41/33
21 395.5 270.3 39/31, 44/35
22 414.3 283.2
23 433.1 296 9/7
24 451.9 308.9 13/10
25 470.8 321.8
26 489.6 334.7
27 508.4 347.5
28 527.3 360.4 19/14, 42/31
29 546.1 373.3 37/27
30 564.9 386.1 18/13, 43/31
31 583.8 399 7/5
32 602.6 411.9
33 621.4 424.8 43/30
34 640.3 437.6 42/29
35 659.1 450.5 19/13
36 677.9 463.4 34/23, 37/25
37 696.8 476.2
38 715.6 489.1
39 734.4 502 29/19
40 753.2 514.9 17/11
41 772.1 527.7 39/25
42 790.9 540.6 30/19
43 809.7 553.5
44 828.6 566.3 21/13
45 847.4 579.2 31/19, 44/27
46 866.2 592.1
47 885.1 605 5/3
48 903.9 617.8
49 922.7 630.7
50 941.6 643.6 31/18
51 960.4 656.4
52 979.2 669.3 37/21, 44/25
53 998.1 682.2
54 1016.9 695 9/5
55 1035.7 707.9
56 1054.5 720.8
57 1073.4 733.7 13/7
58 1092.2 746.5
59 1111 759.4 19/10
60 1129.9 772.3 25/13
61 1148.7 785.1 33/17
62 1167.5 798
63 1186.4 810.9
64 1205.2 823.8
65 1224 836.6
66 1242.9 849.5 39/19, 43/21
67 1261.7 862.4 29/14
68 1280.5 875.2 44/21
69 1299.4 888.1
70 1318.2 901 15/7
71 1337 913.9 13/6
72 1355.8 926.7
73 1374.7 939.6 31/14, 42/19
74 1393.5 952.5
75 1412.3 965.3 43/19
76 1431.2 978.2
77 1450 991.1 30/13
78 1468.8 1004 7/3
79 1487.7 1016.8
80 1506.5 1029.7 31/13, 43/18
81 1525.3 1042.6 29/12, 41/17
82 1544.2 1055.4
83 1563 1068.3 37/15
84 1581.8 1081.2
85 1600.7 1094.1
86 1619.5 1106.9
87 1638.3 1119.8
88 1657.1 1132.7
89 1676 1145.5
90 1694.8 1158.4
91 1713.6 1171.3 35/13
92 1732.5 1184.2
93 1751.3 1197
94 1770.1 1209.9 25/9
95 1789 1222.8
96 1807.8 1235.6
97 1826.6 1248.5
98 1845.5 1261.4 29/10
99 1864.3 1274.3 44/15
100 1883.1 1287.1
101 1902 1300 3/1