68edt

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← 67edt 68edt 69edt →
Prime factorization 22 × 17
Step size 27.9699¢ 
Octave 43\68edt (1202.71¢)
Consistency limit 5
Distinct consistency limit 5

68 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 68edt or 68ed3), is a nonoctave tuning system that divides the interval of 3/1 into 68 equal parts of about 28⁠ ⁠¢ each. Each step represents a frequency ratio of 31/68, or the 68th root of 3.

68EDT is related to 43edo (meride tuning), but with the 3/1 rather than the 2/1 being just. This results in octaves being stretched by about 2.707 cents. Unlike 43edo, it is only consistent up to the 6-integer-limit, with discrepancy for the 7th harmonic.

Lookalikes: 25edf, 28cET, 43edo, 100ed5, 111ed6

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 28 19.1
2 55.9 38.2 31/30, 32/31
3 83.9 57.4 22/21
4 111.9 76.5 16/15
5 139.8 95.6 13/12
6 167.8 114.7
7 195.8 133.8 19/17
8 223.8 152.9 33/29
9 251.7 172.1 22/19, 37/32
10 279.7 191.2 27/23
11 307.7 210.3 31/26, 37/31
12 335.6 229.4 17/14
13 363.6 248.5 21/17, 37/30
14 391.6 267.6
15 419.5 286.8 14/11
16 447.5 305.9 22/17, 35/27
17 475.5 325 29/22
18 503.5 344.1
19 531.4 363.2 19/14
20 559.4 382.4 29/21
21 587.4 401.5
22 615.3 420.6
23 643.3 439.7
24 671.3 458.8 28/19
25 699.2 477.9 3/2
26 727.2 497.1 35/23
27 755.2 516.2 17/11, 31/20
28 783.2 535.3 11/7
29 811.1 554.4 8/5
30 839.1 573.5 13/8
31 867.1 592.6 28/17
32 895 611.8
33 923 630.9 29/17
34 951 650 26/15
35 978.9 669.1
36 1006.9 688.2 34/19
37 1034.9 707.4
38 1062.9 726.5 24/13, 37/20
39 1090.8 745.6 15/8
40 1118.8 764.7 21/11
41 1146.8 783.8 31/16, 33/17
42 1174.7 802.9
43 1202.7 822.1 2/1
44 1230.7 841.2
45 1258.6 860.3 29/14, 31/15
46 1286.6 879.4
47 1314.6 898.5 32/15
48 1342.6 917.6
49 1370.5 936.8
50 1398.5 955.9
51 1426.5 975
52 1454.4 994.1 37/16
53 1482.4 1013.2 33/14
54 1510.4 1032.4
55 1538.3 1051.5 17/7
56 1566.3 1070.6 37/15
57 1594.3 1089.7
58 1622.3 1108.8 23/9
59 1650.2 1127.9
60 1678.2 1147.1 29/11
61 1706.2 1166.2
62 1734.1 1185.3
63 1762.1 1204.4 36/13
64 1790.1 1223.5
65 1818 1242.6
66 1846 1261.8
67 1874 1280.9
68 1902 1300 3/1

Harmonics

Approximation of harmonics in 68edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +2.7 +0.0 +5.4 +10.7 +2.7 -12.4 +8.1 +0.0 +13.4 -11.8 +5.4
Relative (%) +9.7 +0.0 +19.4 +38.2 +9.7 -44.5 +29.0 +0.0 +47.9 -42.1 +19.4
Steps
(reduced)
43
(43)
68
(0)
86
(18)
100
(32)
111
(43)
120
(52)
129
(61)
136
(0)
143
(7)
148
(12)
154
(18)
Approximation of harmonics in 68edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +6.7 -9.7 +10.7 +10.8 -10.2 +2.7 -7.0 -11.9 -12.4 -9.1 -2.1
Relative (%) +23.9 -34.8 +38.2 +38.7 -36.5 +9.7 -25.0 -42.5 -44.5 -32.4 -7.5
Steps
(reduced)
159
(23)
163
(27)
168
(32)
172
(36)
175
(39)
179
(43)
182
(46)
185
(49)
188
(52)
191
(55)
194
(58)