48edt

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← 47edt 48edt 49edt →
Prime factorization 24 × 3
Step size 39.6241 ¢ 
Octave 30\48edt (1188.72 ¢) (→ 5\8edt)
Consistency limit 3
Distinct consistency limit 3
Special properties

48 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 48edt or 48ed3), is a nonoctave tuning system that divides the interval of 3/1 into 48 equal parts of about 39.6 ¢ each. Each step represents a frequency ratio of 31/48, or the 48th root of 3.

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 39.6 27.1
2 79.2 54.2 22/21, 23/22
3 118.9 81.3 15/14, 29/27, 31/29
4 158.5 108.3 23/21
5 198.1 135.4 19/17, 28/25
6 237.7 162.5 31/27
7 277.4 189.6 27/23
8 317 216.7 6/5
9 356.6 243.8 27/22
10 396.2 270.8 29/23
11 435.9 297.9 9/7
12 475.5 325 29/22
13 515.1 352.1 31/23
14 554.7 379.2 29/21
15 594.4 406.3 31/22
16 634 433.3 13/9
17 673.6 460.4 31/21
18 713.2 487.5
19 752.9 514.6 17/11
20 792.5 541.7
21 832.1 568.8 21/13
22 871.7 595.8
23 911.4 622.9 22/13
24 951 650 19/11, 26/15
25 990.6 677.1 23/13
26 1030.2 704.2
27 1069.8 731.3 13/7
28 1109.5 758.3
29 1149.1 785.4
30 1188.7 812.5
31 1228.3 839.6
32 1268 866.7 25/12, 27/13
33 1307.6 893.8
34 1347.2 920.8
35 1386.8 947.9 29/13
36 1426.5 975
37 1466.1 1002.1 7/3
38 1505.7 1029.2 31/13
39 1545.3 1056.3 22/9
40 1585 1083.3 5/2
41 1624.6 1110.4 23/9
42 1664.2 1137.5
43 1703.8 1164.6
44 1743.5 1191.7
45 1783.1 1218.8 14/5
46 1822.7 1245.8
47 1862.3 1272.9
48 1902 1300 3/1

Harmonics

Approximation of harmonics in 48edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Error Absolute (¢) -11.3 +0.0 +17.1 -12.6 -11.3 -0.8 +5.8 +0.0 +15.7 +9.2 +17.1 -2.6 -12.1 -12.6 -5.5
Relative (%) -28.5 +0.0 +43.1 -31.9 -28.5 -2.0 +14.6 +0.0 +39.7 +23.2 +43.1 -6.6 -30.4 -31.9 -13.9
Steps
(reduced) 		30
(30) 		48
(0) 		61
(13) 		70
(22) 		78
(30) 		85
(37) 		91
(43) 		96
(0) 		101
(5) 		105
(9) 		109
(13) 		112
(16) 		115
(19) 		118
(22) 		121
(25)
Approximation of harmonics in 48edt
Harmonic 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Error Absolute (¢) +8.4 -11.3 +14.0 +4.4 -0.8 -2.1 +0.2 +5.8 +14.4 -13.9 +0.0 +16.3 -4.8 +15.7 -1.4 -16.8
Relative (%) +21.3 -28.5 +35.3 +11.2 -2.0 -5.2 +0.6 +14.6 +36.3 -35.1 +0.0 +41.1 -12.2 +39.7 -3.6 -42.3
Steps
(reduced) 		124
(28) 		126
(30) 		129
(33) 		131
(35) 		133
(37) 		135
(39) 		137
(41) 		139
(43) 		141
(45) 		142
(46) 		144
(0) 		146
(2) 		147
(3) 		149
(5) 		150
(6) 		151
(7)
Approximation of harmonics in 48edt
Harmonic 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
Error Absolute (¢) +9.2 -2.8 -13.4 +17.1 +9.3 +2.7 -2.6 -6.8 -10.0 -12.1 -13.2 -13.3 -12.6 -11.1 -8.7 -5.5
Relative (%) +23.2 -7.2 -33.8 +43.1 +23.4 +6.8 -6.6 -17.3 -25.1 -30.4 -33.2 -33.7 -31.9 -27.9 -21.9 -13.9
Steps
(reduced) 		153
(9) 		154
(10) 		155
(11) 		157
(13) 		158
(14) 		159
(15) 		160
(16) 		161
(17) 		162
(18) 		163
(19) 		164
(20) 		165
(21) 		166
(22) 		167
(23) 		168
(24) 		169
(25)
Approximation of harmonics in 48edt
Harmonic 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
Error Absolute (¢) -1.6 +3.1 +8.4 +14.4 -18.5 -11.3 -3.4 +5.0 +14.0 -16.1 -6.1 +4.4 +15.4 -12.7 -0.8 +11.6
Relative (%) -3.9 +7.8 +21.3 +36.4 -46.8 -28.5 -8.6 +12.6 +35.3 -40.7 -15.4 +11.2 +39.0 -32.1 -2.0 +29.2
Steps
(reduced) 		170
(26) 		171
(27) 		172
(28) 		173
(29) 		173
(29) 		174
(30) 		175
(31) 		176
(32) 		177
(33) 		177
(33) 		178
(34) 		179
(35) 		180
(36) 		180
(36) 		181
(37) 		182
(38)
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