25edt
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Prime factorization
52
Step size
76.0782 ¢
Octave
16\25edt (1217.25 ¢)
Consistency limit
6
Distinct consistency limit
6
| ← 24edt | 25edt | 26edt → |
25 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 25edt or 25ed3), is a nonoctave tuning system that divides the interval of 3/1 into 25 equal parts of about 76.1 ¢ each. Each step represents a frequency ratio of 31/25, or the 25th root of 3.
It corresponds to 15.7732 edo, or 16 equal divisions of a stretched octave (1217.25 ¢) and a tritave twin of the Armodue/Hornbostel flat third-tone system:
- 6th = 1065.095 ¢
- squared = 2130.19 cents = 228.235 ¢
- cubed = 1293.33 ¢
- fourth power = 2358.425 ¢ → 456.47 ¢
It can be used as a tuning for Mavila and has an "antidiatonic" (2L 5s) scale which approximates Pelog tunings in Indonesian gamelan music.
Intervals
| Degree | Cents | Hekts | Armodue name |
|---|---|---|---|
| 1 | 76.08 | 52 | 1#/2bb |
| 2 | 152.16 | 104 | 1x/2b |
| 3 | 228.235 | 156 | 2 |
| 4 | 304.31 | 208 | 2#/3bb |
| 5 | 380.39 | 260 | 2x/3b |
| 6 | 456.47 | 312 | 3 |
| 7 | 532.55 | 364 | 3#/4b |
| 8 | 608.625 | 416 | 4 |
| 9 | 684.70 | 468 | 4#/5bb |
| 10 | 760.78 | 520 | 4x/5b |
| 11 | 836.86 | 572 | 5 |
| 12 | 912.94 | 624 | 5#/6bb |
| 13 | 989.02 | 676 | 5x/6b |
| 14 | 1065.095 | 728 | 6 |
| 15 | 1141.17 | 780 | 6#/7bb |
| 16 | 1217.25 | 832 | 6x/7b |
| 17 | 1293.33 | 884 | 7 |
| 18 | 1369.41 | 936 | 7#/8b |
| 19 | 1445.485 | 988 | 8 |
| 20 | 1521.56 | 1040 | 8#/9bb |
| 21 | 1597.64 | 1092 | 8x/9b |
| 22 | 1673.72 | 1144 | 9 |
| 23 | 1749.80 | 1196 | 9#/1bb |
| 24 | 1825.88 | 1248 | 9x/1b |
| 25 | 1901.955 | 1300 | 1 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +17.3 | +0.0 | +28.6 | -21.4 | +33.0 | -28.0 | -36.0 | -0.3 | -26.7 | +28.4 | -10.9 |
| Relative (%) | +22.7 | +0.0 | +37.6 | -28.1 | +43.4 | -36.8 | -47.3 | -0.4 | -35.1 | +37.4 | -14.4 | |
| Steps (reduced) |
16 (16) |
25 (0) |
37 (12) |
44 (19) |
55 (5) |
58 (8) |
64 (14) |
67 (17) |
71 (21) |
77 (2) |
78 (3) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.9 | +37.6 | +31.2 | +29.4 | -26.5 | +16.1 | +34.5 | +24.2 | -0.1 | +27.9 | -32.8 |
| Relative (%) | -17.0 | +49.4 | +41.0 | +38.6 | -34.8 | +21.2 | +45.3 | +31.8 | -0.1 | +36.6 | -43.1 | |
| Steps (reduced) |
82 (7) |
85 (10) |
86 (11) |
88 (13) |
90 (15) |
93 (18) |
94 (19) |
96 (21) |
97 (22) |
98 (23) |
99 (24) | |