User:BudjarnLambeth/Ed255/128
An equal division of reduced harmonic 255 (ed255/128) is an equal-step tuning in which the octave-reduced 255th harmonic (255/128) is justly tuned and is divided in a given number of equal steps. 255/128 is very close to the octave, 2/1, but it is slightly flatter. This makes it suitable as an alternative to edos whose consonances are too sharp, such as 5edo.
5ed255/128
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -7 | +7 | -14 | +77 | +0 | -28 | -20 | +14 | +71 | -94 | -6 |
| Relative (%) | -2.8 | +3.0 | -5.7 | +32.4 | +0.2 | -11.6 | -8.5 | +6.0 | +29.6 | -39.5 | -2.7 | |
| Steps (reduced) |
5 (0) |
8 (3) |
10 (0) |
12 (2) |
13 (3) |
14 (4) |
15 (0) |
16 (1) |
17 (2) |
17 (2) |
18 (3) | |
5edo, 8edt, 14ed7 for comparison:
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0 | +18 | +0 | +94 | +18 | -9 | +0 | +36 | +94 | -71 | +18 |
| Relative (%) | +0.0 | +7.5 | +0.0 | +39.0 | +7.5 | -3.7 | +0.0 | +15.0 | +39.0 | -29.7 | +7.5 | |
| Steps (reduced) |
5 (0) |
8 (3) |
10 (0) |
12 (2) |
13 (3) |
14 (4) |
15 (0) |
16 (1) |
17 (2) |
17 (2) |
18 (3) | |
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11 | +0 | -23 | +67 | -11 | -40 | -34 | +0 | +55 | -110 | -23 |
| Relative (%) | -4.7 | +0.0 | -9.5 | +28.0 | -4.7 | -17.0 | -14.2 | +0.0 | +23.3 | -46.1 | -9.5 | |
| Steps (reduced) |
5 (5) |
8 (0) |
10 (2) |
12 (4) |
13 (5) |
14 (6) |
15 (7) |
16 (0) |
17 (1) |
17 (1) |
18 (2) | |
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3 | +23 | +6 | +101 | +26 | +0 | +9 | +46 | +104 | -61 | +29 |
| Relative (%) | +1.3 | +9.6 | +2.6 | +42.1 | +10.9 | +0.0 | +3.9 | +19.2 | +43.4 | -25.2 | +12.2 | |
| Steps (reduced) |
5 (5) |
8 (8) |
10 (10) |
12 (12) |
13 (13) |
14 (0) |
15 (1) |
16 (2) |
17 (3) |
17 (3) |
18 (4) | |
Intervals
- 238.645
- 477.29
- 715.934
- 954.579
- 1193.224