BudjarnLambeth/Ed257/128: Difference between revisions
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* [[Equal-step tuning]] | * [[Equal-step tuning]] | ||
[[Category:Edonoi]][[Category:7edo]] | [[Category:Edonoi]][[Category:7edo]][[Category:7-tone scales]] | ||
Revision as of 10:34, 4 February 2024
An equal division of reduced harmonic 257 (ed257/128) is an equal-step tuning in which the octave-reduced 257th harmonic (257/128) is justly tuned and is divided in a given number of equal steps. 257/128 is very close to the octave, 2/1, but it is slightly sharper. This makes it suitable as an alternative to edos whose consonances are too flat, such as 7edo.
7ed255/128
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +6.7 | -5.6 | +13.5 | -28.0 | +1.1 | +79.0 | +20.2 | -11.3 | -21.3 | -13.9 | +7.9 |
| Relative (%) | +3.9 | -3.3 | +7.8 | -16.3 | +0.6 | +45.8 | +11.7 | -6.5 | -12.3 | -8.1 | +4.6 | |
| Steps (reduced) |
7 (0) |
11 (4) |
14 (0) |
16 (2) |
18 (4) |
20 (6) |
21 (0) |
22 (1) |
23 (2) |
24 (3) |
25 (4) | |
7edo, 16ed5, 22ed9 for comparison:
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | -16.2 | +0.0 | -43.5 | -16.2 | +59.7 | +0.0 | -32.5 | -43.5 | -37.0 | -16.2 |
| Relative (%) | +0.0 | -9.5 | +0.0 | -25.3 | -9.5 | +34.9 | +0.0 | -18.9 | -25.3 | -21.6 | -9.5 | |
| Steps (reduced) |
7 (0) |
11 (4) |
14 (0) |
16 (2) |
18 (4) |
20 (6) |
21 (0) |
22 (1) |
23 (2) |
24 (3) |
25 (4) | |
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +19.0 | +13.6 | +38.0 | +0.0 | +32.6 | -60.1 | +57.0 | +27.3 | +19.0 | +28.2 | +51.7 |
| Relative (%) | +10.9 | +7.8 | +21.8 | +0.0 | +18.7 | -34.5 | +32.8 | +15.7 | +10.9 | +16.2 | +29.7 | |
| Steps (reduced) |
7 (7) |
11 (11) |
14 (14) |
16 (0) |
18 (2) |
19 (3) |
21 (5) |
22 (6) |
23 (7) |
24 (8) |
25 (9) | |
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.3 | +0.0 | +20.7 | -19.8 | +10.3 | -83.6 | +31.0 | +0.0 | -9.5 | -1.6 | +20.7 |
| Relative (%) | +6.0 | +0.0 | +12.0 | -11.5 | +6.0 | -48.4 | +17.9 | +0.0 | -5.5 | -0.9 | +12.0 | |
| Steps (reduced) |
7 (7) |
11 (11) |
14 (14) |
16 (16) |
18 (18) |
19 (19) |
21 (21) |
22 (0) |
23 (1) |
24 (2) |
25 (3) | |
Intervals
- 172.393
- 344.786
- 517.178
- 689.571
- 861.964
- 1034.357
- 1206.749