2048edo: Difference between revisions
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[[Category:Equal divisions of the octave]] | |||
Revision as of 10:18, 7 June 2022
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.002 | -0.181 | -0.271 | +0.049 | +0.293 | -0.073 | +0.143 | -0.149 | -0.085 | -0.114 |
| Relative (%) | +0.0 | -0.3 | -30.9 | -46.3 | +8.4 | +49.9 | -12.4 | +24.4 | -25.5 | -14.5 | -19.4 | |
| Steps (reduced) |
2048 (0) |
3246 (1198) |
4755 (659) |
5749 (1653) |
7085 (941) |
7579 (1435) |
8371 (179) |
8700 (508) |
9264 (1072) |
9949 (1757) |
10146 (1954) | |
2048edo has an excellent perfect fifth, which derives from 1024edo. It tempers out the breedsma (2401/2400) in the 7-limit, and supports the rank 3 breed temperament.
2048edo is usable as high as 43-limit, with the 2048f val regular temperament having an error of 0.023 cents (0.04 edosteps) per octave, and the no-13s limit patent val is unambiguous and has an error of only 0.019 cents/octave.
2048edo is the 11th power of two EDO.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal
8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3.5 | [54, -37, 2⟩,[-111, -12, 56⟩ | [⟨2048 3246 4755]] | |||
| 2.3.5.7 | 2401/2400, [-18, -13, 13, 3⟩, [49, -38, 0, 4⟩ | [⟨2048 3246 4755 5749]] | |||