563edo
| ← 562edo | 563edo | 564edo → |
563 equal divisions of the octave (abbreviated 563edo or 563ed2), also called 563-tone equal temperament (563tet) or 563 equal temperament (563et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 563 equal parts of about 2.13 ¢ each. Each step represents a frequency ratio of 21/563, or the 563rd root of 2.
Theory
563edo is only consistent to the 5-odd-limit and the error of harmonic 3 is quite large. It is suitable for the 2.9.7.11.19.23 subgroup, tempering out 1863/1862, 3971/3969, 3449952/3447493, 7901568/7891499 and 4333568/4322241.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.712 | -0.523 | +0.979 | +0.708 | +0.725 | -0.741 | +0.896 | -0.515 | +0.888 | +0.267 | +0.500 |
| Relative (%) | -33.4 | -24.6 | +45.9 | +33.2 | +34.0 | -34.8 | +42.1 | -24.2 | +41.7 | +12.5 | +23.5 | |
| Steps (reduced) |
892 (329) |
1307 (181) |
1581 (455) |
1785 (96) |
1948 (259) |
2083 (394) |
2200 (511) |
2301 (49) |
2392 (140) |
2473 (221) |
2547 (295) | |
Subsets and supersets
563edo is the 103rd prime edo. 1689edo, which triples it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [1785 -563⟩ | [⟨563 1785]] | −0.1117 | 0.1117 | 5.24 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 263\563 | 560.57 | 864/625 | Whoosh |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct