User:Francium/1303edo
| ← 1302edo | 1303edo | 1304edo → |
1303 equal divisions of the octave (abbreviated 1303edo or 1303ed2), also called 1303-tone equal temperament (1303tet) or 1303 equal temperament (1303et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1303 equal parts of about 0.921 ¢ each. Each step represents a frequency ratio of 21/1303, or the 1303rd root of 2.
Theory
1303edo is consistent to the 9-odd-limit, tempering out 4375/4374, 32805/32768 and [24 4 22 -29⟩ in the 7-limit, although its harmonic 5 is about halfway its steps. It is strong in the 2.7.17.19.29 subgroup, tempering out 69632/69629, 4857616/4857223, 849301957/849127424 and 197726038040074256384/197694657826980042227.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.190 | -0.435 | +0.015 | -0.380 | +0.332 | +0.301 | +0.296 | +0.033 | -0.046 | -0.175 | -0.185 |
| Relative (%) | -20.6 | -47.2 | +1.7 | -41.2 | +36.1 | +32.7 | +32.2 | +3.6 | -5.0 | -19.0 | -20.1 | |
| Steps (reduced) |
2065 (762) |
3025 (419) |
3658 (1052) |
4130 (221) |
4508 (599) |
4822 (913) |
5091 (1182) |
5326 (114) |
5535 (323) |
5723 (511) |
5894 (682) | |
Subsets and supersets
1303edo is the 213th prime edo. 2606edo, which doubles it, gives a good correction to its harmonics 5 and 11.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-2065 1303⟩ | [⟨1303 2065]] | 0.0599 | 0.0599 | 6.50 |
| 2.3.5 | 32805/32768, [-110 -143 145⟩ | [⟨1303 2065 3025]] | 0.1024 | 0.0775 | 8.42 |
| 2.3.5.7 | 4375/4374, 32805/32768, [24 4 22 -29⟩ | [⟨1303 2065 3025 3658]] | 0.0754 | 0.0817 | 8.87 |