1053edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|1053}} 1053edo is consistent in the 11-odd-limit. 1053edo tempers out the ennealimma, which divides the octave into 9 parts. As expansion..." |
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{{EDO intro|1053}} | {{EDO intro|1053}} | ||
1053edo is [[consistent]] in the 11-odd-limit. | 1053edo is [[consistent]] in the 11-odd-limit. It is a very strong 5-limit tuning where it tempers out the [[astro]] comma, the 13th-octave [[aluminium comma]], and the 9th-octave [[ennealimma]]. As expansions of ennealimmal, it tunes the [[quadraennealimmal]] temperament, as well as the 27th-octave [[trinealimmal]]. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|1053}} | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
1053 factors as {{Factorization|1053}}, therefore 1053edo has subset edos {{EDOs|1, 3, 9, 13, 27, 39, 81, 117, 351}}. | 1053 factors as {{Factorization|1053}}, therefore 1053edo has subset edos {{EDOs|1, 3, 9, 13, 27, 39, 81, 117, 351}}. | ||
Revision as of 00:36, 18 December 2023
| ← 1052edo | 1053edo | 1054edo → |
1053edo is consistent in the 11-odd-limit. It is a very strong 5-limit tuning where it tempers out the astro comma, the 13th-octave aluminium comma, and the 9th-octave ennealimma. As expansions of ennealimmal, it tunes the quadraennealimmal temperament, as well as the 27th-octave trinealimmal.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.039 | +0.011 | -0.165 | +0.249 | +0.498 | -0.112 | -0.077 | -0.354 | -0.517 | +0.264 |
| Relative (%) | +0.0 | +3.4 | +1.0 | -14.5 | +21.9 | +43.7 | -9.8 | -6.8 | -31.1 | -45.4 | +23.1 | |
| Steps (reduced) |
1053 (0) |
1669 (616) |
2445 (339) |
2956 (850) |
3643 (484) |
3897 (738) |
4304 (92) |
4473 (261) |
4763 (551) |
5115 (903) |
5217 (1005) | |
Subsets and supersets
1053 factors as 34 × 13, therefore 1053edo has subset edos 1, 3, 9, 13, 27, 39, 81, 117, 351.