1053edo: Difference between revisions
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1053edo is [[consistent]] in the 11-odd-limit. It is a very strong 5-limit tuning where it tempers out | 1053edo is [[consistent]] in the [[11-odd-limit]]. It is a very strong 5-limit tuning where it [[tempering out|tempers out]] {{monzo| 1 -27 18 }} ([[ennealimma]]), {{monzo| 91 -12 -31 }} ([[astro comma]]), and {{monzo| 92 -39 -13 }} ([[aluminium comma]]). It [[support]]s and gives a good tuning for the [[quadraennealimmal]] temperament, as well as the 27th-octave [[trinealimmal]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
1053 factors as {{ | Since 1053 factors as {{factorization|1053}}, 1053edo has subset edos {{EDOs| 3, 9, 13, 27, 39, 81, 117, 351 }}. | ||
Latest revision as of 17:20, 20 February 2025
| ← 1052edo | 1053edo | 1054edo → |
1053 equal divisions of the octave (abbreviated 1053edo or 1053ed2), also called 1053-tone equal temperament (1053tet) or 1053 equal temperament (1053et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1053 equal parts of about 1.14 ¢ each. Each step represents a frequency ratio of 21/1053, or the 1053rd root of 2.
1053edo is consistent in the 11-odd-limit. It is a very strong 5-limit tuning where it tempers out [1 -27 18⟩ (ennealimma), [91 -12 -31⟩ (astro comma), and [92 -39 -13⟩ (aluminium comma). It supports and gives a good tuning for 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
Since 1053 factors as 34 × 13, 1053edo has subset edos 3, 9, 13, 27, 39, 81, 117, 351.