1065edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
1065edo is [[consistent]] to the [[21-odd-limit]] and is a [[zeta peak integer edo]]. | |||
{{ | The equal temperament [[tempering out|tempers out]] {{monzo| 54 -37 2 }} ([[monzisma]]) and {{monzo| 61 4 -29}} (squarschmidt comma) in the 5-limit; 250047/250000 ([[landscape comma]]) in the 7-limit; [[3025/3024]], 102487/102400, 160083/160000, and 180224/180075 in the 11-limit; [[1716/1715]] and [[4096/4095]] in the 13-limit; [[2601/2600]] and [[12376/12375]] in the 17-limit; and 2376/2375, 2926/2925, 10830/10829, 14080/14079, and 14365/14364 in the 19-limit. | ||
[[Category: | === Prime harmonics === | ||
{{Harmonics in equal|1065|prec=4}} | |||
=== Subsets and supersets === | |||
Since 1065 factors into {{factorization|1065}}, 1065edo has subset edos {{EDOs| 3, 5, 15, 71, 213, and 355 }}. | |||
[[Category:Zeta|####]] <!-- 4-digit number --> | |||
Latest revision as of 17:00, 20 February 2025
| ← 1064edo | 1065edo | 1066edo → |
1065 equal divisions of the octave (abbreviated 1065edo or 1065ed2), also called 1065-tone equal temperament (1065tet) or 1065 equal temperament (1065et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1065 equal parts of about 1.13 ¢ each. Each step represents a frequency ratio of 21/1065, or the 1065th root of 2.
1065edo is consistent to the 21-odd-limit and is a zeta peak integer edo.
The equal temperament tempers out [54 -37 2⟩ (monzisma) and [61 4 -29⟩ (squarschmidt comma) in the 5-limit; 250047/250000 (landscape comma) in the 7-limit; 3025/3024, 102487/102400, 160083/160000, and 180224/180075 in the 11-limit; 1716/1715 and 4096/4095 in the 13-limit; 2601/2600 and 12376/12375 in the 17-limit; and 2376/2375, 2926/2925, 10830/10829, 14080/14079, and 14365/14364 in the 19-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0168 | +0.1652 | +0.1882 | -0.3320 | +0.0357 | -0.1667 | -0.0482 | +0.4580 | +0.2820 | -0.2468 |
| Relative (%) | +0.0 | +1.5 | +14.7 | +16.7 | -29.5 | +3.2 | -14.8 | -4.3 | +40.7 | +25.0 | -21.9 | |
| Steps (reduced) |
1065 (0) |
1688 (623) |
2473 (343) |
2990 (860) |
3684 (489) |
3941 (746) |
4353 (93) |
4524 (264) |
4818 (558) |
5174 (914) |
5276 (1016) | |
Subsets and supersets
Since 1065 factors into 3 × 5 × 71, 1065edo has subset edos 3, 5, 15, 71, 213, and 355.