1330edo: Difference between revisions
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1330edo is [[ | 1330edo is [[enfactoring|enfactored]] in the 7-limit and has the same tuning as [[665edo]]. It corrects 665edo's approximation of harmonic 11, only to be [[consistent]] up to the [[11-odd-limit]], unfortunately. It [[tempering out|tempers out]] [[3025/3024]], [[9801/9800]], and 234375/234256, supporting [[hemienneadecal]], though [[1178edo]] is a better tuning for that purpose. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 1330 factors into | Since 1330 factors into {{factorization|1330}}, it has subset edos {{EDOs| 2, 5, 7, 19, 35, 70, 95, 133, 190, 266, and 665 }}. A step of 1330edo is exactly 24 imps ([[31920edo|24\31920]]). | ||
Latest revision as of 23:15, 20 February 2025
| ← 1329edo | 1330edo | 1331edo → |
1330 equal divisions of the octave (abbreviated 1330edo or 1330ed2), also called 1330-tone equal temperament (1330tet) or 1330 equal temperament (1330et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1330 equal parts of about 0.902 ¢ each. Each step represents a frequency ratio of 21/1330, or the 1330th root of 2.
1330edo is enfactored in the 7-limit and has the same tuning as 665edo. It corrects 665edo's approximation of harmonic 11, only to be consistent up to the 11-odd-limit, unfortunately. It tempers out 3025/3024, 9801/9800, and 234375/234256, supporting hemienneadecal, though 1178edo is a better tuning for that purpose.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.000 | -0.148 | +0.197 | -0.040 | +0.375 | -0.294 | +0.231 | -0.304 | -0.104 | -0.073 |
| Relative (%) | +0.0 | -0.0 | -16.4 | +21.8 | -4.4 | +41.5 | -32.6 | +25.6 | -33.7 | -11.5 | -8.1 | |
| Steps (reduced) |
1330 (0) |
2108 (778) |
3088 (428) |
3734 (1074) |
4601 (611) |
4922 (932) |
5436 (116) |
5650 (330) |
6016 (696) |
6461 (1141) |
6589 (1269) | |
Subsets and supersets
Since 1330 factors into 2 × 5 × 7 × 19, it has subset edos 2, 5, 7, 19, 35, 70, 95, 133, 190, 266, and 665. A step of 1330edo is exactly 24 imps (24\31920).