338edo: Difference between revisions
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The equal temperament [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[ | The equal temperament [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnu comma]]) in the [[5-limit]], and [[2401/2400]], [[5120/5103]] and [[10976/10935]] in the [[7-limit]]. It provides the [[optimal patent val]] for 7-limit [[hemififths]], the {{nowrap| 99 & 239 }} temperament. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 338 factors into {{ | Since 338 factors into {{nowrap| 2 × 13<sup>2</sup> }}, 338edo has subset edos {{EDOs| 2, 13, 26, and 169 }}. | ||
[[Category:Hemififths]] | [[Category:Hemififths]] | ||
Latest revision as of 06:44, 18 June 2026
| ← 337edo | 338edo | 339edo → |
338 equal divisions of the octave (abbreviated 338edo or 338ed2), also called 338-tone equal temperament (338tet) or 338 equal temperament (338et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 338 equal parts of about 3.55 ¢ each. Each step represents a frequency ratio of 21/338, or the 338th root of 2.
The equal temperament tempers out [23 6 -14⟩ (vishnu comma) in the 5-limit, and 2401/2400, 5120/5103 and 10976/10935 in the 7-limit. It provides the optimal patent val for 7-limit hemififths, the 99 & 239 temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.00 | +0.67 | +0.40 | -1.54 | -1.02 | +0.89 | +1.67 | +1.55 | +0.71 | +1.41 | +0.13 |
| Relative (%) | +28.3 | +18.8 | +11.4 | -43.5 | -28.8 | +25.1 | +47.1 | +43.8 | +20.1 | +39.7 | +3.6 | |
| Steps (reduced) |
536 (198) |
785 (109) |
949 (273) |
1071 (57) |
1169 (155) |
1251 (237) |
1321 (307) |
1382 (30) |
1436 (84) |
1485 (133) |
1529 (177) | |
Subsets and supersets
Since 338 factors into 2 × 132, 338edo has subset edos 2, 13, 26, and 169.