228edo: Difference between revisions
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Relocate the infobox; +odd harmonics table |
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{{Infobox ET | {{Infobox ET | ||
| Prime factorization = 19 × 3 × 2<sup>2</sup> | | Prime factorization = 19 × 3 × 2<sup>2</sup> | ||
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| Consistency = 7 | | Consistency = 7 | ||
}} | }} | ||
The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each. It tempers out the Pythagorean comma, 531441/524288, in the 3-limit, and 225/224 and 250047/250000 in the 7-limit, so that it [[support]]s 7-limit [[Pythagorean_family|compton temperament]] and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|228}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 17:52, 12 September 2022
| ← 227edo | 228edo | 229edo → |
The 228 equal division divides the octave into 228 equal parts of 5.263 cents each. It tempers out the Pythagorean comma, 531441/524288, in the 3-limit, and 225/224 and 250047/250000 in the 7-limit, so that it supports 7-limit compton temperament and in fact provides the optimal patent val. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the enneadeca or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.96 | -2.10 | -0.40 | +1.35 | +1.31 | +1.58 | +1.20 | +0.31 | +2.49 | -2.36 | -1.96 |
| Relative (%) | -37.1 | -40.0 | -7.7 | +25.7 | +25.0 | +30.0 | +22.9 | +5.8 | +47.3 | -44.8 | -37.2 | |
| Steps (reduced) |
361 (133) |
529 (73) |
640 (184) |
723 (39) |
789 (105) |
844 (160) |
891 (207) |
932 (20) |
969 (57) |
1001 (89) |
1031 (119) | |