424edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|424}} == Theory == 424et is consistent to the 9-odd-limit and the harmonic 5 is halfway between its steps. It tempers out 32805/32768 in th..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
424edo is [[consistent]] to the [[9-odd-limit]], but the [[harmonic]] [[5/1|5]] is about halfway between its steps. It is [[enfactoring|enfactored]] in the 7-limit, with the same tuning as [[212edo]]. The approximation to [[11/1|11]], although closer to just than 212edo's, tends sharp, so its improvement is debatable. All things considered, a 2.3.13.17.19.23 [[subgroup]] interpretation with optional additions of 7, 11, or both, seems most reasonable. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
424 factors into 2<sup>3</sup> × 53, | Since 424 factors into 2<sup>3</sup> × 53, 424edo has subset edos {{EDOs| 2, 4, 8, 53, 106, and 212 }}. [[848edo]], which doubles it, gives a good correction to the harmonic 5. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |- | ||
|2.3 | ! rowspan="2" | [[Subgroup]] | ||
|{{monzo|- | ! rowspan="2" | [[Comma list]] | ||
|{{mapping|424 672}} | ! rowspan="2" | [[Mapping]] | ||
| 0. | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
| 0. | ! colspan="2" | Tuning error | ||
| | |- | ||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3.7.11 | |||
| 41503/41472, 117649/117128, {{monzo| -26 19 1 -2 }} | |||
| {{mapping| 424 672 1190 1467 }} | |||
| +0.0499 | |||
| 0.1747 | |||
| 6.17 | |||
|} | |} | ||