449edo: Difference between revisions
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{{Infobox ET}} | |||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
449edo is [[consistent]] to the [[7-odd-limit]], but the errors of [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are all quite large, giving us the option of treating it as a full 7-limit temperament, or a 2.9.15.21.11.13 [[subgroup]] temperament. | |||
===Odd harmonics=== | |||
Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[4375/4374]] and 26873856/26796875 in the 7-limit; [[41503/41472]], 160083/160000, 539055/537824, 805255/802816, and 825000/823543 in the 11-limit. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|449}} | {{Harmonics in equal|449}} | ||
===Subsets and supersets=== | |||
=== Subsets and supersets === | |||
449edo is the 87th [[prime edo]]. 898edo, which doubles it, gives a good correction to the harmonic 3, 5 and 7. | 449edo is the 87th [[prime edo]]. 898edo, which doubles it, gives a good correction to the harmonic 3, 5 and 7. | ||
==Regular temperament properties== | |||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |- | ||
|2.9 | ! rowspan="2" | [[Subgroup]] | ||
|{{monzo|-1423 449}} | ! rowspan="2" | [[Comma list]] | ||
|{{ | ! rowspan="2" | [[Mapping]] | ||
| 0.1249 | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.9 | |||
| {{monzo| -1423 449 }} | |||
| {{mapping| 449 1423 }} | |||
| +0.1249 | |||
| 0.1249 | | 0.1249 | ||
| 4.67 | | 4.67 | ||
| Line 28: | Line 35: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | |- | ||
! Generator | ! Periods<br />per 8ve | ||
! Cents | ! Generator* | ||
! Associated<br>ratio | ! Cents* | ||
! Associated<br />ratio* | |||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|127\449 | | 127\449 | ||
|339.421 | | 339.421 | ||
|243\200 | | 243\200 | ||
|[[Amity]] (7-limit) | | [[Amity]] (7-limit) | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Music == | == Music == | ||
*[https://www.youtube.com/watch?v=vLZuStkREoE Little Victorious Dance] | ; [[Francium]] | ||
* [https://www.youtube.com/watch?v=vLZuStkREoE ''Little Victorious Dance''] (2023) | |||
[[Category:Listen]] | |||