439edo: Difference between revisions
→Regular temperament properties: 2.3.15 is equivalent to 2.3.5 and 2.3.15.35 is equivalent to 2.3.5.7. Rework to address alternative vals |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
439edo is in[[consistent]] in the 5-odd-limit. In the 7-limit, the [[patent val]] {{val| 439 696 1019 1232 }}, and the 439cd val {{val| 439 696 '''1020''' '''1233''' }} are about as viable. | |||
===Prime harmonics=== | |||
The patent val tempers out [[10976/10935]], [[15625/15552]] and [[703125/702464]] in the 7-limit; [[3025/3024]], 4375/4356, 14700/14641, 59290/59049, [[131072/130977]], and 184877/184320 in the 11-limit. | |||
The 439cd val tempers out [[3136/3125]], 2097152/2083725, and 4096000/4084101 in the 7-limit; 3136/3125, 15488/15435, [[16384/16335]], [[19712/19683]], 24057/24010, 43923/43750, 43923/43904, and 46656/46585 in the 11-limit. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|439}} | {{Harmonics in equal|439}} | ||
===Subsets and supersets=== | |||
=== Subsets and supersets === | |||
439edo is the 85th [[prime edo]]. | 439edo is the 85th [[prime edo]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 20: | Line 29: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 696 -439 }} | | {{monzo| 696 -439 }} | ||
| {{ | | {{mapping| 439 696 }} | ||
| | | −0.1737 | ||
| 0.1737 | | 0.1737 | ||
| 6.36 | | 6.36 | ||
|- | |- style="border-top: double;" | ||
| 2.3.5 | |||
| 15625/15552, {{monzo| 115 -74 1 }} | |||
| {{mapping| 439 696 1019 }} (439) | |||
| +0.0122 | |||
| 0.2988 | |||
| 10.9 | |||
|- | |- | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 10976/10935, 15625/15552, {{monzo| -25 6 -3 8 }} | | 10976/10935, 15625/15552, {{monzo| -25 6 -3 8 }} | ||
| {{ | | {{mapping| 439 696 1019 1232 }} (439) | ||
| +0.1135 | | +0.1135 | ||
| 0.3127 | | 0.3127 | ||
| 11.4 | | 11.4 | ||
|- | |- style="border-top: double;" | ||
| 2.3.5 | |||
| {{monzo| 24 -21 4 }}, {{monzo| 36 11 -23 }} | |||
| {{mapping| 439 696 1020 }} (439c) | |||
| | | −0.3801 | ||
| 0.3244 | |||
| 11.9 | |||
|- | |- | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 3136/3125, 2097152/2083725, 43046721/42875000 | | 3136/3125, 2097152/2083725, 43046721/42875000 | ||
| {{ | | {{mapping| 439 696 1020 1233 }} (439cd) | ||
| | | −0.4241 | ||
| 0.2911 | | 0.2911 | ||
| 10.7 | | 10.7 | ||
|} | |} | ||
== Scales == | |||
* [[Helayo24]] | |||
== Music == | |||
; [[Francium]] | |||
* "In The Black Hole" from ''Helayo EP'' (2023) – [https://open.spotify.com/track/3M2keEmTeY1J1j4cugAjXG Spotify] | [https://francium223.bandcamp.com/track/in-the-black-hole Bandcamp] | [https://youtu.be/ouGndPvLLso?si=fEI5pzfIydWHPF2l YouTube] – helayo in 439edo tuning | |||
[[Category:Listen]] | |||