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439edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|439}}
{{ED intro}}
 
== Theory ==
== Theory ==
439et tempers out [[703125/702464]] in the 7-limit; 55296000/55240493, 100663296/100656875, 820125/819896, 2097152/2096325, 759375/758912, [[131072/130977]], 352947/352000, 85937500/85766121, 1879453125/1879048192, 184549376/184528125, 184877/184320, [[3025/3024]] and [[1771561/1771470]] in the 11-limit.
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" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! rowspan="2" | [[Subgroup]]
![[TE simple badness|Relative]] (%)
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
|2.3
! [[TE error|Absolute]] (¢)
|{{monzo|696 -439}}
! [[TE simple badness|Relative]] (%)
|{{val|439 696}}
|-
| -0.1737
| 2.3
| {{monzo| 696 -439 }}
| {{mapping| 439 696 }}
| −0.1737
| 0.1737
| 0.1737
| 6.35
| 6.36
|-
|- style="border-top: double;"
|2.3.15
| 2.3.5
|15625/15552, {{monzo|121 -64 -5}}
| 15625/15552, {{monzo| 115 -74 1 }}
|{{val|439 696 1715}}
| {{mapping| 439 696 1019 }} (439)
| -0.0867
| +0.0122
| 0.1878
| 0.2988
| 6.87
| 10.9
|-
|2.3.15.35
|5120/5103, 15625/15552, 1992903750/1977326743
|{{val|439 696 1715 2252}}
| -0.0976
| 0.1637
| 5.99
|-
|-
|2.3.15.35.11
| 2.3.5.7
|540/539, 5120/5103, 15625/15552, 43923/43904
| 10976/10935, 15625/15552, {{monzo| -25 6 -3 8 }}
|{{val|439 696 1715 2252 1519}}
| {{mapping| 439 696 1019 1232 }} (439)
| -0.1270
| +0.1135
| 0.1578
| 0.3127
| 5.77
| 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
|-
|-
|2.3.15.35.11.65
| 2.3.5.7
|540/539, 1716/1715, 5120/5103, 4225/4224, 81675/81536
| 3136/3125, 2097152/2083725, 43046721/42875000
|{{val|439 696 1715 2252 1519 2644}}
| {{mapping| 439 696 1020 1233 }} (439cd)
| -0.1195
| −0.4241
| 0.1450
| 0.2911
| 5.30
| 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]]
Retrieved from "https://en.xen.wiki/w/439edo"