Xenharmonic Wiki

409edo: Difference between revisions

VisualWikitext
Francium (talk | contribs)
4,840 edits
Created page with "{{Infobox ET}} {{EDO intro|409}} == Theory == 409et is only consistent to the 3-odd-limit. Using the patent val, it tempers out 2460375/2458624 and 201768035/201326592 in..."
 
ArrowHead294 (talk | contribs)
15,220 edits
mNo edit summary
 
(4 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|409}}
{{ED intro}}


== Theory ==
== Theory ==
409et is only consistent to the [[3-odd-limit]]. Using the patent val, it tempers out 2460375/2458624 and 201768035/201326592 in the 7-limit; 1073741824/1071794405, 161280/161051, 1835008/1830125, 2097152/2096325, 496125/495616, 117649/117612, 226492416/226474325, [[441/440]], 2460375/2458624, 201768035/201326592, 24057/24010, [[5632/5625]], 16808715/16777216, 4108797/4096000 and 102487/102400 in the 11-limit. It [[support]]s [[rank-4]] [[werckismic]] and [[snape]].  
409et is in[[consistent]] to the [[5-odd-limit]]. In the 7-limit, the 409c [[val]] {{val| 409 648 '''949''' 1148 }} is about as viable as the [[patent val]] {{val| 409 648 '''950''' 1148 }}. The 409c val [[tempering out|tempers out]] [[15625/15552]] and [[16875/16807]], [[support]]ing [[sqrtphi]]. The patent val tempers out [[3136/3125]] and [[19683/19600]], supporting [[subpental]].  


=== Odd harmonics ===
=== Odd harmonics ===
Line 13: Line 13:
== 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]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|-648 409}}
! rowspan="2" | [[Comma list]]
|{{mapping|409 648}}
! rowspan="2" | [[Mapping]]
| 0.2311
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -648 409 }}
| {{mapping| 409 648 }}
| +0.2311
| 0.2311
| 0.2311
| 7.88
| 7.88
|-
|-
|2.3.7
| 2.3.7
|{{monzo|-44 26 1}}, {{monzo|12 19 -15}}
| {{monzo| -44 26 1 }}, {{monzo| 12 19 -15 }}
|{{mapping|409 648 1148}}
| {{mapping| 409 648 1148 }}
| 0.2266
| +0.2266
| 0.1888
| 0.1888
| 6.43
| 6.43
|-
|-
|2.3.7.11
| 2.3.7.11
|117649/117612, 5038848/5021863, 134775333/134217728
| 117649/117612, 5038848/5021863, 134775333/134217728
|{{mapping|409 648 1148 1415}}
| {{mapping| 409 648 1148 1415 }}
| 0.1503
| +0.1503
| 0.2102
| 0.2102
| 7.16
| 7.16
|-
|-
|2.3.7.11.13
| 2.3.7.11.13
|729/728, 19773/19712, 50421/50336, 718848/717409
| 729/728, 19773/19712, 50421/50336, 718848/717409
|{{mapping|409 648 1148 1415 1513}}
| {{mapping| 409 648 1148 1415 1513 }}
| 0.1963
| +0.1963
| 0.2093
| 0.2093
| 7.13
| 7.13
|}
|}
== Music ==
; [[Francium]]
* "End Of Sartorius Membranes" from ''End of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/5aNPRLUiI5PIvhKEl2XPc9 Spotify] | [https://francium223.bandcamp.com/track/end-of-sartorius-membranes Bandcamp] | [https://www.youtube.com/watch?v=QuxTb_pyG2Y YouTube]
* "Look Lady?" from ''Questions'' (2024) – [https://open.spotify.com/track/3alyeoProiPiuxHyXZB1Ii Spotify] | [https://francium223.bandcamp.com/track/look-lady Bandcamp] | [https://www.youtube.com/watch?v=jqPSMmkw8HM YouTube] – snape in 409edo tuning
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/409edo"