User:Francium/5413edo: Difference between revisions
Created page with "{{Infobox ET}} {{ED intro}} == Theory == 5413edo is inconsistent to the 5-limit and its harmonic 3 is about halfway its steps. As a equal temperament, 5413edo is strong in the 2.9.15.11.19.23.31 subgroup, tempering out 178125/178112, 253952/253935, 173861875/173840256, 44921875/44914176, 14156615/14155776 and 484525998080/484404751413. === Odd harmonics === {{Harmonics in equal|5413}} === Subsets and supersets === 5413edo is the 714th pri..." |
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=== Subsets and supersets === | === Subsets and supersets === | ||
5413edo is the 714th [[prime edo]]. | 5413edo is the 714th [[prime edo]]. [[10826edo]], which doubles it, gives a good correction to its harmonics 3 and [[5/1|5]]. | ||
== Regular temperament properties == | |||
{| 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]] (%) | |||
|- | |||
| 2.9 | |||
| {{monzo|17159 -5413}} | |||
| {{mapping|5413 17159}} | |||
| −0.0069 | |||
| 0.0069 | |||
| 3.11 | |||
|- | |||
| 2.9.15 | |||
| {{monzo|200 -52 -9}}, {{monzo|-49 -93 88}} | |||
| {{mapping|5413 17159 21148}} | |||
| −0.0046 | |||
| 0.0064 | |||
| 2.89 | |||
|- | |||
| 2.9.15.7 | |||
| 4747561509943/4746093750000, 27033764064453125/27021597764222976, 16689300537109375/16677181699666569 | |||
| {{mapping|5413 17159 21148 15196}} | |||
| +0.0007 | |||
| 0.0108 | |||
| 4.87 | |||
|- | |||
| 2.9.15.7.11 | |||
| 151263/151250, 246071287/246037500, 369140625/369098752, 409600000000000000/409370033518213779 | |||
| {{mapping|5413 17159 21148 15196 18726}} | |||
| −0.0006 | |||
| 0.0100 | |||
| 4.51 | |||
|} | |||
== Music == | |||
; [[Francium]] | |||
* "Artificial Gorilla Blood" from ''Check Us Out'' (2026) – [https://open.spotify.com/track/7jvngwlo9OYUB34VFfG6ip Spotify] | [https://francium223.bandcamp.com/track/artificial-gorilla-blood Bandcamp] | [https://www.youtube.com/watch?v=hrS4KLSPimM YouTube] – in Godzilla, 5413edo tuning | |||