2711edo: Difference between revisions
→Regular temperament properties: review the comma bases. This et definitely doesn't support either hemischis or lafa in any obvious way (if it does in a certain val, the val should be given in the theory section) |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
2711edo is [[consistency|distinctly consistent]] to the [[15-odd-limit]], or the no-11 [[19-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[78125000/78121827]] in the 7-limit; 35156250/35153041, 14348907/14348180, 21437500/21434787, 151263/151250, 2359296/2358125, 5767168/5764801 and 199297406/199290375 in the 11-limit. | |||
===Prime harmonics=== | |||
=== Prime harmonics === | |||
{{Harmonics in equal|2711}} | {{Harmonics in equal|2711}} | ||
===Subsets and supersets=== | |||
=== Subsets and supersets === | |||
2711edo is the 395th [[prime edo]]. | 2711edo is the 395th [[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]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
| Line 20: | Line 25: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 4297 -2711 }} | | {{monzo| 4297 -2711 }} | ||
| {{ | | {{mapping| 2711 4297 }} | ||
| | | −0.0233 | ||
| 0.0233 | | 0.0233 | ||
| 5.26 | | 5.26 | ||
| Line 27: | Line 32: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| 77 -31 -12 }}, {{monzo| 18 -89 53 }} | | {{monzo| 77 -31 -12 }}, {{monzo| 18 -89 53 }} | ||
| {{ | | {{mapping| 2711 4297 6295 }} | ||
| | | −0.0316 | ||
| 0.0223 | | 0.0223 | ||
| 5.04 | | 5.04 | ||
| Line 34: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| {{monzo| 3 -13 10 -2 }}, {{monzo| 37 -9 -11 1 }}, {{monzo| 0 -11 -7 12 }} | | {{monzo| 3 -13 10 -2 }}, {{monzo| 37 -9 -11 1 }}, {{monzo| 0 -11 -7 12 }} | ||
| {{ | | {{mapping| 2711 4297 6295 7611 }} | ||
| | | −0.0340 | ||
| 0.0198 | | 0.0198 | ||
| 4.47 | | 4.47 | ||
| Line 41: | Line 46: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 151263/151250, 14348907/14348180, 2359296/2358125, 21437500/21434787 | | 151263/151250, 14348907/14348180, 2359296/2358125, 21437500/21434787 | ||
| {{ | | {{mapping| 2711 4297 6295 7611 9379 }} | ||
| | | −0.0395 | ||
| 0.0209 | | 0.0209 | ||
| 4.72 | | 4.72 | ||
| Line 48: | Line 53: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 4096/4095, 43940/43923, 67392/67375, 151263/151250, 4429568/4428675 | | 4096/4095, 43940/43923, 67392/67375, 151263/151250, 4429568/4428675 | ||
| {{ | | {{mapping| 2711 4297 6295 7611 9379 10032 }} | ||
| | | −0.0351 | ||
| 0.0215 | | 0.0215 | ||
| 4.86 | | 4.86 | ||
|} | |} | ||
== Scales == | |||
* [[Hemischis53]] | |||
== Music == | == Music == | ||
*[https:// | ; [[User:Francium|Francium]] | ||
* "Ballad From A Broken Record" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/3oiWeSOUJKFohcxBPcGjGt Spotify] | [https://francium223.bandcamp.com/track/ballad-from-a-broken-record Bandcamp] | [https://youtu.be/8prB_mBdKlo?si=os7KzZC6N8NWUFDe YouTube] – [[hemischis]] in 2711edo tuning | |||
[[Category:Listen]] | |||