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2711edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|2711}}
{{ED intro}}
 
== Theory ==
== Theory ==
2711et 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.
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" |[[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|4297 -2711}}
! rowspan="2" | [[Comma list]]
|{{val|2711 4297}}
! rowspan="2" | [[Mapping]]
| -0.0233
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 4297 -2711 }}
| {{mapping| 2711 4297 }}
| −0.0233
| 0.0233
| 0.0233
| 5.26
| 5.26
|-
|-
|2.3.5
| 2.3.5
|{{monzo|77 -31 -12}}, {{monzo|18 -89 53}}
| {{monzo| 77 -31 -12 }}, {{monzo| 18 -89 53 }}
|{{val|2711 4297 6295}}
| {{mapping| 2711 4297 6295 }}
| -0.0316
| −0.0316
| 0.0223
| 0.0223
| 5.04
| 5.04
|-
|-
|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 }}
|{{val|2711 4297 6295 7611}}
| {{mapping| 2711 4297 6295 7611 }}
| -0.0340
| −0.0340
| 0.0198
| 0.0198
| 4.47
| 4.47
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|151263/151250, 2359296/2358125, 21437500/21434787, 14348907/14348180
| 151263/151250, 14348907/14348180, 2359296/2358125, 21437500/21434787
|{{val|2711 4297 6295 7611 9379}}
| {{mapping| 2711 4297 6295 7611 9379 }}
| -0.0395
| −0.0395
| 0.0209
| 0.0209
| 4.72
| 4.72
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|4096/4095, 43940/43923, 67392/67375, 123201/123200, 151263/151250, 1063348/1063125, 4429568/4428675
| 4096/4095, 43940/43923, 67392/67375, 151263/151250, 4429568/4428675
|{{val|2711 4297 6295 7611 9379 10032}}
| {{mapping| 2711 4297 6295 7611 9379 10032 }}
| -0.0351
| −0.0351
| 0.0215
| 0.0215
| 4.86
| 4.86
|}
|}


=== Rank-2 temperaments ===
== Scales ==
{| class="wikitable center-all left-5"
* [[Hemischis53]]
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator<br>(reduced)
! Cents<br>(reduced)
! Associated<br>ratio
! Temperaments
|-
|1
|563\2711
|249.207
|81/70
|[[Hemischis]]
|-
|1
|584\2711
|258.502
|{{monzo|-32 13 5}}
|[[Lafa]]
|}


== Music ==
== Music ==
*[https://www.youtube.com/watch?v=8prB_mBdKlo Ballad From A Broken Record] by [[User:Francium|Francium]]
; [[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]]
Retrieved from "https://en.xen.wiki/w/2711edo"