2711edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|2711}} == Theory == 2711et tempers out 78125000/78121827 in the 7-limit; 35156250/35153041, 14348907/14348180, 21437500/21434787, 151263/151250,..."
 
→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)
Line 7: Line 7:
===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|Comma List]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
! colspan="2" | Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{monzo|4297 -2711}}
| {{monzo| 4297 -2711 }}
|{{val|2711 4297}}
| {{val| 2711 4297 }}
| -0.0233
| -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}}
| {{val| 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}}
| {{val| 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}}
| {{val| 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}}
| {{val| 2711 4297 6295 7611 9379 10032 }}
| -0.0351
| -0.0351
| 0.0215
| 0.0215
| 4.86
| 4.86
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+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]]
*[https://www.youtube.com/watch?v=8prB_mBdKlo Ballad From A Broken Record] by [[User:Francium|Francium]]

Revision as of 14:12, 16 May 2023

← 2710edo 2711edo 2712edo →
Prime factorization 2711 (prime)
Step size 0.442641 ¢ 
Fifth 1586\2711 (702.029 ¢)
Semitones (A1:m2) 258:203 (114.2 ¢ : 89.86 ¢)
Consistency limit 15
Distinct consistency limit 15

Template:EDO intro

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.

Prime harmonics

Approximation of prime harmonics in 2711edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.074 +0.112 +0.115 +0.213 +0.048 -0.049 -0.058 -0.167 +0.006 +0.077
Relative (%) +0.0 +16.7 +25.3 +26.1 +48.1 +10.8 -11.2 -13.1 -37.6 +1.4 +17.4
Steps
(reduced) 		2711
(0) 		4297
(1586) 		6295
(873) 		7611
(2189) 		9379
(1246) 		10032
(1899) 		11081
(237) 		11516
(672) 		12263
(1419) 		13170
(2326) 		13431
(2587)

Subsets and supersets

2711edo is the 395th prime edo.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [4297 -2711⟩ ⟨2711 4297] -0.0233 0.0233 5.26
2.3.5 [77 -31 -12⟩, [18 -89 53⟩ ⟨2711 4297 6295] -0.0316 0.0223 5.04
2.3.5.7 [3 -13 10 -2⟩, [37 -9 -11 1⟩, [0 -11 -7 12⟩ ⟨2711 4297 6295 7611] -0.0340 0.0198 4.47
2.3.5.7.11 151263/151250, 14348907/14348180, 2359296/2358125, 21437500/21434787 ⟨2711 4297 6295 7611 9379] -0.0395 0.0209 4.72
2.3.5.7.11.13 4096/4095, 43940/43923, 67392/67375, 151263/151250, 4429568/4428675 ⟨2711 4297 6295 7611 9379 10032] -0.0351 0.0215 4.86

Music

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