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 ===
Line 12: 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" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[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]] (%)
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| 2.3
| 2.3
| {{monzo| 4297 -2711 }}
| {{monzo| 4297 -2711 }}
| {{val| 2711 4297 }}
| {{mapping| 2711 4297 }}
| -0.0233
| −0.0233
| 0.0233
| 0.0233
| 5.26
| 5.26
Line 30: Line 32:
| 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
Line 37: 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 }}
| {{val| 2711 4297 6295 7611 }}
| {{mapping| 2711 4297 6295 7611 }}
| -0.0340
| −0.0340
| 0.0198
| 0.0198
| 4.47
| 4.47
Line 44: 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
| {{val| 2711 4297 6295 7611 9379 }}
| {{mapping| 2711 4297 6295 7611 9379 }}
| -0.0395
| −0.0395
| 0.0209
| 0.0209
| 4.72
| 4.72
Line 51: 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
| {{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
|}
|}
== Scales ==
* [[Hemischis53]]


== Music ==
== Music ==
; [[User:Francium|Francium]]
; [[User:Francium|Francium]]
* [https://www.youtube.com/watch?v=8prB_mBdKlo ''Ballad From A Broken Record''] (2023) – [[hemischis]] in 2711edo tuning
* "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]]

Latest revision as of 12:53, 21 February 2025

← 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

2711 equal divisions of the octave (abbreviated 2711edo or 2711ed2), also called 2711-tone equal temperament (2711tet) or 2711 equal temperament (2711et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2711 equal parts of about 0.443 ¢ each. Each step represents a frequency ratio of 21/2711, or the 2711th root of 2.

Theory

2711edo is distinctly consistent to the 15-odd-limit, or the no-11 19-odd-limit. The equal temperament 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

Scales

Music

Francium
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