2711edo: Difference between revisions
Jump to navigation
Jump to search
m Cleanup |
Cleanup; linking |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|2711}} | {{EDO intro|2711}} | ||
== 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. | 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. | ||
| Line 23: | Line 24: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 4297 -2711 }} | | {{monzo| 4297 -2711 }} | ||
| {{ | | {{mapping| 2711 4297 }} | ||
| -0.0233 | | -0.0233 | ||
| 0.0233 | | 0.0233 | ||
| Line 30: | Line 31: | ||
| 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 | | -0.0316 | ||
| 0.0223 | | 0.0223 | ||
| Line 37: | Line 38: | ||
| 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 | | -0.0340 | ||
| 0.0198 | | 0.0198 | ||
| Line 44: | Line 45: | ||
| 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 | | -0.0395 | ||
| 0.0209 | | 0.0209 | ||
| Line 51: | Line 52: | ||
| 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 | | -0.0351 | ||
| 0.0215 | | 0.0215 | ||
| Line 59: | Line 60: | ||
== Music == | == Music == | ||
; [[User:Francium|Francium]] | ; [[User:Francium|Francium]] | ||
* [https:// | * "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 | ||
Revision as of 12:42, 21 October 2023
| ← 2710edo | 2711edo | 2712edo → |
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
| 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 |