2711edo: Difference between revisions
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== 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. | ||
===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" | ||
| Line 55: | Line 58: | ||
== Music == | == Music == | ||
*[https://www.youtube.com/watch?v=8prB_mBdKlo Ballad From A Broken Record] | ; [[User:Francium|Francium]] | ||
* [https://www.youtube.com/watch?v=8prB_mBdKlo ''Ballad From A Broken Record''] (2023) – [[hemischis]] in 2711edo tuning | |||
Revision as of 11:54, 15 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 |
Music
- Ballad From A Broken Record (2023) – hemischis in 2711edo tuning