2711edo: Difference between revisions
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→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) |
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== Theory == | == Theory == | ||
Revision as of 04:35, 9 July 2023
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
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This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 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 |