109edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
109edo is the 29th [[prime EDO]]. | 109edo is the 29th [[prime EDO]]. | ||
=== Nonoctave temperaments === | |||
Taking every 8 degree of 109edo produces a scale extremely close to [[88cET]]. | |||
[[Category:Equal divisions of the octave|###]]<!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]]<!-- 3-digit number --> | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||
Revision as of 21:47, 16 January 2024
| ← 108edo | 109edo | 110edo → |
Theory
109edo tempers out 20000/19683 in the 5-limit; 245/243, 2401/2400 and 65625/65536 in the 7-limit; 385/384, 1375/1372, and 4000/3993 in the 11-limit. It provides the optimal patent val for 7-limit octacot temperament, and 11 and 13 limit leapweek; plus 109ef provides an excellent tuning for 11- and 13-limit octacot.
109edo is a strong 2.5.7.11.19.23.31 subgroup tuning, with errors of less than 10% on all harmonics and an exceptionally small error of 0.16% on the 7th harmonic.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +2.63 | -0.99 | -0.02 | -0.86 | -3.83 | +5.14 | -0.27 | -0.75 | +5.29 | -0.08 |
| Relative (%) | +0.0 | +23.9 | -9.0 | -0.2 | -7.8 | -34.8 | +46.7 | -2.4 | -6.8 | +48.0 | -0.7 | |
| Steps (reduced) |
109 (0) |
173 (64) |
253 (35) |
306 (88) |
377 (50) |
403 (76) |
446 (10) |
463 (27) |
493 (57) |
530 (94) |
540 (104) | |
Subsets and supersets
109edo is the 29th prime EDO.
Nonoctave temperaments
Taking every 8 degree of 109edo produces a scale extremely close to 88cET.