119edo: Difference between revisions
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=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|119|columns= | {{Harmonics in equal|119|columns=12}} | ||
{{Harmonics in equal|119|columns=12|start=13|collapsed=1|title=Approximation of odd harmonics in 84edo (continued)}} | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 119edo factors as {{Factorization|119}}, it contains [[7edo]] and [[17edo]] as a subset. Hence it supports circles of fifths of those respective equal temperaments. | Since 119edo factors as {{Factorization|119}}, it contains [[7edo]] and [[17edo]] as a subset. Hence it supports circles of fifths of those respective equal temperaments. | ||
Revision as of 09:48, 25 January 2024
| ← 118edo | 119edo | 120edo → |
Theory
119edo is inconsistent in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.
Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the optimal patent val for the 11-limit androboh and quasitemp temperaments. The patent val also tunes the 11-limit quadrawell temperament. 119c val tunes treecreeper, sensus, and senator as high as the 17-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.93 | -3.12 | -0.76 | -2.23 | +3.30 | -3.55 | +0.81 | -4.12 | +5.01 | +3.17 | -3.06 | +3.84 |
| Relative (%) | +38.9 | -30.9 | -7.5 | -22.1 | +32.8 | -35.2 | +8.0 | -40.8 | +49.7 | +31.4 | -30.4 | +38.1 | |
| Steps (reduced) |
189 (70) |
276 (38) |
334 (96) |
377 (20) |
412 (55) |
440 (83) |
465 (108) |
486 (10) |
506 (30) |
523 (47) |
538 (62) |
553 (77) | |
| Harmonic | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | 47 | 49 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.70 | -1.01 | +4.54 | -2.85 | -3.88 | +0.76 | +0.37 | +4.55 | +2.77 | +4.73 | +0.04 | -1.52 |
| Relative (%) | +16.8 | -10.0 | +45.1 | -28.3 | -38.5 | +7.5 | +3.7 | +45.1 | +27.4 | +46.9 | +0.4 | -15.0 | |
| Steps (reduced) |
566 (90) |
578 (102) |
590 (114) |
600 (5) |
610 (15) |
620 (25) |
629 (34) |
638 (43) |
646 (51) |
654 (59) |
661 (66) |
668 (73) | |
Subsets and supersets
Since 119edo factors as 7 × 17, it contains 7edo and 17edo as a subset. Hence it supports circles of fifths of those respective equal temperaments.
Scales
- Approximation of 2/7 comma meantone: 19 19 19 12 19 19 19 19 12
- Approximation of half comma eventone: 23 23 2 23 23 23 2, 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2