335edo
Theory
335et only is consistent to the 5-odd-limit. Using the patent val, it tempers out the parakleisma in the 5-limit; 4375/4374 and 3136/3125 in the 7-limit, supporting turan, quintosec, tricot, pseudotrillium, lifthrasir, tritomere, counterwürschmidt and gaster. Using the 335d val (⟨335 531 778 ‚‘‘991‘‘‘]), it tempers out 6144/6125, 16875/16807 and 14348907/14336000 in the 7-limit, supporting grendel.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.13 | +0.55 | -1.66 | +0.32 | +1.26 | -1.07 | -0.20 | -1.41 | -1.52 | +1.23 |
| Relative (%) | +0.0 | +3.8 | +15.4 | -46.4 | +9.0 | +35.3 | -30.0 | -5.6 | -39.3 | -42.4 | +34.4 | |
| Steps (reduced) |
335 (0) |
531 (196) |
778 (108) |
940 (270) |
1159 (154) |
1240 (235) |
1369 (29) |
1423 (83) |
1515 (175) |
1627 (287) |
1660 (320) | |
Subsets and supersets
335 factors into 5 × 67 with 5edo and 67edo as its subset edos. 670edo, which doubles it, gives a good correction to the harmonic 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [531 -335⟩ | [⟨335 531]] | -0.0424 | 0.0424 | 1.18 |
| 2.3.5 | [8 14 -13⟩, [47 -15 -10⟩ | [⟨335 531 778]] | -0.1075 | 0.0984 | 2.75 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced)* |
Cents (reduced)* |
Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 88\335 | 315.22 | 6/5 | Parakleismic |
| 1 | 158\335 | 565.97 | 104/75 | Tricot |
| 5 | 232\335 (31\335) |
831.04 (111.04) |
80/49 (16/15) |
Qintosec |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct