497edo
| ← 496edo | 497edo | 498edo → |
Theory
497et only is consistent to the 5-limit. Using the patent val, it tempers out 67108864/66976875, 48828125/48771072, 2100875/2097152 and 200120949/200000000 in the 7-limit; 117440512/117406179, 26796875/26763264, 151263/151250, 131072/130977, 42875/42768, 4302592/4296875, 5632/5625, 537109375/536870912, 9453125/9437184, 160083/160000, 1362944/1361367, 391314/390625, 43923/43904 and 644204/643125 in the 11-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.66 | +0.00 | -0.62 | -1.09 | -0.81 | -0.29 | +0.66 | -1.13 | -0.53 | +0.04 | -0.51 |
| Relative (%) | +27.4 | +0.2 | -25.5 | -45.3 | -33.8 | -11.9 | +27.5 | -46.9 | -22.0 | +1.8 | -21.0 | |
| Steps (reduced) |
788 (291) |
1154 (160) |
1395 (401) |
1575 (84) |
1719 (228) |
1839 (348) |
1942 (451) |
2031 (43) |
2111 (123) |
2183 (195) |
2248 (260) | |
Subsets and supersets
497 factors into 7 × 41, with 7edo and 41edo as its subset edos. 1491edo, which triples 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 | [788 -497⟩ | [⟨497 788]] | -0.2084 | 0.2084 | 8.63 |
| 2.3.5 | [38 -2 -15⟩, ⟨12 -31 16] | [⟨497 788 1154]] | -0.1396 | 0.1961 | 8.12 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced)* |
Cents (reduced)* |
Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 80\497 | 193.16 | 262144/234375 | Luna |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct