277edo
Theory
277et tempers out 32805/32768 (schisma) and |-11 -37 30> in the 5-limit.
Using the patent val, it tempers out 4375/4374, 65625/65536, and 829440/823543 in the 7-limit; 540/539, 6250/6237, 15488/15435, and 35937/35840 in the 11-limit; 625/624, 729/728, 1573/1568, 2080/2079, and 2200/2197 in the 13-limit.
Using the 277d val, it tempers out 1029/1024, 10976/10935, and 48828125/48771072 in the 7-limit; 385/384, 441/440, 19712/19683, and 234375/234256 in the 11-limit; 625/624, 847/845, 1001/1000, and 1575/1573 in the 13-limit.
The patent val supports the pontiac, and the 277d val supports the guiron and the widefourth.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.15 | -0.75 | +1.57 | -1.14 | -0.09 | -0.98 | +1.40 | -0.12 | +1.47 | -1.35 |
| Relative (%) | +0.0 | -3.5 | -17.4 | +36.3 | -26.3 | -2.2 | -22.7 | +32.4 | -2.7 | +33.9 | -31.2 | |
| Steps (reduced) |
277 (0) |
439 (162) |
643 (89) |
778 (224) |
958 (127) |
1025 (194) |
1132 (24) |
1177 (69) |
1253 (145) |
1346 (238) |
1372 (264) | |
Subsets and supersets
277edo is the 59th prime EDO.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-439 277⟩ | ⟨277 439] | 0.0473 | 0.0473 | 1.09 |
| 2.3.5 | 32805/32768, [-11 -37 30⟩ | ⟨277 439 643] | 0.1398 | 0.1364 | 3.15 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 115\277 | 498.19 | 4/3 | Helmholtz |