398edo
Theory
398et is only consistent to the 5-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 1280000000/1275989841, 65625/65536, 102760448/102515625 and 200120949/200000000 in the 7-limit; 1073741824/1071794405, 100663296/100656875, 161280/161051, 35156250/35153041, 2097152/2096325, 4000/3993, 2734375/2725888, 496125/495616, 131072/130977, 6250/6237, 9765625/9732096, 4302592/4296875, 352947/352000, 422576/421875, 184877/184320, 3025/3024, 9453125/9437184 and 456533/455625 in the 11-limit. It supports quartonic, yarman, bisupermajor and semiquindromeda.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.56 | -0.38 | -0.99 | +0.44 | +0.68 | +0.57 | +0.98 | -1.14 | -1.44 | +0.69 |
| Relative (%) | +0.0 | +18.5 | -12.7 | -32.7 | +14.6 | +22.5 | +19.0 | +32.5 | -37.8 | -47.6 | +23.0 | |
| Steps (reduced) |
398 (0) |
631 (233) |
924 (128) |
1117 (321) |
1377 (183) |
1473 (279) |
1627 (35) |
1691 (99) |
1800 (208) |
1933 (341) |
1972 (380) | |
Subsets and supersets
398 factors into 2 × 199, with 2edo and 199edo as its subset edos.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [631 -398⟩ | [⟨398 631]] | -0.1759 | 0.1759 | 5.83 |
| 2.3.5 | 390625000/387420489, [-53 10 16⟩ | [⟨398 631 924]] | -0.0622 | 0.2157 | 7.15 |
| 2.3.5.7 | 10976/10935, 65625/65536, 1280000000/1275989841 | [⟨398 631 924 1117]] | +0.0412 | 0.2588 | 8.58 |
| 2.3.5.7.11 | 3025/3024, 6250/6237, 10976/10935, 496125/495616 | [⟨398 631 924 1117 1377]] | +0.0075 | 0.2411 | 8.00 |
| 2.3.5.7.11.13 | 2080/2079, 625/624, 3025/3024, 4096/4095, 10976/10935 | [⟨398 631 924 1117 1377 1473]] | -0.0243 | 0.2313 | 7.67 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 5\398 | 15.08 | 126/125 | Yarman |
| 1 | 183\398 | 551.76 | 11/8 | Emka / Emkay |
| 2 | 54\398 | 162.81 | 11/10 | Kwazy / Bisupermajor |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct