451edo
Theory
451et is consistent to the 7-odd-limit. Using the patent val, it tempers out 52734375/52706752, 703125/702464, 65625/65536, 2401/2400, 2100875/2097152 and 201768035/201326592 in the 7-limit; 117440512/117406179, 35156250/35153041, 234375/234256, 536870912/535869675, 104857600/104825259, 131072/130977, 6250/6237, 200704/200475, 42875/42768, 1879453125/1879048192, 1362944/1361367, 42592/42525, 166375/165888, 456533/455625, 3294225/3294172, 43923/43904 and 102487/102400 in the 11-limit. It supports hemermacomp, quartonic and tertiseptisix.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.48 | -0.50 | -0.31 | -0.54 | +0.27 | -1.19 | +0.49 | -0.34 | +0.13 | -0.91 |
| Relative (%) | +0.0 | +18.2 | -19.0 | -11.7 | -20.4 | +10.2 | -44.6 | +18.5 | -12.6 | +5.1 | -34.3 | |
| Steps (reduced) |
451 (0) |
715 (264) |
1047 (145) |
1266 (364) |
1560 (207) |
1669 (316) |
1843 (39) |
1916 (112) |
2040 (236) |
2191 (387) |
2234 (430) | |
Subsets and supersets
451 factors into 11 × 41, with 11edo and 41edo as its subset edos.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [65 -41⟩ | [⟨451 715]] | -0.1527 | 0.1527 | 5.74 |
| 2.3.5 | [3 -18 11⟩, [-59 5 22⟩ | [⟨451 715 1047]] | -0.0294 | 0.2144 | 8.06 |
| 2.3.5.7 | 2401/2400, 703125/702464, 390625000/387420489 | [⟨451 715 1047 1266]] | +0.0057 | 0.1953 | 7.34 |
| 2.3.5.7.11 | 2401/2400, 6250/6237, 42592/42525, 43923/43904 | [⟨451 715 1047 1266 1560]] | +0.0359 | 0.1849 | 6.95 |
| 2.3.5.7.11.13 | 2080/2079, 625/624, 4459/4455, 2200/2197, 20449/20412 | [⟨451 715 1047 1266 1560 1669]] | +0.0177 | 0.1736 | 6.52 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 29\451 | 77.16 | 256/245 | Tertiaseptal |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct