429edo
| ← 428edo | 429edo | 430edo → |
Theory
429et is consistent to the 11-odd-limit. The equal temperament tempers out 65625/65536, 250047/250000, and 823543/820125 in the 7-limit; 3025/3024, 12005/11979, 19712/19683, 42875/42768, and 102487/102400 in the 11-limit. It supports vavoom, turkey, counterhanson and aluminium.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.14 | -0.30 | -0.99 | -0.27 | -1.37 | +1.34 | -1.01 | +1.10 | -0.21 | -0.98 |
| Relative (%) | +0.0 | +5.1 | -10.7 | -35.5 | -9.6 | -48.9 | +47.8 | -36.1 | +39.2 | -7.4 | -35.0 | |
| Steps (reduced) |
429 (0) |
680 (251) |
996 (138) |
1204 (346) |
1484 (197) |
1587 (300) |
1754 (38) |
1822 (106) |
1941 (225) |
2084 (368) |
2125 (409) | |
Subsets and supersets
429 factors into 3 × 11 × 13, with subset edos 3, 11, 13, 33, 39, and 143.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [680 -429⟩ | [⟨429 680]] | −0.0451 | 0.0451 | 1.61 |- | 2.3.5 | [24 -21 4⟩, [-20 -24 25⟩ | [⟨429 680 996]] | +0.0130 | 0.0900 | 3.22 |- | 2.3.5.7 | 65625/65536, 250047/250000, 823543/820125 | [⟨429 680 996 1204]] | +0.0982 | 0.1670 | 5.97 |- | 2.3.5.7.11 | 3025/3024, 12005/11979, 19712/19683, 102487/102400 | [⟨429 680 996 1204 1484]] | +0.0941 | 0.1496 | 5.35 |- | 2.3.5.7.11.13 | 676/675, 1001/1000, 3025/3024, 12005/11979, 19712/19683 | [⟨429 680 996 1204 1484 1587]] | +0.1400 | 0.1708 | 6.11 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 40\429
| 111.89
| 16/15
| Vavoom
|-
| 1
| 113\429
| 316.08
| 6/5
| Counterhanson
|-
| 1
| 170\429
| 475.52
| 320/243
| Vulture
|-
| 3
| 138\429
(5\429)
| 386.01
(13.99)
| 5/4
(126/125)
| Mutt
Template:Rank-2 end
Template:Orf