1429edo
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Prime factorization
1429 (prime)
Step size
0.839748¢
Fifth
836\1429 (702.029¢)
Semitones (A1:m2)
136:107 (114.2¢ : 89.85¢)
Consistency limit
9
Distinct consistency limit
9
| ← 1428edo | 1429edo | 1430edo → |
1429 equal divisions of the octave (1429edo), or 1429-tone equal temperament (1429tet), 1429 equal temperament (1429et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1429 equal parts of about 0.84 ¢ each.
Theory
1429et tempers out 4375/4374 in the 7-limit; 2657205/2656192, 759375/758912, 1953125/1951488, 2359296/2358125, 131072/130977, 369140625/369098752, 184549376/184528125, 645922816/645700815 and 3294225/3294172 in the 11-limit. It supports the gross temperament and the trillium temperament.
Subsets and supersets
1429edo is the 226th prime edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | +0.074 | -0.030 | +0.243 | +0.397 | +0.060 | +0.013 | -0.242 | -0.143 | -0.046 | +0.381 |
| relative (%) | +0 | +9 | -4 | +29 | +47 | +7 | +2 | -29 | -17 | -5 | +45 | |
| Steps (reduced) |
1429 (0) |
2265 (836) |
3318 (460) |
4012 (1154) |
4944 (657) |
5288 (1001) |
5841 (125) |
6070 (354) |
6464 (748) |
6942 (1226) |
7080 (1364) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [2265 -1429⟩ | ⟨1429 2265] | -0.0235 | 0.0234 | 2.80 |
| 2.3.5 | [39 -29 3⟩, [-66 -36 53⟩ | ⟨1429 2265 3318] | -0.0114 | 0.0257 | 3.06 |
| 2.3.5.7 | 4375/4374, [41 -15 -5 -2⟩, [-16 12 12 -11⟩ | ⟨1429 2265 3318 4012] | -0.0302 | 0.0395 | 4.70 |
| 2.3.5.7.11 | 4375/4374, 131072/130977, 759375/758912, 3294225/3294172 | ⟨1429 2265 3318 4012 4944] | -0.0471 | 0.0488 | 5.81 |
| 2.3.5.7.11.13 | 2080/2079, 4225/4224, 59319/59290, 67392/67375, 91125/91091, 27227340/27217619 | ⟨1429 2265 3318 4012 4944 5288] | -0.0420 | 0.0460 | 5.48 |
| 2.3.5.7.11.13.17 | 2080/2079, 2500/2499, 4225/4224, 12376/12375, 14875/14872, 108086/108045, 149175/149072, 1783600/1783419 | ⟨1429 2265 3318 4012 4944 5288 5841] | -0.0364 | 0.0447 | 5.32 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 109\1429 | 91.533 | [144 -22 -47⟩ | Gross |
| 1 | 674\1429 | 565.990 | 25/18 | Tricot |
Scales
Music
- Gross Pattern by Francium