1429edo

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← 1428edo1429edo1430edo →
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

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

Approximation of prime harmonics in 1429edo
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

Table of rank-2 temperaments by generator
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