2129edo

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← 2128edo2129edo2130edo →
Prime factorization 2129 (prime)
Step size 0.563645¢
Fifth 1245\2129 (701.738¢)
Semitones (A1:m2) 199:162 (112.2¢ : 91.31¢)
Dual sharp fifth 1246\2129 (702.302¢)
Dual flat fifth 1245\2129 (701.738¢)
Dual major 2nd 362\2129 (204.039¢)
Consistency limit 5
Distinct consistency limit 5

2129 equal divisions of the octave (2129edo), or 2129-tone equal temperament (2129tet), 2129 equal temperament (2129et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 2129 equal parts of about 0.564 ¢ each.

Theory

2129et tempers out 95703125/95664294, 5767168/5764801, 47265625/47258883, 67110351/67108864 and 43923/43904 in the 11-limit; 33792000/33787663, 200000/199927, 34034175/34027136, 2250423/2249390, 78125/78078, 1449459/1449175, 1990656/1990625, 67392/67375, 4225/4224, 8858304/8857805, 59319/59290 and 4084223/4084101 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 2129edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) -0.217 -0.217 +0.080 +0.129 -0.073 -0.133 +0.130 -0.117 +0.091 -0.137 +0.190
relative (%) -39 -38 +14 +23 -13 -24 +23 -21 +16 -24 +34
Steps
(reduced)
3374
(1245)
4943
(685)
5977
(1719)
6749
(362)
7365
(978)
7878
(1491)
8318
(1931)
8702
(186)
9044
(528)
9351
(835)
9631
(1115)

Subsets and supersets

2129edo is the 320th prime edo. 4258edo, which doubles it, gives a good correction to the harmonics 3 and 5.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [-6749 2129 2129 6749] -0.0204 0.0204 3.62
2.9.15 [37 29 -33, [209 -61 -4 2129 6749 8318] -0.0247 0.0177 3.14
2.9.15.7 24414062500/24407490807, 13841287201/13839609375, 2199023255552/2197176384375 2129 6749 8318 5977] -0.0256 0.0154 2.73
2.9.15.7.11 9800/9801, 5767168/5764801, 104857600/104825259, 13841287201/13839609375 2129 6749 8318 5977 7365] -0.0162 0.0232 4.12
2.9.15.7.11.13 10648/10647, 9801/9800, 196625/196608, 36924979/36905625, 304117528/303807105 2129 6749 8318 5977 7365 7878] -0.0075 0.0288 5.11
2.9.15.7.11.13.17 2431/2430, 10648/10647, 9801/9800, 845325/845152, 297440/297381, 11275335/11275264, 15980544/15978655 2129 6749 8318 5977 7365 7878 8702] -0.0024 0.0295 5.2

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator
(reduced)
Cents
(reduced)
Associated
ratio
Temperaments
1 442\2129 249.131 81/70 Hemischis (5-limit)
1 884\2129 498.262 4/3 Helmholtz

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