4380edo

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← 4379edo4380edo4381edo →
Prime factorization 22 × 3 × 5 × 73
Step size 0.273973¢
Fifth 2562\4380 (701.918¢) (→427\730)
Semitones (A1:m2) 414:330 (113.4¢ : 90.41¢)
Consistency limit 31
Distinct consistency limit 31

4380 equal divisions of the octave (abbreviated 4380edo), or 4380-tone equal temperament (4380tet), 4380 equal temperament (4380et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4380 equal parts of about 0.274 ¢ each. Each step of 4380edo represents a frequency ratio of 21/4380, or the 4380th root of 2.

4380edo is consistent in the 31-odd-limit and has the lowest relative error in the 47-limit, being only beaten by the 7361o val.

In light of having 60 as a divisor, 4380edo is a tuning for the neodymium temperament in the 17-limit. It is worth noting that 4380edo tempers out the magnetisma on its 43-limit patent val, and therefore tunes the extension neodymium magnet.

Prime harmonics

Approximation of prime harmonics in 4380edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 -0.037 -0.012 -0.059 -0.085 +0.020 -0.024 +0.021 -0.055 +0.012 -0.104
relative (%) +0 -14 -5 -21 -31 +7 -9 +8 -20 +4 -38
Steps
(reduced)
4380
(0)
6942
(2562)
10170
(1410)
12296
(3536)
15152
(2012)
16208
(3068)
17903
(383)
18606
(1086)
19813
(2293)
21278
(3758)
21699
(4179)

Subsets and supersets

4380edo has subset edos 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 73, 146, 219, 292, 365, 438, 730, 876, 1095, 1460, 2190. One step of 4380edo is one sixth of a Woolhouse unit (1\730).