1419edo

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← 1418edo1419edo1420edo →
Prime factorization 3 × 11 × 43
Step size 0.845666¢
Fifth 830\1419 (701.903¢)
Semitones (A1:m2) 134:107 (113.3¢ : 90.49¢)
Consistency limit 25
Distinct consistency limit 25

1419 equal divisions of the octave (abbreviated 1419edo), or 1419-tone equal temperament (1419tet), 1419 equal temperament (1419et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1419 equal parts of about 0.846 ¢ each. Each step of 1419edo represents a frequency ratio of 21/1419, or the 1419th root of 2.

1419edo is consistent in the 25-odd-limit, and with excellent representation of 31/16 it is a strong no-29's 37-limit tuning. It is also an impressive system in even higher limits, with good tunings on harmonics 43, 47, and 53.

Prime harmonics

Approximation of prime harmonics in 1419edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 -0.052 +0.156 +0.307 +0.056 +0.064 -0.093 +0.161 +0.055 -0.402 -0.004
relative (%) +0 -6 +18 +36 +7 +8 -11 +19 +7 -48 -0
Steps
(reduced)
1419
(0)
2249
(830)
3295
(457)
3984
(1146)
4909
(652)
5251
(994)
5800
(124)
6028
(352)
6419
(743)
6893
(1217)
7030
(1354)

Subsets and supersets

Since 1419 factors into 3 × 11 × 43, 1419edo has subset edos 3, 11, 33, 43, 129, and 473.