3224edo

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← 3223edo3224edo3225edo →
Prime factorization 23 × 13 × 31
Step size 0.372208¢ 
Fifth 1886\3224 (701.985¢) (→943\1612)
Semitones (A1:m2) 306:242 (113.9¢ : 90.07¢)
Consistency limit 17
Distinct consistency limit 17

3224 equal divisions of the octave (abbreviated 3224edo or 3224ed2), also called 3224-tone equal temperament (3224tet) or 3224 equal temperament (3224et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3224 equal parts of about 0.372 ¢ each. Each step represents a frequency ratio of 21/3224, or the 3224th root of 2.

3224edo is consistent in the 17-odd-limit and is a strong no-19s 29-limit tuning. It improves 1612edo's mapping of 7 and 11.

It tunes a number of rank-3 very high accuracy temperaments, tempering out [3 -24 3 10, [0 -11 -7 12, [-3 2 -17 14.

Prime harmonics

Approximation of prime harmonics in 3224edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 +0.030 +0.039 +0.033 -0.077 -0.081 +0.007 -0.118 +0.013 -0.049 -0.122
relative (%) +0 +8 +10 +9 -21 -22 +2 -32 +4 -13 -33
Steps
(reduced)
3224
(0)
5110
(1886)
7486
(1038)
9051
(2603)
11153
(1481)
11930
(2258)
13178
(282)
13695
(799)
14584
(1688)
15662
(2766)
15972
(3076)