324296edo

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← 324295edo 324296edo 324297edo →
Prime factorization 23 × 7 × 5791
Step size 0.00370032¢ 
Fifth 189701\324296 (701.955¢)
Semitones (A1:m2) 30723:24383 (113.7¢ : 90.22¢)
Consistency limit 59
Distinct consistency limit 59

324296 equal divisions of the octave (abbreviated 324296edo or 324296ed2), also called 324296-tone equal temperament (324296tet) or 324296 equal temperament (324296et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 324296 equal parts of about 0.0037 ¢ each. Each step represents a frequency ratio of 21/324296, or the 324296th root of 2.

324296edo is notable for being an exceptionally good representation of the 47-limit, being the first EDO with Dirichlet badness in this limit less than 1, and is distinctly consistent in the 59-limit.

Odd harmonics

Approximation of prime harmonics in 324296edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59
Error Absolute (¢) +0.00000 +0.00000 +0.00002 +0.00010 +0.00061 +0.00074 +0.00056 +0.00037 -0.00018 +0.00072 -0.00017 +0.00041 +0.00117 +0.00017 +0.00020 +0.00114 +0.00144
Relative (%) +0.0 +0.1 +0.7 +2.8 +16.4 +20.1 +15.0 +9.9 -4.8 +19.5 -4.7 +11.1 +31.5 +4.5 +5.4 +30.8 +39.0
Steps
(reduced)
324296
(0)
513997
(189701)
752992
(104400)
910414
(261822)
1121880
(148992)
1200038
(227150)
1325548
(28364)
1377586
(80402)
1466973
(169789)
1575424
(278240)
1606626
(309442)
1689405
(67925)
1737433
(115953)
1759716
(138236)
1801331
(179851)
1857542
(236062)
1907718
(286238)