20160edo

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← 20159edo20160edo20161edo →
Prime factorization 26 × 32 × 5 × 7
Step size 0.0595238¢
Fifth 11793\20160 (701.964¢) (→3931\6720)
Semitones (A1:m2) 1911:1515 (113.8¢ : 90.18¢)
Consistency limit 7
Distinct consistency limit 7
Special properties

20160 equal divisions of the octave (abbreviated 20160edo), or 20160-tone equal temperament (20160tet), 20160 equal temperament (20160et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 20160 equal parts of about 0.0595 ¢ each. Each step of 20160edo represents a frequency ratio of 21/20160, or the 20160th root of 2.

20160edo is the 23rd highly composite edo, although it is not a member of the superabundant edos. It is also a highly factorable number edo, carrying the trait of being broken down into subsets into more ways than any number before it.

Aside from divisors, it is an excellent no-7s 29-limit system, having errors of 25% or less, and with the 28% error on the 7th harmonic it is overall a satisfactory 29-limit tuning, making it a candidate for an interval size measure.

Eliora proposes that one step of 20160edo be called pian, since piano manufacturers have a tendency to avoid the prominence of 7th harmonic in their sound. A semitone is therefore 1680 pians, a step of 224edo is 90 pians, and the Dröbisch angle, one step of 360edo, is 56 pians.

Prime harmonics

Approximation of prime harmonics in 20160edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.0000 +0.0093 -0.0042 -0.0164 -0.0084 +0.0081 -0.0149 -0.0130 -0.0005 +0.0061 +0.0240
relative (%) +0 +16 -7 -28 -14 +14 -25 -22 -1 +10 +40
Steps
(reduced)
20160
(0)
31953
(11793)
46810
(6490)
56596
(16276)
69742
(9262)
74601
(14121)
82403
(1763)
85638
(4998)
91195
(10555)
97937
(17297)
99877
(19237)