78005edo

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← 78004edo78005edo78006edo →
Prime factorization 5 × 15601
Step size 0.0153836¢ 
Fifth 45630\78005 (701.955¢) (→9126\15601)
Semitones (A1:m2) 7390:5865 (113.7¢ : 90.22¢)
Consistency limit 21
Distinct consistency limit 21

78005 equal divisions of the octave (abbreviated 78005edo or 78005ed2), also called 78005-tone equal temperament (78005tet) or 78005 equal temperament (78005et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 78005 equal parts of about 0.0154 ¢ each. Each step represents a frequency ratio of 21/78005, or the 78005th root of 2.

While 78005edo is distinctly consistent through the 21-odd-limit, its notability stems from the fact that it is a very strong 5-limit system, with lower 5-limit relative error than any smaller edo, and lower 5-limit TE logflat badness than any smaller edo excepting 4296. The equal temperament tempers out [232 -183 25, [324 8 -145, [92 191 -170, [140 -374 195, the selenia [-433 -137 280, and the quark [-573 237 85.

Prime harmonics

Approximation of prime harmonics in 78005edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.00000 +0.00000 -0.00002 +0.00430 +0.00056 +0.00307 +0.00709 +0.00637 -0.00693 +0.00296 -0.00128
relative (%) +0 +0 -0 +28 +4 +20 +46 +41 -45 +19 -8
Steps
(reduced)
78005
(0)
123635
(45630)
181122
(25112)
218988
(62978)
269853
(35838)
288653
(54638)
318843
(6823)
331360
(19340)
352860
(40840)
378947
(66927)
386452
(74432)

Subsets and supersets

78005edo contains 15601edo, from which the approximation of the 3rd harmonic is derived.