810edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 809edo810edo811edo →
Prime factorization 2 × 34 × 5
Step size 1.48148¢ 
Fifth 474\810 (702.222¢) (→79\135)
Semitones (A1:m2) 78:60 (115.6¢ : 88.89¢)
Consistency limit 9
Distinct consistency limit 9

810 equal divisions of the octave (abbreviated 810edo or 810ed2), also called 810-tone equal temperament (810tet) or 810 equal temperament (810et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 810 equal parts of about 1.48 ¢ each. Each step represents a frequency ratio of 21/810, or the 810th root of 2.

Prime harmonics

Approximation of prime harmonics in 810edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error Absolute (¢) +0.000 +0.267 +0.353 +0.063 -0.207 -0.528 +0.230 +0.265 -0.126 +0.052 +0.150 +0.508 +0.567 -0.407 -0.321
Relative (%) +0.0 +18.0 +23.8 +4.3 -14.0 -35.6 +15.5 +17.9 -8.5 +3.5 +10.1 +34.3 +38.3 -27.4 -21.7
Steps
(reduced)
810
(0)
1284
(474)
1881
(261)
2274
(654)
2802
(372)
2997
(567)
3311
(71)
3441
(201)
3664
(424)
3935
(695)
4013
(773)
4220
(170)
4340
(290)
4395
(345)
4499
(449)

Subsets and supersets

Since 810 factors into 2 × 34 × 5, 810edo has subset edos 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405.


Icon-Stub.png This page is a stub. You can help the Xenharmonic Wiki by expanding it.