636edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 635edo636edo637edo →
Prime factorization 22 × 3 × 53
Step size 1.88679¢ 
Fifth 372\636 (701.887¢) (→31\53)
Semitones (A1:m2) 60:48 (113.2¢ : 90.57¢)
Consistency limit 5
Distinct consistency limit 5

636 equal divisions of the octave (abbreviated 636edo or 636ed2), also called 636-tone equal temperament (636tet) or 636 equal temperament (636et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 636 equal parts of about 1.89 ¢ each. Each step represents a frequency ratio of 21/636, or the 636th root of 2.

Theory

636 = 12 × 53, and 636edo shares the excellent harmonic 3 with 53edo.

Odd harmonics

Approximation of odd harmonics in 636edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.068 +0.479 -0.901 -0.136 -0.375 -0.905 +0.411 +0.705 +0.600 +0.917 +0.028
Relative (%) -3.6 +25.4 -47.8 -7.2 -19.9 -48.0 +21.8 +37.4 +31.8 +48.6 +1.5
Steps
(reduced)
1008
(372)
1477
(205)
1785
(513)
2016
(108)
2200
(292)
2353
(445)
2485
(577)
2600
(56)
2702
(158)
2794
(250)
2877
(333)

Subsets and supersets

Since 636 factors into 22 × 3 × 53, 636edo has subset edos 2, 3, 4, 6, 12, 53, 106, 159, 212, and 318.

Intervals

see Table of 636edo intervals