446edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 445edo446edo447edo →
Prime factorization 2 × 223
Step size 2.69058¢
Fifth 261\446 (702.242¢)
Semitones (A1:m2) 43:33 (115.7¢ : 88.79¢)
Consistency limit 5
Distinct consistency limit 5

446 equal divisions of the octave (abbreviated 446edo or 446ed2), also called 446-tone equal temperament (446tet) or 446 equal temperament (446et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 446 equal parts of about 2.691 ¢ each. Each step represents a frequency ratio of 21/446, or the 446th root of 2.

446edo is only consistent to the 5-odd-limit and the error of harmonic 5 is quite large. The equal temperament tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the optimal patent val for the hemimean temperament tempering out 3136/3125, and sengagen, the 99 & 347 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 198 & 248 temperament.

Odd harmonics

Approximation of odd harmonics in 446edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +0.29 +1.13 -0.22 +0.57 +0.25 -1.07 -1.27 -0.02 +1.14 +0.07 +1.32
relative (%) +11 +42 -8 +21 +9 -40 -47 -1 +42 +3 +49
Steps
(reduced)
707
(261)
1036
(144)
1252
(360)
1414
(76)
1543
(205)
1650
(312)
1742
(404)
1823
(39)
1895
(111)
1959
(175)
2018
(234)

Subsets and supersets

Since 446 factors into 2 × 223, 446edo contains 2edo and 223edo as subsets.