911edo

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← 910edo911edo912edo →
Prime factorization 911 (prime)
Step size 1.31723¢
Fifth 533\911 (702.086¢)
Semitones (A1:m2) 87:68 (114.6¢ : 89.57¢)
Consistency limit 5
Distinct consistency limit 5

911 equal divisions of the octave (abbreviated 911edo), or 911-tone equal temperament (911tet), 911 equal temperament (911et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 911 equal parts of about 1.32 ¢ each. Each step of 911edo represents a frequency ratio of 21/911, or the 911th root of 2.

911edo is consistent in the 5-odd-limit, tempering out the vulture comma, and is also a suitable 2.3.5.13.19.23 system, with a comma basis {41600/41553, 59375/59319, 186875/186624, 253125/252928, 2167425/2166784}. Though inconsistent to the 11-limit, the patent val tunes the rank-3 temperament hanuman.

Aside from the patent val, there is a number of mappings to be considered. 911c val provides an additional 282 & 911c extension to the escapade temperament, and 911cde val is a tuning for the 11-limit arch temperament of the same family.

Odd harmonics

Approximation of odd harmonics in 911edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +0.131 -0.364 +0.658 +0.261 +0.603 -0.132 -0.234 +0.423 +0.182 -0.528 +0.046
relative (%) +10 -28 +50 +20 +46 -10 -18 +32 +14 -40 +4
Steps
(reduced)
1444
(533)
2115
(293)
2558
(736)
2888
(155)
3152
(419)
3371
(638)
3559
(826)
3724
(80)
3870
(226)
4001
(357)
4121
(477)