281edo

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← 280edo281edo282edo →
Prime factorization 281 (prime)
Step size 4.27046¢ 
Fifth 164\281 (700.356¢)
Semitones (A1:m2) 24:23 (102.5¢ : 98.22¢)
Dual sharp fifth 165\281 (704.626¢)
Dual flat fifth 164\281 (700.356¢)
Dual major 2nd 48\281 (204.982¢)
Consistency limit 5
Distinct consistency limit 5

281 equal divisions of the octave (abbreviated 281edo or 281ed2), also called 281-tone equal temperament (281tet) or 281 equal temperament (281et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 281 equal parts of about 4.27 ¢ each. Each step represents a frequency ratio of 21/281, or the 281st root of 2.

The equal temperament tempers out 225/224 in the 7-limit, and 243/242 and 4000/3993 in the 11-limit, so that it supports marvo and provides the optimal patent val; it also gives the optimal patent val for the rank-3 spectacle temperament.

Odd harmonics

Approximation of odd harmonics in 281edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.60 -1.97 +0.57 +1.07 -0.43 +0.75 +0.70 +1.81 +1.42 -1.03 -0.52
Relative (%) -37.4 -46.2 +13.3 +25.1 -10.0 +17.6 +16.4 +42.3 +33.2 -24.1 -12.1
Steps
(reduced)
445
(164)
652
(90)
789
(227)
891
(48)
972
(129)
1040
(197)
1098
(255)
1149
(25)
1194
(70)
1234
(110)
1271
(147)

Subsets and supersets

281edo is the 60th prime edo.