873edo

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← 872edo873edo874edo →
Prime factorization 32 × 97
Step size 1.37457¢
Fifth 511\873 (702.405¢)
Semitones (A1:m2) 85:64 (116.8¢ : 87.97¢)
Consistency limit 7
Distinct consistency limit 7

873 equal divisions of the octave (abbreviated 873edo), or 873-tone equal temperament (873tet), 873 equal temperament (873et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 873 equal parts of about 1.37 ¢ each. Each step of 873edo represents a frequency ratio of 21/873, or the 873rd root of 2.

873edo is consistent to the 7-odd-limit, but the error of harmonic 3 is quite large. The equal temperament is most notable for tempering out the amity comma, 1600000/1594323, in the 5-limit, providing the optimal patent val for it.

Odd harmonics

Approximation of odd harmonics in 873edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +0.450 -0.059 +0.246 -0.474 -0.115 -0.665 +0.391 -0.488 -0.606 -0.678 -0.096
relative (%) +33 -4 +18 -34 -8 -48 +28 -36 -44 -49 -7
Steps
(reduced)
1384
(511)
2027
(281)
2451
(705)
2767
(148)
3020
(401)
3230
(611)
3411
(792)
3568
(76)
3708
(216)
3834
(342)
3949
(457)

Subsets and supersets

Since 873 factors into 32 × 97, 873edo has subset edos 3, 9, 97, and 291.