848edo

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← 847edo848edo849edo →
Prime factorization 24 × 53
Step size 1.41509¢
Fifth 496\848 (701.887¢) (→31\53)
Semitones (A1:m2) 80:64 (113.2¢ : 90.57¢)
Consistency limit 15
Distinct consistency limit 15

848 equal divisions of the octave (abbreviated 848edo), or 848-tone equal temperament (848tet), 848 equal temperament (848et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 848 equal parts of about 1.42 ¢ each. Each step of 848edo represents a frequency ratio of 21/848, or the 848th root of 2.

848edo is consistent to the 15-odd-limit and contains the famous 53edo as a subset. In the 5-limit, it is a very strong system, which tempers out the Mercator's comma. It also tunes kwazy and provides the optimal patent val for the 5-limit geb temperament.

In higher limits, it is a strong 2.3.5.13.23 subgroup system, with optional additions of either 7 and 11 or 17 and 19. It provides the optimal patent val for sextantonic, the rank-4 temperament tempering out 2601/2600 in the 2.3.5.13.17 subgroup.

Prime harmonics

Approximation of prime harmonics in 848edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 -0.068 +0.007 +0.514 +0.569 +0.038 -0.238 -0.343 +0.028 +0.611 -0.224
relative (%) +0 -5 +0 +36 +40 +3 -17 -24 +2 +43 -16
Steps
(reduced)
848
(0)
1344
(496)
1969
(273)
2381
(685)
2934
(390)
3138
(594)
3466
(74)
3602
(210)
3836
(444)
4120
(728)
4201
(809)

Subsets and supersets

Since 848 factors into 24 × 53, 848edo has subset edos 2, 4, 8, 16, 53, 106, 212, and 424.