888edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 887edo888edo889edo →
Prime factorization 23 × 3 × 37
Step size 1.35135¢
Fifth 519\888 (701.351¢) (→173\296)
Semitones (A1:m2) 81:69 (109.5¢ : 93.24¢)
Sharp fifth 520\888 (702.703¢) (→65\111)
Flat fifth 519\888 (701.351¢) (→173\296)
Major 2nd 151\888 (204.054¢)
Consistency limit 3
Distinct consistency limit 3

888 equal divisions of the octave (888edo), or 888-tone equal temperament (888tet), 888 equal temperament (888et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 888 equal parts of about 1.35 ¢ each.

Theory

Approximation of odd harmonics in 888edo
Harmonic 3 5 7 9 11 13 15 17 19 21
Error absolute (¢) -0.604 +0.173 +0.093 +0.144 +0.033 +0.013 -0.431 +0.450 -0.216 -0.511
relative (%) -45 +13 +7 +11 +2 +1 -32 +33 -16 -38
Steps
(reduced)
1407
(519)
2062
(286)
2493
(717)
2815
(151)
3072
(408)
3286
(622)
3469
(805)
3630
(78)
3772
(220)
3900
(348)

888edo is excellent in the no-threes 13-limit, and it may possibly have little attention due to its lack of a perfect fifth. The usage of 3/2 is so deeply entrenched into nearly all musical traditions of the world, that temperaments which lack a perfect fifth do not get considered, even if other harmonics are excellently approximated.

888edo tempers out 6656/6655, 105644/105625, 4917248/4915625 and 35153041/35152000 in the no-threes 13 limit.