789edo

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← 788edo789edo790edo →
Prime factorization 3 × 263
Step size 1.52091¢ 
Fifth 462\789 (702.662¢) (→154\263)
Semitones (A1:m2) 78:57 (118.6¢ : 86.69¢)
Dual sharp fifth 462\789 (702.662¢) (→154\263)
Dual flat fifth 461\789 (701.141¢)
Dual major 2nd 134\789 (203.802¢)
Consistency limit 7
Distinct consistency limit 7

789 equal divisions of the octave (abbreviated 789edo or 789ed2), also called 789-tone equal temperament (789tet) or 789 equal temperament (789et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 789 equal parts of about 1.52 ¢ each. Each step represents a frequency ratio of 21/789, or the 789th root of 2.

789edo is notable for an extremely good approximation of the 2.5.7 subgroup, unbeaten until 3945edo. It also has a very accurate representation of the 17th harmonic and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

1578edo, which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong 11-limit and higher-limit system.

Odd harmonics

Approximation of odd harmonics in 789edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.707 -0.002 -0.005 -0.108 -0.748 +0.537 +0.705 -0.012 +0.586 +0.702 -0.137
Relative (%) +46.5 -0.1 -0.3 -7.1 -49.2 +35.3 +46.3 -0.8 +38.5 +46.2 -9.0
Steps
(reduced)
1251
(462)
1832
(254)
2215
(637)
2501
(134)
2729
(362)
2920
(553)
3083
(716)
3225
(69)
3352
(196)
3466
(310)
3569
(413)
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