789edo: Difference between revisions

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{{EDO intro|789}}
{{EDO intro|789}}


789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]].
789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]. It also has very accurate representations of the 9th, 17th, and 23rd harmonics.  


=== Odd harmonics ===
=== Odd harmonics ===

Revision as of 11:11, 4 September 2024

← 788edo 789edo 790edo →
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

Template:EDO intro

789edo is notable for an extremely good approximation of the 2.5.7 subgroup, unbeaten until 5902edo. It also has very accurate representations of the 9th, 17th, and 23rd harmonics.

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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