759edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|759}}
{{EDO intro|759}}


759edo is [[enfactoring|enfactored]] in the [[5-limit]], with the same tuning as [[253edo]]. With octave stretching, one may use 2.7.11.13 subgroup, all sharp, or 2.5.17.19.23.29.31 subgroup, all tuned flat. 759def val tunes [[noletaland]], 282 & 1323 temperament, in the 23-limit. 759edo is an amazingly accurate 2.3.37.103.229 system.
759 = 3 × 253, and 759edo shares its excellent perfect fifth with [[253edo]]. However, the primes [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]] are mapped differently. With [[stretched and compressed tuning|octave stretching]], one may use 2.7.11.13 subgroup, all sharp, or 2.5.17.19.23.29.31 subgroup, all tuned flat. The 759def val [[support]]s [[noletaland]], the 282 & 759def temperament, in the 23-limit. 759edo is an amazingly accurate 2.3.37.103.229 system. <!-- explain the significance of this subgroup -->


=== Prime harmonics ===
{{Harmonics in equal|759}}
{{Harmonics in equal|759}}


=== Subsets and supersets ===
=== Subsets and supersets ===
759edo notably contains [[253edo]].
759edo notably contains [[253edo]].

Revision as of 09:37, 14 February 2025

← 758edo 759edo 760edo →
Prime factorization 3 × 11 × 23
Step size 1.58103 ¢ 
Fifth 444\759 (701.976 ¢) (→ 148\253)
Semitones (A1:m2) 72:57 (113.8 ¢ : 90.12 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro

759 = 3 × 253, and 759edo shares its excellent perfect fifth with 253edo. However, the primes 5, 7, 11, and 13 are mapped differently. With octave stretching, one may use 2.7.11.13 subgroup, all sharp, or 2.5.17.19.23.29.31 subgroup, all tuned flat. The 759def val supports noletaland, the 282 & 759def temperament, in the 23-limit. 759edo is an amazingly accurate 2.3.37.103.229 system.

Prime harmonics

Approximation of prime harmonics in 759edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.021 -0.543 +0.344 +0.461 +0.579 -0.608 -0.280 -0.606 -0.328 -0.372
Relative (%) +0.0 +1.3 -34.3 +21.8 +29.1 +36.6 -38.4 -17.7 -38.4 -20.8 -23.5
Steps
(reduced)
759
(0)
1203
(444)
1762
(244)
2131
(613)
2626
(349)
2809
(532)
3102
(66)
3224
(188)
3433
(397)
3687
(651)
3760
(724)

Subsets and supersets

759edo notably contains 253edo.