56edo: Difference between revisions
→Music: Add Bryan Deister's ''Curious Light - DOORS (microtonal cover in 56edo)'' (2025) |
Change "See also" to "Instruments" since the only thing in there was Lumatone mapping for 56edo, and move it before the Music section to be consistent with most other EDO pages. Also fix note about syntonic comma mapping, including moving it back into the Theory section where it belongs. |
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== Theory == | == Theory == | ||
56edo shares its near perfect quality of classical major third with [[28edo]], which it doubles, while also adding a superpythagorean 5th that is a convergent towards the [[Metallic harmonic series|bronze metallic mean]], following [[17edo]] and preceding [[185edo]]. Because it contains 28edo's major third and also has a step size very close to the syntonic comma, 56edo contains very accurate approximations of both the classic major third [[5/4]] and the Pythagorean major third [[81/64]]. Unfortunately, this "Pythagorean major third" is not the major third as is stacked by fifths in 56edo. | 56edo shares its near perfect quality of classical major third with [[28edo]], which it doubles, while also adding a superpythagorean 5th that is a convergent towards the [[Metallic harmonic series|bronze metallic mean]], following [[17edo]] and preceding [[185edo]]. Because it contains 28edo's major third and also has a step size very close to the syntonic comma, 56edo contains very accurate approximations of both the classic major third [[5/4]] and the Pythagorean major third [[81/64]]. Unfortunately, this "Pythagorean major third" is not the major third as is stacked by fifths in 56edo. | ||
One step of 56edo is the closest direct approximation to the syntonic comma, [[81/80]], with the number of directly approximated syntonic commas per octave being 55.7976. (However, note that by [[patent val]] mapping, 56edo actually maps the syntonic comma inconsistently, to two steps.) [[Barium]] temperament realizes this proximity through regular temperament theory, and is supported by notable edos like [[224edo]], [[1848edo]], and [[2520edo]], which is a highly composite edo. | |||
56edo can be used to tune [[hemithirds]], [[superkleismic]], [[sycamore]] and [[keen]] temperaments, and using {{val| 56 89 130 158 }} (56d) as the equal temperament val, for [[pajara]]. It provides the [[optimal patent val]] for 7-, 11- and 13-limit [[sycamore]], and the 11-limit 56d val is close to the [[POTE tuning]] for 11-limit pajara. | 56edo can be used to tune [[hemithirds]], [[superkleismic]], [[sycamore]] and [[keen]] temperaments, and using {{val| 56 89 130 158 }} (56d) as the equal temperament val, for [[pajara]]. It provides the [[optimal patent val]] for 7-, 11- and 13-limit [[sycamore]], and the 11-limit 56d val is close to the [[POTE tuning]] for 11-limit pajara. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 56 factors into {{nowrap|2<sup>3</sup> × 7}}, 56edo has subset edos {{EDOs| 2, 4, 7, 8, 14, 28 }}. | Since 56 factors into {{nowrap|2<sup>3</sup> × 7}}, 56edo has subset edos {{EDOs| 2, 4, 7, 8, 14, 28 }}. | ||
== Intervals == | == Intervals == | ||
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** Evened minor pentatonic (approximated from [[72edo]]): 321.4 - 492.9 - 685.7 - 1028.6 - 1200.0 | ** Evened minor pentatonic (approximated from [[72edo]]): 321.4 - 492.9 - 685.7 - 1028.6 - 1200.0 | ||
== Instruments == | |||
[[Lumatone mapping for 56edo|Lumatone mappings for 56edo]] are available. | |||
== Music == | == Music == | ||
; [[Bryan Deister]] | ; [[Bryan Deister]] | ||
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* [https://www.youtube.com/watch?v=s1h083BRWXU ''Canon 3-in-1 on a Ground''] (2020) | * [https://www.youtube.com/watch?v=s1h083BRWXU ''Canon 3-in-1 on a Ground''] (2020) | ||
[[Category:Hemithirds]] | [[Category:Hemithirds]] | ||
[[Category:Keen]] | [[Category:Keen]] | ||