56edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 56 factors into 2<sup>3</sup> | Since 56 factors into {{nowrap|2<sup>3</sup> × 7}}, 56edo has subset edos {{EDOs| 2, 4, 7, 8, 14, 28 }}. | ||
One step of 56edo is the closest direct approximation to the syntonic comma, [[81/80]], with the unrounded value being 55.7976. 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. | One step of 56edo is the closest direct approximation to the syntonic comma, [[81/80]], with the unrounded value being 55.7976. 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. | ||
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== Intervals == | == Intervals == | ||
{| class="wikitable center-all right-2 left-3" | {| class="wikitable center-all right-2 left-3" | ||
! # | |- | ||
! # | |||
! Cents | ! Cents | ||
! Approximate Ratios | ! Approximate Ratios* | ||
! [[Ups and downs notation | ! [[Ups and downs notation]] | ||
|- | |- | ||
| 0 | | 0 | ||
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| … | | … | ||
|} | |} | ||
<nowiki>* | <nowiki />* The following table assumes the [[patent val]] {{val| 56 89 130 157 194 207 }}. Other approaches are possible. Inconsistent intervals are marked ''italic''. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| 89 -56 }} | | {{monzo| 89 -56 }} | ||
| {{mapping| 56 89 }} | | {{mapping| 56 89 }} | ||
| | | −1.64 | ||
| 1.63 | | 1.63 | ||
| 7.64 | | 7.64 | ||
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| 2048/2025, 1953125/1889568 | | 2048/2025, 1953125/1889568 | ||
| {{mapping| 56 89 130 }} | | {{mapping| 56 89 130 }} | ||
| | | −1.01 | ||
| 1.61 | | 1.61 | ||
| 7.50 | | 7.50 | ||
| Line 202: | Line 195: | ||
| 686/675, 875/864, 1029/1024 | | 686/675, 875/864, 1029/1024 | ||
| {{mapping| 56 89 130 157 }} | | {{mapping| 56 89 130 157 }} | ||
| | | −0.352 | ||
| 1.80 | | 1.80 | ||
| 8.38 | | 8.38 | ||
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| 100/99, 245/242, 385/384, 686/675 | | 100/99, 245/242, 385/384, 686/675 | ||
| {{mapping| 56 89 130 157 194 }} | | {{mapping| 56 89 130 157 194 }} | ||
| | | −0.618 | ||
| 1.69 | | 1.69 | ||
| 7.90 | | 7.90 | ||
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| 91/90, 100/99, 169/168, 245/242, 385/384 | | 91/90, 100/99, 169/168, 245/242, 385/384 | ||
| {{mapping| 56 89 130 157 194 207 }} | | {{mapping| 56 89 130 157 194 207 }} | ||
| | | −0.299 | ||
| 1.70 | | 1.70 | ||
| 7.95 | | 7.95 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
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|- | |- | ||
| 2 | | 2 | ||
| 23\56<br>(5\56) | | 23\56<br />(5\56) | ||
| 492.86<br>(107.14) | | 492.86<br />(107.14) | ||
| 4/3<br>(17/16) | | 4/3<br />(17/16) | ||
| [[Keen]] / keenic | | [[Keen]] / keenic | ||
|- | |- | ||
| 4 | | 4 | ||
| 23\56<br>(5\56) | | 23\56<br />(5\56) | ||
| 492.86<br>(107.14) | | 492.86<br />(107.14) | ||
| 4/3<br>(17/16) | | 4/3<br />(17/16) | ||
| [[Bidia]] (7-limit) | | [[Bidia]] (7-limit) | ||
|- | |- | ||
| 7 | | 7 | ||
| 23\56<br>(1\56) | | 23\56<br />(1\56) | ||
| 492.86<br>(21.43) | | 492.86<br />(21.43) | ||
| 4/3<br>(250/243) | | 4/3<br />(250/243) | ||
| [[Sevond]] | | [[Sevond]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Scales == | == Scales == | ||
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== Music == | == Music == | ||
; [[Claudi Meneghin]] | ; [[Claudi Meneghin]] | ||
* [https://www.youtube.com/watch?v=xWKa59qDkXQ ''Prelude & Fugue in Pajara''] (2020) | * [https://www.youtube.com/watch?v=xWKa59qDkXQ ''Prelude & Fugue in Pajara''] (2020) – in pajara, 56edo tuning | ||
* [https://www.youtube.com/watch?v=3oO1SIVWBgI ''Mirror Canon in F''] (2020) | * [https://www.youtube.com/watch?v=3oO1SIVWBgI ''Mirror Canon in F''] (2020) | ||
* [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) | ||
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[[Category:Hemithirds]] | [[Category:Hemithirds]] | ||
[[Category:Keen]] | [[Category:Keen]] | ||
[[Category:Listen]] | |||
[[Category:Pajara]] | [[Category:Pajara]] | ||
[[Category:Superkleismic]] | [[Category:Superkleismic]] | ||
[[Category:Sycamore]] | [[Category:Sycamore]] | ||