53edo: Difference between revisions
→21st century: Bryan Deister's''Waltz in 53edo'' (2026): Add full version |
Dave Keenan (talk | contribs) →Sagittal notation: In the table, swapped the order of sagittal and conventional to agree with the staff notation below it. |
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== Notation == | == Notation == | ||
=== | === Stein–Zimmermann–Gould notation === | ||
53edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down). | [[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows: | ||
{{Sharpness-sharp5-szg}} | |||
=== Kite's ups and downs notation === | |||
53edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down). | |||
{{Ups and downs sharpness}} | {{Ups and downs sharpness}} | ||
=== Sagittal notation === | |||
53edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation#Spartan|Spartan set]], with the apotome equal to 5 edosteps and the limma to 4 edosteps. Here is a simplified table: | |||
{| class="wikitable" style="text-align: center;" | {| class="wikitable" style="text-align: center;" | ||
! | ! colspan="2" | Steps | ||
!'''0''' | |||
! 1 | |||
! 2 | |||
! 3 | |||
! 4 | |||
!'''5''' | |||
|- | |- | ||
!Evo | ! rowspan="2" | Symbol | ||
| rowspan="2" |<big>{{sagittal||//|}}</big> | ! Evo | ||
| rowspan="2" |<big>{{sagittal|/|}}</big> | | rowspan="2" | <big>{{sagittal||//|}}</big> | ||
| rowspan="2" |<big>{{sagittal|//|}}</big> | | rowspan="2" | <big>{{sagittal|/|}}</big> | ||
| | | rowspan="2" | <big>{{sagittal|//|}}</big> | ||
| | | {{sagittal|\\!}}{{sagittal|#}} | ||
|<big>{{sagittal|#}}</big> | | {{sagittal|\!}}{{sagittal|#}} | ||
| <big>{{sagittal|#}}</big> | |||
|- | |- | ||
!Revo | ! Revo | ||
|<big>{{sagittal|)||(}}</big> | | <big>{{sagittal|)||(}}</big> | ||
|<big>{{sagittal|||\}}</big> | | <big>{{sagittal|||\}}</big> | ||
|<big>{{sagittal|/||\}}</big> | | <big>{{sagittal|/||\}}</big> | ||
|} | |} | ||
The following enharmonics from the Spartan set are present (comma tempered out): | The following enharmonics from the Spartan set are present (comma tempered out): | ||
* {{sagittal|//|}} = {{Sagittal|/|)}} = {{Sagittal|/|\}} ([[325/324]], [[352/351]]) | * {{sagittal|//|}} = {{Sagittal|/|)}} = {{Sagittal|/|\}} ([[325/324]], [[352/351]]) | ||
* {{sagittal|/|}} = {{sagittal||)}} ([[225/224]]) | * {{sagittal|/|}} = {{sagittal||)}} ([[225/224]]) | ||
* {{sagittal||(}} = {{sagittal||//|}} ([[5120/5103]]) | * {{sagittal||(}} = {{sagittal||//|}} ([[5120/5103]]) | ||
See [[Sagittal notation#Revo|apotome complements]] for equivalent accidental pairs. | See [[Sagittal notation #Revo|apotome complements]] for equivalent accidental pairs. | ||
Featured below is the 53edo gamut notated using the best accidental approximants; in this case, pai/pao and phai/phao. | Featured below is the 53edo gamut notated using the best accidental approximants; in this case, pai/pao and phai/phao. | ||
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{{Sagittal chart}} | {{Sagittal chart}} | ||
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this | In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo. | ||
== Relationship to 12edo == | == Relationship to 12edo == | ||
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| [[Untriton]] / [[aufo]] | | [[Untriton]] / [[aufo]] | ||
|} | |} | ||
<nowiki/>* [[Normal | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave | ||
== Scales == | == Scales == | ||
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* [https://www.youtube.com/watch?v=DCENVnxH6bI ''Bande-announce''] – rendered by MortisTheneRd (2024) | * [https://www.youtube.com/watch?v=DCENVnxH6bI ''Bande-announce''] – rendered by MortisTheneRd (2024) | ||
=== 21st century === | ==== 21st century ==== | ||
; [[ALLY195]] | |||
* [https://www.bilibili.com/video/BV1f54y1r7XG/ ''My Soul adaptation''] (2020) | |||
; [[Alxeusxiao]] | |||
* [https://www.bilibili.com/video/BV1zM4m1m7Gz/ ''53edo exploration''] (2024) | |||
; [[Bryan Deister]] | ; [[Bryan Deister]] | ||
* [https://www.youtube.com/shorts/r-Tzq33OGM4 ''microtonal improvisation in 53edo''] (2025) | * [https://www.youtube.com/shorts/r-Tzq33OGM4 ''microtonal improvisation in 53edo''] (2025) | ||
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; [[Aaron Krister Johnson]] ([http://www.akjmusic.com site]{{dead link}}) | ; [[Aaron Krister Johnson]] ([http://www.akjmusic.com site]{{dead link}}) | ||
* [http://www.akjmusic.com/audio/desert_prayer.mp3 ''Desert Prayer'']{{dead link}} | * [http://www.akjmusic.com/audio/desert_prayer.mp3 ''Desert Prayer'']{{dead link}} | ||
; [[Logan02A4]] | |||
* [https://www.bilibili.com/video/BV1mBCRYmEhg/ ''53edo try''] (2024) | |||
; [[Claudi Meneghin]] | ; [[Claudi Meneghin]] | ||