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m →Intervals: 36/25 and 25/18 were missing, but also, 53edo is a model of 2.3.5.7.13 JI so it helps to have more accurate descriptors, but also, the cent values feel wrong and this is amplified by stacking them
 
(9 intermediate revisions by 5 users not shown)
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| ''[[50/49]]'', [[64/63]], [[81/80]]
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| ^1
| ^1
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| [[33/32]], [[36/35]], [[49/48]], [[128/125]]
| [[33/32]], [[36/35]], [[49/48]], [[128/125]]
| ^^1, vvm2
| ^^1, vvm2
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| vvA1, vm2
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| 90.57
| [[19/18]], [[20/19]], [[21/20]], [[256/243]]
| [[19/18]], [[20/19]], [[21/20]], [[256/243]]
| vA1, m2
| vA1, m2
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| A1, ^m2
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| [[13/12]], [[14/13]], [[27/25]]
| [[13/12]], [[14/13]], [[27/25]]
| ^^m2
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| [[11/10]], [[12/11]], [[35/32]], [[57/52]], [[800/729]]
| [[11/10]], [[12/11]], [[35/32]], [[57/52]], [[800/729]]
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| [[9/8]]
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| [[8/7]], [[256/225]]
| [[8/7]], [[256/225]]
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| [[15/13]], [[22/19]], [[125/108]], [[144/125]]
| [[15/13]], [[22/19]], [[125/108]], [[144/125]]
| ^^M2, vvm3
| ^^M2, vvm3
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| [[7/6]], [[75/64]]
| [[7/6]], [[75/64]]
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| [[13/11]], [[19/16]], [[32/27]]
| m3
| m3
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| [[6/5]]
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| [[11/9]], [[243/200]]
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| [[16/13]], [[100/81]]
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| [[19/15]], [[24/19]], [[81/64]]
| M3
| M3
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| [[9/7]], ''[[14/11]]''
| [[9/7]], ''[[14/11]]''
| ^M3
| ^M3
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| 452.83
| [[13/10]], [[125/96]], [[162/125]]
| [[13/10]], [[125/96]], [[162/125]]
| ^^M3, vv4
| ^^M3, vv4
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| 475.47
| [[21/16]], [[25/19]], [[320/243]], [[675/512]]
| [[21/16]], [[25/19]], [[320/243]], [[675/512]]
| v4
| v4
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| [[4/3]]
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| [[19/14]], [[27/20]]
| ^4
| ^4
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| 543.40
| [[11/8]], [[15/11]], [[26/19]]
| [[11/8]], [[15/11]], [[26/19]]
| ^^4
| ^^4
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| [[18/13]]
| [[18/13]], [[25/18]]
| vvA4, vd5
| vvA4, vd5
| dudaug 4th, downdim 5th
| dudaug 4th, downdim 5th
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| [[7/5]], [[45/32]]
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| vA4, d5
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| [[10/7]], [[64/45]]
| [[10/7]], [[64/45]]
| A4, ^d5
| A4, ^d5
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| 633.96
| [[13/9]]
| [[13/9]], [[36/25]]
| ^A4, ^^d5
| ^A4, ^^d5
| upaug 4th, dupdim 5th
| upaug 4th, dupdim 5th
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| [[16/11]], [[19/13]], [[22/15]]
| [[16/11]], [[19/13]], [[22/15]]
| vv5
| vv5
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| [[28/19]], [[40/27]]
| v5
| v5
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| [[3/2]]
| [[3/2]]
| P5
| P5
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| [[32/21]], [[38/25]], [[243/160]], [[1024/675]]
| ^5
| ^5
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| [[20/13]], [[125/81]], [[192/125]]
| ^^5, vvm6
| ^^5, vvm6
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| ''[[11/7]]'', [[14/9]], [[25/16]]
| ''[[11/7]]'', [[14/9]], [[25/16]]
| vm6
| vm6
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| [[19/12]], [[30/19]], [[128/81]]
| m6
| m6
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| [[8/5]]
| [[8/5]]
| ^m6
| ^m6
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| [[13/8]], [[81/50]]
| ^^m6
| ^^m6
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| [[18/11]], [[400/243]]
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| vvM6
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| [[5/3]]
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| [[22/13]], [[27/16]], [[32/19]]
| [[22/13]], [[27/16]], [[32/19]]
| M6
| M6
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| [[19/11]], [[26/15]], [[125/72]], [[216/125]]
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| ^^M6, vvm7
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| [[11/6]], [[20/11]], [[64/35]], [[729/400]]
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| ^^m7
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| [[13/7]], [[24/13]], [[50/27]]
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| vvM7
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| [[19/10]], [[36/19]], [[40/21]], [[243/128]]
| M7
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| ''[[21/11]]'', [[25/13]], [[27/14]], [[52/27]], [[48/25]]
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| ^M7
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| [[35/18]], [[64/33]], [[96/49]], [[125/64]]
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| ^^M7, vv8
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| v8
| v8
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== Notation ==
== Notation ==
=== Ups and downs 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}}


Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
=== Sagittal notation ===
{{Sharpness-sharp5}}
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:


=== Sagittal notation ===
53edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation#Spartan extension single-shaft|Spartan extension]], 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;"
!Degree
! colspan="2" | Steps
|'''0'''
!'''0'''
| +1
! 1
| +2
! 2
| +3
! 3
| +4
! 4
|'''+5'''
!'''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>
|<small>{{sagittal|#}}{{sagittal|\\!}}</small>
| rowspan="2" | <big>{{sagittal|//|}}</big>
|<small>{{sagittal|#}}{{sagittal|\!}}</small>
| {{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 EDO.
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 lists|Octave-reduced form]], reduced to the first half-octave
<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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* ''Fantasy in 53edo'' ([https://www.youtube.com/shorts/fgsT-1pBw8g abstract version]; [https://www.youtube.com/watch?v=-q-T3HuGehk visualizer version] (2025)
* ''Fantasy in 53edo'' ([https://www.youtube.com/shorts/fgsT-1pBw8g abstract version]; [https://www.youtube.com/watch?v=-q-T3HuGehk visualizer version] (2025)
* [https://www.youtube.com/shorts/zCthwbPH2cY ''Finale - Undertale (microtonal cover in 53edo)''] (2026)
* [https://www.youtube.com/shorts/zCthwbPH2cY ''Finale - Undertale (microtonal cover in 53edo)''] (2026)
* [https://www.youtube.com/shorts/WtSaDQCyfVc ''Waltz in 53edo''] (2026)
* ''Waltz in 53edo'' (2026)
** [https://www.youtube.com/shorts/WtSaDQCyfVc <nowiki>[Short]</nowiki>] (with Lumatone view))
** [https://www.youtube.com/watch?v=_xumSANdf-g <nowiki>[Full version]</nowiki>]


; [[Francium]]
; [[Francium]]
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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]]
Retrieved from "https://en.xen.wiki/w/53edo"