53edo: Difference between revisions

Eufalesio (talk | contribs)
m Standardize format Sagittal
Dave Keenan (talk | contribs)
Sagittal notation: In the table, swapped the order of sagittal and conventional to agree with the staff notation below it.
 
(6 intermediate revisions by 3 users not shown)
Line 633: Line 633:


== 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;"
! colspan="2" |Steps
! colspan="2" | Steps
!'''0'''
!'''0'''
! 1
! 1
Line 651: Line 653:
!'''5'''
!'''5'''
|-
|-
! rowspan="2" |Symbol
! rowspan="2" | Symbol
!Evo
! 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>
| rowspan="2" | <big>{{sagittal|//|}}</big>
|<small>{{sagittal|#}}{{sagittal|\\!}}</small>
| {{sagittal|\\!}}{{sagittal|#}}
|<small>{{sagittal|#}}{{sagittal|\!}}</small>
| {{sagittal|\!}}{{sagittal|#}}
|<big>{{sagittal|#}}</big>
| <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.
Line 681: Line 682:
{{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 ==
Line 1,110: Line 1,111:
| [[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 ==
Line 1,184: Line 1,185:
* [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)
Line 1,217: Line 1,224:
; [[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]]