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Alternative symbols for ups and downs notation: Difference between revisions

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→Limitations: Removed the following sentence: "Some notes cannot be reached in ETs with a very flat fifth due to MuseScore not providing multiple sharps and flats. ETs below 72 known to be impractical for this reason: 21, 26, 28, 33, 35, 40, 45, 47, "
Fredg999 (talk | contribs)
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Changed header levels, moved sharpness table to Sharpness, modified ET lists and added those missing in higher sharpness sections, misc. edits
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# One may prefer a more conventional look of the score;  
# One may prefer a more conventional look of the score;  
# The up and down symbols may not be quite accessible in computer-aided score typing.  
# The up and down symbols may not be quite accessible in computer-aided score typing.  
All symbols proposed in this article are available in [[MuseScore|MuseScore 3]], and is used by the [https://github.com/euwbah/musescore-n-tet-plugins n-Edo Retuner Plugin]. (Feel free to address others.)  
All symbols proposed in this article are available in [[MuseScore|MuseScore 3]], and is used by the [https://github.com/euwbah/musescore-microtonal-edo-plugin Microtonal plugin for Musescore 3.4+]. (Feel free to address others.)  


== Detail ==
== Symbol set ==
 
The symbol set comprises traditional accidentals (sharps, flats, and naturals), Stein-Zimmermann quartertone accidentals (semisharps and semiflats), and up and down arrows in Gould arrow quartertone symbols or part of [[Helmholtz-Ellis notation|Helmholtz-Ellis just intonation accidentals]].   
=== Symbol set ===
The symbol set comprises traditional accidentals (sharps, flats, and naturals), Stein-Zimmermann quartertone accidentals (semisharps and semiflats), and up and down arrows in Gould arrow quartertone symbols or part of [[Helmholtz-Ellis notation|Helmholtz-Ellis Just Intonation accidentals]].   


The traditional accidentals, as specified in ups and downs notation, modify the note by the sharpness value, which equals the steps of a chromatic semitone (apotome, [[2187/2048]]).   
The traditional accidentals, as specified in ups and downs notation, modify the note by the sharpness value, which equals the steps of a chromatic semitone (apotome, [[2187/2048]]).   


The Stein-Zimmermann quartertone accidentals modify the note by half the sharpness value. They apply to ETs of even sharpness value only.   
The Stein-Zimmermann quartertone accidentals modify the note by half the sharpness value. They apply to [[edo]]s of even sharpness value only.   
 
The Gould arrow quartertone symbols are up and down arrows attached to sharps, flats or naturals. They modify the note by one step. The syntonic comma in Helmholtz-Ellis Just Intonation accidentals looks very similar, and ''can be used interchangeably''. 
 
Below is a table showing the characteristics of each ET below 72 in the context of traditional fifth-generator heptatonic ups and downs notation. Each row represents the steps of a chromatic semitone. Each column represents the steps of a diatonic semitone (limma, [[256/243]]), located between E–F and B–C.


{| class="wikitable center-all"
The Gould arrow quartertone symbols are up and down arrows attached to sharps, flats or naturals. They modify the note by one step. The syntonic comma in Helmholtz-Ellis just intonation accidentals looks very similar, and ''can be used interchangeably''. 
|+Sharpness value \ steps of a diatonic semitone
!|
!|-2
!|-1
!|0
!|1
!|2
!|3
!|4
!|5
!|6
!|7
!|8
|-
!|-3
|
|
|
|
|
|6b
|
|
|
|
|
|-
!|-2
|
|
|
|
|4
|11
|18b
|
|
|
|
|-
!|-1
|
|
|
|2
|9
|16
|23
|30b
|
|
|
|-
!|0
|
|
|
|7
|14
|21
|28
|35
|42b
|
|
|-
!|1
|
|
|5
|12
|19
|26
|33
|40
|47
|54b
|
|-
!|2
|
|3
|10
|17
|24
|31
|38
|45
|52
|59b
|
|-
!|3
|1
|8
|15
|22
|29
|36
|43
|50
|57
|64
|71b
|-
!|4
|6
|13
|20
|27
|34
|41
|48
|55
|62
|69
|…
|-
!|5
|11b
|18
|25
|32
|39
|46
|53
|60
|67
|…
|
|-
!|6
|
|23b
|30
|37
|44
|51
|58
|65
|72
|…
|
|-
!|7
|
|
|35b
|42
|49
|56
|63
|70
|…
|
|
|-
!|8
|
|
|
|47b
|54
|61
|68
|…
|
|
|
|-
!|9
|
|
|
|52b
|59
|66
|…
|
|
|
|
|-
!|10
|
|
|
|
|64b
|71
|…
|
|
|
|
|}


=== Usage guide for each sharpness value ===
== Usage guide for each sharpness value ==
A usage guide for ETs of sharpness value below 8 will be provided here.  
{{See also|Sharpness}}
A usage guide for edos of sharpness value below 8 will be provided here.  


==== Sharp 1 ====
=== Sharp 1 ===


Sharp-1 ETs have a sharp that raises 1 step. ETs of this category include 5, 12, 19, 26, etc.  
Sharp-1 edos have a sharp that raises 1 step. Edos of this category include {{EDOs|5, 12, 19, 26}}, etc.  


Traditional notation can be used since an up is exactly equivalent to a sharp.  
Traditional notation can be used since an up is exactly equivalent to a sharp.


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 231: Line 30:
| +1
| +1
| 0
| 0
| -1
| −1
| -2
| −2
|-
|-
!|Symbol
!|Symbol
Line 242: Line 41:
|}
|}


==== Sharp 2 ====
=== Sharp 2 ===
Sharp-2 ETs have a sharp that raises 2 steps. ETs of this category include 10, 17, 24, 31, etc.  
Sharp-2 edos have a sharp that raises 2 steps. Edos of this category include {{EDOs|10, 17, 24, 31}}, etc.  


As are commonly seen in 24-edo and 31-edo, semisharps and semiflats could be used for a substitution of the tilde.  
As are commonly seen in 24edo and 31edo, semisharps and semiflats could be used for a substitution of the tilde.  


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 254: Line 53:
| +1
| +1
| 0
| 0
| -1
| −1
| -2
| −2
| -3
| −3
| -4
| −4
|-
|-
!|Symbol
!|Symbol
Line 271: Line 70:
|}
|}


==== Sharp-3 ====
=== Sharp-3 ===
Sharp-3 ETs have a sharp that raises 3 steps. ETs of this category include 22, 29, 36, 43, etc.  
Sharp-3 edos have a sharp that raises 3 steps. Edos of this category include {{EDOs|8, 15, 22, 29}}, etc.  


This is where you ''really'' want to use ups and downs.  
This is where you ''really'' want to use ups and downs.  
Line 307: Line 106:
|}
|}


==== Sharp-4 ====
=== Sharp-4 ===
Sharp-4 ETs have a sharp that raises 4 steps. ETs of this category include 27, 34, 41, 48, etc.  
Sharp-4 edos have a sharp that raises 4 steps. Edos of this category include {{EDOs|13, 20, 27, 34}}, etc.  


A full combination of semisharps, semiflats, ups and downs looks very neat.  
A full combination of semisharps, semiflats, ups and downs looks very neat.  
Line 349: Line 148:
|}
|}


==== Sharp-5 ====
=== Sharp-5 ===
Sharp-5 edos have a sharp that raises 5 steps. Edos of this category include {{EDOs|18, 25, 32, 39}}, etc.
 
Starting with sharp-5, which includes the famous [[53edo]], you'll have to use double ups and downs.


Starting with sharp-5, which includes the famous 53-ET, you'll have to use double ups and downs. 
{| class="wikitable center-all"
{| class="wikitable center-all"
!|Step offset
!|Step offset
Line 398: Line 199:
|}
|}


==== Sharp-6 ====
=== Sharp-6 ===
Sharp-6 edos have a sharp that raises 6 steps. Edos of this category include {{EDOs|30, 37, 44, 51}}, etc.
 
{| class="wikitable center-all"
{| class="wikitable center-all"
!|Step offset
!|Step offset
Line 451: Line 254:
|}
|}


==== Sharp-7 ====
=== Sharp-7 ===
Sharp-7 edos have a sharp that raises 7 steps. Edos of this category include {{EDOs|42, 49, 56, 63}}, etc.
 
{| class="wikitable center-all"
{| class="wikitable center-all"
!|Step offset
!|Step offset
Line 513: Line 318:
|}
|}


==== Sharp-8 ====
=== Sharp-8 ===
Sharp-8 edos have a sharp that raises 8 steps. Edos of this category include {{EDOs|54, 61, 68}}, etc.
 
{| class="wikitable center-all"
{| class="wikitable center-all"
!|Step offset
!|Step offset
Line 581: Line 388:
|}
|}


Provided with more stacks of arrows, ETs of higher sharpness value can be notated in the same method as above.   
Provided with more stacks of arrows, edos of higher sharpness value can be notated in the same method as above.   


The rest will be discussed below.  
The rest will be discussed below.  


==== Flat-1 ====
=== Flat-1 ===


Flat-1 ETs have a sharp that ''lowers'' 1 step. ETs of this category include 9, 16, and 23. To have a sharp that actually lowers the tone can be counter-intuitive, yet reasonable for the system. Regardless, you could just flip it around.  
Flat-1 edos have a sharp that ''lowers'' 1 step. Edos of this category include {{EDOs|9, 16, and 23}}. To have a sharp that actually lowers the tone can be counter-intuitive, yet reasonable for the system. Regardless, you could just flip it around.  


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 594: Line 401:
| +1
| +1
| 0
| 0
| -1
| −1
| -2
| −2
|-
|-
!|Symbol
!|Symbol
Line 605: Line 412:
|}
|}


==== Flat-2 ====
=== Flat-2 ===
Flat-2 ETs (virtually 11-ET only) have a sharp that ''lowers'' 2 steps. So besides the special flavor of the sharps and flats, there are also semisharps and semiflats to fill up the spaces between.  
Flat-2 edos (virtually [[11edo]] only) have a sharp that ''lowers'' 2 steps. So besides the special flavor of the sharps and flats, there are also semisharps and semiflats to fill up the spaces between.  


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 615: Line 422:
| +1
| +1
| 0
| 0
| -1
| −1
| -2
| −2
| -3
| −3
| -4
| −4
|-
|-
!|Symbol
!|Symbol
Line 632: Line 439:
|}
|}


==== Zero ====
=== Zero ===
Perfect edos (sharp-0 edos) are even more special in that the traditional accidentals cannot raise or lower the pitch, so the notes can only be modified by arrows. Edos of this category include {{EDOs|7, 14, 21, 28, and 35}.


The zero row is even more special in that the traditional accidentals cannot raise or lower the pitch, so the note can only be modified by arrows. ETs of this category include 7, 14, 21, 28, and 35.
{| class="wikitable center-all"
{| class="wikitable center-all"
!|Step offset
!|Step offset
Line 641: Line 448:
| +1
| +1
| 0
| 0
| -1
| −1
| -2
| −2
| -3
| −3
|-
|-
!|Symbol
!|Symbol
Line 656: Line 463:


== Limitations ==
== Limitations ==
Some notes cannot be reached in edos of sharpness value higher than 9 due to MuseScore not providing the stacks of arrows required. Edos below 72 known to be impractical for this reason: 59, 66, 71. Therefore, such edos are capped from its full strength. 


Some notes cannot be reached in ETs of sharpness value higher than 9 due to MuseScore not providing the stacks of arrows required. ETs below 72 known to be impractical for this reason: 59, 66, 71. Therefore, such ETs are capped from its full strength. 
Conclusively, this set of symbols still covers most edos up to 72.   
 
Conclusively, this set of symbols still cover most ETs below 72.   


[[Category:Notation]]
[[Category:Notation]]
[[Category:Ups and Downs Notation]]
[[Category:Ups and Downs Notation]]
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