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This article discusses about an alternative set of symbols based on current practice of microtonal music with some experimental extrapolation. The notation is, in essence, [[Ups and Downs Notation|ups and downs notation]] with a different look.  
{{main|Ups and downs notation}}
 
This article discusses about an alternative set of symbols based on current practice of microtonal music with some experimental extrapolation. The notation is, in essence, [[Ups and downs notation|ups and downs notation]] with a different look.  


Alternative symbols may be useful for the following reasons:  
Alternative symbols may be useful for the following reasons:  
# 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 ===
== 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 symbol set comprises traditional accidentals (sharps, flats, and naturals), Stein–Zimmermann quartertone accidentals (semisharps and semiflats) with and up and down arrows via Gould arrow quarter tone symbols or [[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"
|+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 ===
A usage guide for ETs of sharpness value below 8 will be provided here.  
 
==== Sharp 1 ====
 
Sharp-1 ETs have a sharp that raises 1 step. ETs of this category include 5, 12, 19, 26, etc.
 
Traditional notation can be used since an up is exactly equivalent to a sharp.
 
{| class="wikitable center-all"
!|Step offset
| +2
| +1
| 0
| -1
| -2
|-
!|Symbol
|[[File:accidental doublesharp.png]]
|[[File:accidental sharp.png]]
|[[File:accidental natural.png]]
|[[File:accidental flat.png]]
|[[File:accidental doubleflat.png]]
|}


==== Sharp 2 ====
The Gould arrow accidentals are up and down arrows attached to sharps, flats, or naturals, and modify the note by one step. They appear very similar to Helmholtz–Ellis accidentals, and are fully interchangeable with them.
Sharp-2 ETs have a sharp that raises 2 steps. ETs of this category include 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.  
== Usage guide for each sharpness value ==
{{See also| Sharpness }}
A usage guide for edos of sharpness value below 8 will be provided here.  


{| class="wikitable center-all"
=== Sharp-1 ===
!|Step offset
Sharp-1 edos have a sharp that raises 1 step. Edos of this category are {{EDOs| 5, 12, 19, 26, and 33 }}.
| +4
Traditional notation can be used since an up is exactly equivalent to a sharp.
| +3
{{Sharpness-sharp1}}
| +2
| +1
| 0
| -1
| -2
| -3
| -4
|-
!|Symbol
|[[File:accidental doublesharp.png]]
|[[File:accidental sesquisharp.png]]
|[[File:accidental sharp.png]]
|[[File:accidental semisharp.png]]
|[[File:accidental natural.png]]
|[[File:accidental semiflat.png]]
|[[File:accidental flat.png]]
|[[File:accidental sesquiflat.png]]
|[[File:accidental doubleflat.png]]
|}


==== Sharp-3 ====
=== Sharp-2 ===
Sharp-3 ETs have a sharp that raises 3 steps. ETs of this category include 22, 29, 36, 43, etc.  
Sharp-2 edos have a sharp that raises 2 steps. Edos of this category are {{EDOs| 10, 17, 24, 31, 38, 45, and 52 }}.
As are commonly seen in 24edo and 31edo, semisharps and semiflats could be used for a substitution of the tilde.
{{Sharpness-sharp2}}


=== Sharp-3 ===
Sharp-3 edos have a sharp that raises 3 steps. Edos of this category are {{EDOs| 8, 15, 22, 29, 36, 43, 50, 57, and 64 }}.
This is where you ''really'' want to use ups and downs.  
This is where you ''really'' want to use ups and downs.  
{{Sharpness-sharp3}}
In some cases, some notes or intervals may be best spelled with double arrows:
{{Sharpness-sharp3-extended}}


{| class="wikitable center-all"
=== Sharp-4 ===
!|Step offset
Sharp-4 edos have a sharp that raises 4 steps. Edos of this category are {{EDOs| 13, 20, 27, 34, 41, 48, 55, 62, 69, and 76 }}.
| 7
Many consider a full combination of semisharps, semiflats, ups and down to appear very neat.  
| '''6'''
{{Sharpness-sharp4}}
| 5
| 4
| '''3'''
| 2
| 1
| '''0'''
|-
!|Sharp symbol
|[[File:accidental doublesharp up.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp down.png]]
|[[File:accidental sharp up.png]]
|[[File:accidental sharp.png]]
|[[File:accidental sharp down.png]]
|[[File:accidental natural up.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
!|Flat symbol
|[[File:accidental doubleflat down.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat up.png]]
|[[File:accidental flat down.png]]
|[[File:accidental flat.png]]
|[[File:accidental flat up.png]]
|[[File:accidental natural down.png]]
|}
 
==== Sharp-4 ====
Sharp-4 ETs have a sharp that raises 4 steps. ETs of this category include 27, 34, 41, 48, etc.  
 
A full combination of semisharps, semiflats, ups and downs looks very neat.  
 
{| class="wikitable center-all"
!|Step offset
| 9
| '''8'''
| 7
| 6
| 5
| '''4'''
| 3
| 2
| 1
| '''0'''
|-
!|Sharp symbol
|[[File:accidental doublesharp up.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp down.png]]
|[[File:accidental sesquisharp.png]]
|[[File:accidental sharp up.png]]
|[[File:accidental sharp.png]]
|[[File:accidental sharp down.png]]
|[[File:accidental semisharp.png]]
|[[File:accidental natural up.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
!|Flat symbol
|[[File:accidental doubleflat down.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat up.png]]
|[[File:accidental sesquiflat.png]]
|[[File:accidental flat down.png]]
|[[File:accidental flat.png]]
|[[File:accidental flat up.png]]
|[[File:accidental semiflat.png]]
|[[File:accidental natural down.png]]
|}
 
==== Sharp-5 ====


Starting with sharp-5, which includes the famous 53-ET, you'll have to use double ups and downs. 
=== Sharp-5 ===
{| class="wikitable center-all"
Sharp-5 edos have a sharp that raises 5 steps. Edos of this category are {{EDOs| 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, and 88 }}.
!|Step offset
{{Sharpness-sharp5}}
| 12
| 11
| '''10'''
| 9
| 8
| 7
| 6
| '''5'''
| 4
| 3
| 2
| 1
| '''0'''
|-
!|Sharp symbol
|[[File:accidental doublesharp up2.png]]
|[[File:accidental doublesharp up1.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp down1.png]]
|[[File:accidental doublesharp down2.png]]
|[[File:accidental sharp up2.png]]
|[[File:accidental sharp up1.png]]
|[[File:accidental sharp.png]]
|[[File:accidental sharp down1.png]]
|[[File:accidental sharp down2.png]]
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
!|Flat symbol
|[[File:accidental doubleflat down2.png]]
|[[File:accidental doubleflat down1.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat up1.png]]
|[[File:accidental doubleflat up2.png]]
|[[File:accidental flat down2.png]]
|[[File:accidental flat down1.png]]
|[[File:accidental flat.png]]
|[[File:accidental flat up1.png]]
|[[File:accidental flat up2.png]]
|[[File:accidental natural down2.png]]
|[[File:accidental natural down1.png]]
|}


==== Sharp-6 ====
In some cases, some notes or intervals may be best spelled with triple arrows:
{| class="wikitable center-all"
{{Sharpness-sharp5-extended}}
!|Step offset
| 14
| 13
| '''12'''
| 11
| 10
| 9
| 8
| 7
| '''6'''
| 5
| 4
| 3
| 2
| 1
| '''0'''
|-
!|Sharp symbol
|[[File:accidental doublesharp up2.png]]
|[[File:accidental doublesharp up1.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp down1.png]]
|[[File:accidental doublesharp down2.png]]
|[[File:accidental sesquisharp.png]]
|[[File:accidental sharp up2.png]]
|[[File:accidental sharp up1.png]]
|[[File:accidental sharp.png]]
|[[File:accidental sharp down1.png]]
|[[File:accidental sharp down2.png]]
|[[File:accidental semisharp.png]]
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
!|Flat symbol
|[[File:accidental doubleflat down2.png]]
|[[File:accidental doubleflat down1.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat up1.png]]
|[[File:accidental doubleflat up2.png]]
|[[File:accidental sesquiflat.png]]
|[[File:accidental flat down2.png]]
|[[File:accidental flat down1.png]]
|[[File:accidental flat.png]]
|[[File:accidental flat up1.png]]
|[[File:accidental flat up2.png]]
|[[File:accidental semiflat.png]]
|[[File:accidental natural down2.png]]
|[[File:accidental natural down1.png]]
|}


==== Sharp-7 ====
=== Sharp-6 ===
{| class="wikitable center-all"
Sharp-6 edos have a sharp that raises 6 steps. Edos of this category are {{EDOs| 30, 37, 44, 51, 58, 65, 72, 79, 86, 93, and 100 }}.
!|Step offset
{{Sharpness-sharp6}}
| 17
| 16
| 15
| '''14'''
| 13
| 12
| 11
| 10
| 9
| 8
| '''7'''
| 6
| 5
| 4
| 3
| 2
| 1
| '''0'''
|-
!|Sharp symbol
|[[File:accidental doublesharp up3.png]]
|[[File:accidental doublesharp up2.png]]
|[[File:accidental doublesharp up1.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp down1.png]]
|[[File:accidental doublesharp down2.png]]
|[[File:accidental doublesharp down3.png]]
|[[File:accidental sharp up3.png]]
|[[File:accidental sharp up2.png]]
|[[File:accidental sharp up1.png]]
|[[File:accidental sharp.png]]
|[[File:accidental sharp down1.png]]
|[[File:accidental sharp down2.png]]
|[[File:accidental sharp down3.png]]
|[[File:accidental natural up3.png]]
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
!|Flat symbol
|[[File:accidental doubleflat down3.png]]
|[[File:accidental doubleflat down2.png]]
|[[File:accidental doubleflat down1.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat up1.png]]
|[[File:accidental doubleflat up2.png]]
|[[File:accidental doubleflat up3.png]]
|[[File:accidental flat down3.png]]
|[[File:accidental flat down2.png]]
|[[File:accidental flat down1.png]]
|[[File:accidental flat.png]]
|[[File:accidental flat up1.png]]
|[[File:accidental flat up2.png]]
|[[File:accidental flat up3.png]]
|[[File:accidental natural down3.png]]
|[[File:accidental natural down2.png]]
|[[File:accidental natural down1.png]]
|}


==== Sharp-8 ====
Attaching arrows to semi- and sesquisharps and flats is also another option instead of using double arrows:
{| class="wikitable center-all"
{{Sharpness-sharp6-qt}}
!|Step offset
| 19
| 18
| 17
| '''16'''
| 15
| 14
| 13
| 12
| 11
| 10
| 9
| '''8'''
| 7
| 6
| 5
| 4
| 3
| 2
| 1
| '''0'''
|-
!|Sharp symbol
|[[File:accidental doublesharp up3.png]]
|[[File:accidental doublesharp up2.png]]
|[[File:accidental doublesharp up1.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp down1.png]]
|[[File:accidental doublesharp down2.png]]
|[[File:accidental doublesharp down3.png]]
|[[File:accidental sesquisharp.png]]
|[[File:accidental sharp up3.png]]
|[[File:accidental sharp up2.png]]
|[[File:accidental sharp up1.png]]
|[[File:accidental sharp.png]]
|[[File:accidental sharp down1.png]]
|[[File:accidental sharp down2.png]]
|[[File:accidental sharp down3.png]]
|[[File:accidental semisharp.png]]
|[[File:accidental natural up3.png]]
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
!|Flat symbol
|[[File:accidental doubleflat down3.png]]
|[[File:accidental doubleflat down2.png]]
|[[File:accidental doubleflat down1.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat up1.png]]
|[[File:accidental doubleflat up2.png]]
|[[File:accidental doubleflat up3.png]]
|[[File:accidental sesquiflat.png]]
|[[File:accidental flat down3.png]]
|[[File:accidental flat down2.png]]
|[[File:accidental flat down1.png]]
|[[File:accidental flat.png]]
|[[File:accidental flat up1.png]]
|[[File:accidental flat up2.png]]
|[[File:accidental flat up3.png]]
|[[File:accidental semiflat.png]]
|[[File:accidental natural down3.png]]
|[[File:accidental natural down2.png]]
|[[File:accidental natural down1.png]]
|}


Provided with more stacks of arrows, ETs of higher sharpness value can be notated in the same method as above.
=== Sharp-7 ===
Sharp-7 edos have a sharp that raises 7 steps. Edos of this category are {{EDOs| 42, 49, 56, 63, 70, 77, 84, 91, 98, and 105 }}.  
{{Sharpness-sharp7}}


The rest will be discussed below.  
=== Sharp-8 ===
Sharp-8 edos have a sharp that raises 8 steps. Edos of this category are {{EDOs| 54, 61, 68, 75, 82, 89, 96, 103, 110, and 117 }}.
{{Sharpness-sharp8}}


==== Flat-1 ====
=== Higher sharpness values ===
Provided with more stacks of arrows, or the ability to attach arrows to demi- and sesqui-sharps and flats, edos of higher sharpness value can be notated in the same method as above.


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.  
{{w|SMuFL}} curently supplies [https://w3c.github.io/smufl/latest/tables/extended-stein-zimmermann-accidentals.html extended Stein-Zimmermann accidentals (U+E290–U+E29F)], which contains demi- and sesqui-sharps and flats with a single arrow.  
The rest will be discussed below.


{| class="wikitable center-all"
==== Sharp-10 (example) ====
!|Step offset
Sharp-10 edos have a sharp that raises 10 steps. Edos of this category are {{EDOs| 71, 78, 85, 92, 99, 106, 113, 120, 127, 134, and 141 }}.
| +2
{{Sharpness-sharp10-qt1}}
| +1
| 0
| -1
| -2
|-
!|Symbol
|[[File:accidental doubleflat.png]]
|[[File:accidental flat.png]]
|[[File:accidental natural.png]]
|[[File:accidental sharp.png]]
|[[File:accidental doublesharp.png]]
|}


==== Flat-2 ====
==== Sharp-14 (example) ====
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.
Sharp-14 edos have a sharp that raises 14 steps.
{{Sharpness-sharp14-qt1}}


{| class="wikitable center-all"
=== Flat-1 ===
!|Step offset
For edos such as {{EDOs| 9, 16, 23, and 30 }}, if you notate them as if their native antidiatonic scales were diatonic, you would find that the sharp actually ''lowers'' by one step. If one wishes to "translate" diatonic songs into these edos, this is useful.
| +4
{{Sharpness-flat1}}
| +3
However, a much more intuitive solution is to swap the meaning of sharps and flats in regards to fifthspan (so that sharp still raises and flat still lowers), allowing the accidentals to more naturally notate these edos' native antidiatonic (in this case, the normal set of sharp-1 accidentals would be used).
| +2
| +1
| 0
| -1
| -2
| -3
| -4
|-
!|Symbol
|[[File:accidental doubleflat.png]]
|[[File:accidental sesquiflat.png]]
|[[File:accidental flat.png]]
|[[File:accidental semiflat.png]]
|[[File:accidental natural.png]]
|[[File:accidental semisharp.png]]
|[[File:accidental sharp.png]]
|[[File:accidental sesquisharp.png]]
|[[File:accidental doublesharp.png]]
|}


==== Zero ====
=== Flat-2 ===
Flat-2 edos (virtually [[11edo]] only), if you pretend their native antidiatonic scales are diatonic, 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. It makes the most sense to notate them as subsets.
{{Sharpness-flat2}}


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.
=== Zero ===
{| class="wikitable center-all"
On the other hand, the lower five multiples of 7 ({{EDOs| 7, 14, 21, 28, and 35}}) are known as "perfect" or sharp-0 edos, since, by tempering out the Pythagorean apotome of [[2187/2048]], the traditional sharps and flats are redundant and cannot raise or lower the pitch. Here, the notes can only be modified by arrows.
!|Step offset
{{Sharpness-0}}
| +3
| +2
| +1
| 0
| -1
| -2
| -3
|-
!|Symbol
|[[File:accidental natural up3.png]]
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural.png]]
|[[File:accidental natural down1.png]]
|[[File:accidental natural down2.png]]
|[[File:accidental natural down3.png]]
|}


== Limitations ==
== Limitations ==
Some edos have odd-numbered sharpness values 9 and above, and are difficult to notate due to the lack of support for the stacks of arrows required. Edos below 72 known to be impractical for this reason are {{EDOs| 59 and 66 }}. Therefore, such edos are capped from their 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. 
{{Navbox notation}}


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