Xenharmonic Wiki

Alternative symbols for ups and downs notation: Difference between revisions

← Older edit
VisualWikitext
m Clarify that the complex system uses symbols of Helmholtz-Ellis notation
Fredg999 (talk | contribs)
autopatrolled, Interface administrators, Sysops
6,129 edits
m Text replacement - "Ups and Downs Notation" to "Ups and downs notation"
 
(40 intermediate revisions by 8 users not shown)
Line 1: Line 1:
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 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 3, and [https://github.com/FloraCanou/musescore-n-tet-plugins one approach to the n-Edo Retuner Plugin] is based on this. (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.)  
 
== What It Resolves ==
How is the conventional notation for 31-ET related to that for 22-ET? Is there a logical unity despite the apparent differences?
 
== Detail ==
Below is a table showing the characteristics of each ET in the context of heptatonic ups and downs notation.
 
Each row represents the steps of a sharp/flat (apotome, [[2187/2048]]), to be called "sharp value" below. The sharp value is the basic criterion to determine the symbol set to be used.
 
Each column represents the steps of a small tone (limma, [[256/243]]), located between E–F and B–C.
 
{| class="wikitable"
|+Sharp value \ step size of a small tone
!|
!|-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
|…
|
|
|
|
|}
 
The symbol set comprises traditional sharps, flats, semisharps, semiflats, and up and down arrows attached to sharps and flats. Semisharps and semiflats apply to even sharp values only.
 
=== Sharp Value 1 to 4 ===


'''Sharp-1''' ETs have a sharp that raises 1 step. ETs of this category include 5, 12, 19, 26, etc.  
== Symbol set ==
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]].


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


{| class="wikitable"
The Stein–Zimmermann quartertone accidentals modify the note by half the sharpness value. They apply to [[edo]]s of even sharpness value only.
!|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''' ETs have a sharp that raises 2 steps. ETs of this category include 10, 17, 24, 31, etc.  
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.


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"
=== 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''' ETs have a sharp that raises 3 steps. ETs of this category include 22, 29, 36, 43, etc.  
=== Sharp-2 ===
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"
=== 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''' 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"
!|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 Value 5 to 8 ===
 
Starting with sharp-5, which includes the famous 53-ET, you'll have to use double ups and downs.
 
There's a small version of the arrow symbol available that can be stacked twice or thrice as part of the [[Helmholtz-Ellis notation]], termed raise/lower by one syntonic comma, for which the step size of 53-edo is a close approximation. These arrow symbols, possibly combined with semisharps and semiflats, could be used through sharp-5 to sharp-8 ETs.
 
It is basically another system, to be called the "complex system", in contrast to the "simple system" above. The complex system is compatible with lower sharp values. For example, you could use the sharp-8 68-ET for the notation of 34-ET, but the reason the former should not take priority is obvious. However you do, using arrow symbols of both systems should be definitely avoided, because they look too similar.


'''Sharp-5'''
=== Sharp-5 ===
{| class="wikitable"
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"
{{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"
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"
{{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]]
|}


The rest will be discussed below.  
=== 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}}


=== Negative Sharp Values ===
=== 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''' 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.  
=== 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.


{| class="wikitable"
{{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.  
!|Step offset
The rest will be discussed below.
| +2
| +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''' 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-10 (example) ====
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 }}.
{{Sharpness-sharp10-qt1}}


{| class="wikitable"
==== Sharp-14 (example) ====
!|Step offset
Sharp-14 edos have a sharp that raises 14 steps.
| +4
{{Sharpness-sharp14-qt1}}
| +3
| +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]]
|}


=== Sharp Value 0 ===
=== Flat-1 ===
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.
{{Sharpness-flat1}}
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). 


The '''zero''' row is even more special in that the conventional meaning of the sharp or flat does not apply. As a result, this system is not a good solution and it virtually only works for 14-ET.
=== 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}}


'''14-ET'''
=== Zero ===
{| class="wikitable"
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}}
| +1
| 0
| -1
|-
!|Symbol
|[[File:accidental natural up.png]]
|[[File:accidental natural.png]]
|[[File:accidental natural down.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. 


Sharp value higher than 9 cannot be notated at all. ETs below 72 known to be impractical for this reason: 59, 66, 71. 
Conclusively, this set of symbols still covers most edos up to 72.  
 
Sometimes the symbols available are not sufficient for every key of an ET. When the max step offset of an ET exceeds its accidental symbol set, some of the keys are capped from its full strength. This occurs with ETs that have a very flat fifth. ETs below 72 known to be impractical for this reason: 21, 26, 28, 33, 35, 40, 45, 47, 52, 64.  


Conclusively, this set of symbols still cover most ETs below 72. 
{{Navbox notation}}


[[Category:Notation]]
[[Category:Notation]]
[[Category:Ups and downs notation]]
Retrieved from "https://en.xen.wiki/w/Alternative_symbols_for_ups_and_downs_notation"