Alternative symbols for ups and downs notation: Difference between revisions

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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 with a different look.  
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 3, and is used by the [https://github.com/euwbah/musescore-n-tet-plugins n-Edo Retuner Plugin]. (Feel free to address others.)  


== What It Resolves ==
== Detail ==
How is the conventional notation for 31-ET related to that for 22-ET? Is there a logical unity despite the apparent differences?
 
=== 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]]). 


== Detail ==
The Stein-Zimmermann quartertone accidentals modify the note by half the sharpness value. They apply to ETs of even sharpness value only.
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.  
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''.


Each column represents the steps of a small tone (limma, [[256/243]]), located between E–F and B–C.  
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"
{| class="wikitable center-all"
|+Sharp value \ step size of a small tone
|+Sharpness value \ steps of a diatonic semitone
!|
!|
!|-2
!|-2
Line 214: Line 217:
|}
|}


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.  
=== Usage guide for each sharpness value ===
A usage guide for ETs of sharpness value below 8 will be provided here.  


=== Sharp Value 1 to 4 ===
==== Sharp 1 ====


'''Sharp-1''' ETs have a sharp that raises 1 step. ETs of this category include 5, 12, 19, 26, etc.  
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.  
Traditional notation can be used since an up is exactly equivalent to a sharp.  


{| class="wikitable"
{| class="wikitable center-all"
!|Step offset
!|Step offset
| +2
| +2
Line 238: Line 242:
|}
|}


'''Sharp-2''' ETs have a sharp that raises 2 steps. ETs of this category include 10, 17, 24, 31, etc.  
==== Sharp 2 ====
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.  
As are commonly seen in 24-edo and 31-edo, semisharps and semiflats could be used for a substitution of the tilde.  


{| class="wikitable"
{| class="wikitable center-all"
!|Step offset
!|Step offset
| +4
| +4
Line 266: Line 271:
|}
|}


'''Sharp-3''' ETs have a sharp that raises 3 steps. ETs of this category include 22, 29, 36, 43, etc.  
==== Sharp-3 ====
Sharp-3 ETs have a sharp that raises 3 steps. ETs of this category include 22, 29, 36, 43, etc.  


This is where you ''really'' want to use ups and downs.  
This is where you ''really'' want to use ups and downs.  


{| class="wikitable"
{| class="wikitable center-all"
!|Step offset
!|Step offset
| 7
| 7
Line 301: Line 307:
|}
|}


'''Sharp-4''' ETs have a sharp that raises 4 steps. ETs of this category include 27, 34, 41, 48, etc.  
==== 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.  
A full combination of semisharps, semiflats, ups and downs looks very neat.  


{| class="wikitable"
{| class="wikitable center-all"
!|Step offset
!|Step offset
| 9
| 9
Line 342: Line 349:
|}
|}


=== Sharp Value 5 to 8 ===
==== Sharp-5 ====


Starting with sharp-5, which includes the famous 53-ET, 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"
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'''
{| class="wikitable"
!|Step offset
!|Step offset
| 12
| 12
Line 398: Line 399:


'''Sharp-6'''
'''Sharp-6'''
{| class="wikitable"
{| class="wikitable center-all"
!|Step offset
!|Step offset
| 14
| 14
Line 451: Line 452:


'''Sharp-7'''
'''Sharp-7'''
{| class="wikitable"
{| class="wikitable center-all"
!|Step offset
!|Step offset
| 17
| 17
Line 513: Line 514:


'''Sharp-8'''
'''Sharp-8'''
{| class="wikitable"
{| class="wikitable center-all"
!|Step offset
!|Step offset
| 19
| 19
Line 579: Line 580:
|[[File:accidental natural down1.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. 


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


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


{| class="wikitable"
{| class="wikitable center-all"
!|Step offset
!|Step offset
| +2
| +2
Line 602: Line 605:
|}
|}


'''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 ====
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.  


{| class="wikitable"
{| class="wikitable center-all"
!|Step offset
!|Step offset
| +4
| +4
Line 628: Line 632:
|}
|}


=== Sharp Value 0 ===
==== Zero ====


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.  
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"
'''14-ET'''
{| class="wikitable"
!|Step offset
!|Step offset
| +3
| +2
| +1
| +1
| 0
| 0
| -1
| -1
| -2
| -3
|-
|-
!|Symbol
!|Symbol
|[[File:accidental natural up.png]]
|[[File:accidental natural up3.png]]
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural.png]]
|[[File:accidental natural.png]]
|[[File:accidental natural down.png]]
|[[File:accidental natural down1.png]]
|[[File:accidental natural down2.png]]
|[[File:accidental natural down3.png]]
|}
|}


== Limitations ==
== Limitations ==


Sharp value higher than 9 cannot be notated at all. ETs below 72 known to be impractical for this reason: 59, 66, 71.
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. 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, 52, 64. Therefore, such ETs are capped from its full strength.   
 
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.   
Conclusively, this set of symbols still cover most ETs below 72.   


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

Revision as of 05:43, 23 August 2020

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.

Alternative symbols may be useful for the following reasons:

  1. One may prefer a more conventional look of the score;
  2. 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 is used by the n-Edo Retuner Plugin. (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 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 Stein-Zimmermann quartertone accidentals modify the note by half the sharpness value. They apply to ETs 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.

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.

Step offset +2 +1 0 -1 -2
Symbol

Sharp 2

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.

Step offset +4 +3 +2 +1 0 -1 -2 -3 -4
Symbol

Sharp-3

Sharp-3 ETs have a sharp that raises 3 steps. ETs of this category include 22, 29, 36, 43, etc.

This is where you really want to use ups and downs.

Step offset 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

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.

Step offset 9 8 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

Sharp-5

Starting with sharp-5, which includes the famous 53-ET, you'll have to use double ups and downs.

Step offset 12 11 10 9 8 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

Sharp-6

Step offset 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

Sharp-7

Step offset 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

Sharp-8

Step offset 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

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

The rest will be discussed below.

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.

Step offset +2 +1 0 -1 -2
Symbol

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.

Step offset +4 +3 +2 +1 0 -1 -2 -3 -4
Symbol

Zero

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.

Step offset +3 +2 +1 0 -1 -2 -3
Symbol

Limitations

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. 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, 52, 64. Therefore, such ETs are capped from its full strength.

Conclusively, this set of symbols still cover most ETs below 72.

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