Stein–Zimmermann–Gould notation: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
|Step offset
|Step offset
| +2
| '''+2'''
| +1
| '''+1'''
| 0
| '''0'''
| -1
| '''-1'''
| -2
| '''-2'''
|-
|-
|Symbol
|Symbol
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{| class="wikitable"
{| class="wikitable"
|Step offset
|Step offset
| +4
| '''+4'''
| +3
| +3
| +2
| '''+2'''
| +1
| +1
| 0
| '''0'''
| -1
| -1
| -2
| '''-2'''
| -3
| -3
| -4
| '''-4'''
|-
|-
|Symbol
|Symbol
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{| class="wikitable"
{| class="wikitable"
|Step offset
|Step offset
| +7
| 7
| +6
| '''6'''
| +5
| 5
| +4
| 4
| +3
| '''3'''
| +2
| 2
| +1
| 1
| 0
| '''0'''
| -1
| -2
| -3
| -4
| -5
| -6
| -7
|-
|-
|Symbol
|Sharp symbol
|[[File:accidental doublesharp up.png]]
|[[File:accidental doublesharp up.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp.png]]
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|[[File:accidental natural up.png]]
|[[File:accidental natural up.png]]
|[[File:accidental natural.png]]
|[[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]]
|[[File:accidental natural down.png]]
|[[File:accidental flat up.png]]
|
|[[File:accidental flat.png]]
|[[File:accidental flat down.png]]
|[[File:accidental doubleflat up.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat down.png]]
|}
|}


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{| class="wikitable"
{| class="wikitable"
|Step offset
|Step offset
| +9
| 9
| +8
| '''8'''
| +7
| 7
| +6
| 6
| +5
| 5
| +4
| '''4'''
| +3
| 3
| +2
| 2
| +1
| 1
| 0
| '''0'''
| -1
| -2
| -3
| -4
| -5
| -6
| -7
| -8
| -9
|-
|-
|Symbol
|Sharp symbol
|[[File:accidental doublesharp up.png]]
|[[File:accidental doublesharp up.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp.png]]
Line 343: Line 330:
|[[File:accidental natural up.png]]
|[[File:accidental natural up.png]]
|[[File:accidental natural.png]]
|[[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]]
|[[File:accidental natural down.png]]
|[[File:accidental semiflat.png]]
|
|[[File:accidental flat up.png]]
|[[File:accidental flat.png]]
|[[File:accidental flat down.png]]
|[[File:accidental sesquiflat.png]]
|[[File:accidental doubleflat up.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat down.png]]
|}
|}


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


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.  


There's a small version of the arrow symbol available that can be stacked twice or thrice, 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.  
There's a small version of the arrow symbol available that can be stacked twice or thrice, 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.  
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
| 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]]
|[[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'''
{| class="wikitable"
|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]]
|[[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'''
{| class="wikitable"
|Step offset
| 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]]
|[[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'''
{| class="wikitable"
|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]]
|[[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.  
The rest will be discussed below.  
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{| class="wikitable"
{| class="wikitable"
|Step offset
|Step offset
| +2
| '''+2'''
| +1
| '''+1'''
| 0
| '''0'''
| -1
| '''-1'''
| -2
| '''-2'''
|-
|-
|Symbol
|Symbol
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{| class="wikitable"
{| class="wikitable"
|Step offset
|Step offset
| +4
| '''+4'''
| +3
| +3
| +2
| '''+2'''
| +1
| +1
| 0
| '''0'''
| -1
| -1
| -2
| '''-2'''
| -3
| -3
| -4
| '''-4'''
|-
|-
|Symbol
|Symbol
Line 415: Line 639:


One possible solution is to use the simple system for 14- and 21-ET, and the complex system for 28- and 35-ET.  
One possible solution is to use the simple system for 14- and 21-ET, and the complex system for 28- and 35-ET.  
'''14- and 21-ET'''
{| class="wikitable"
|Step offset
| +1
| '''0'''
| -1
|-
|Symbol
|[[File:accidental natural up.png]]
|[[File:accidental natural.png]]
|[[File:accidental natural down.png]]
|}
'''28- and 35-ET'''
{| class="wikitable"
|Step offset
| +2
| +1
| '''0'''
| -1
| -2
|-
|Symbol
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural.png]]
|[[File:accidental natural down1.png]]
|[[File:accidental natural down2.png]]
|}


Conclusively, this set of symbols cover all ETs below 72 except 59, 66, and 71.
Conclusively, this set of symbols cover all ETs below 72 except 59, 66, and 71.
== Limitations ==
Sharp value higher than 9 cannot be notated at all.
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.


[[Category:Notation]]
[[Category:Notation]]

Revision as of 15:49, 3 May 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. (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 edo in the context of heptatonic ups and downs notation.

Each row represents the step size of a sharp/flat, to be called "sharp value" below. The sharp value is the basic category to determine the symbol set to be used.

Each column represents the step size of a small tone, located between E–F and B–C.

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.

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

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

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 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 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 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, 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

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

The rest will be discussed below.

Negative Sharp Values

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 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

Sharp Value 0

The zero row is even more special in that the conventional meaning of the sharp or flat does not apply.

One possible solution is to use the simple system for 14- and 21-ET, and the complex system for 28- and 35-ET.

14- and 21-ET

Step offset +1 0 -1
Symbol

28- and 35-ET

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

Conclusively, this set of symbols cover all ETs below 72 except 59, 66, and 71.

Limitations

Sharp value higher than 9 cannot be notated at all.

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.

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