Stein–Zimmermann–Gould notation: Difference between revisions

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:  

# 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?

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.  

{| class="wikitable"

|+Sharp value \ step size of a small tone

|8

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.

{| class="wikitable"

| -1

| -2

|[[File:accidental sharp.png]]

|[[File:accidental natural.png]]

|[[File:accidental flat.png]]

|}

'''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.

{| class="wikitable"

| -1

|-

|[[File:accidental sharp.png]]

|[[File:accidental semisharp.png]]

|}

'''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.  

{| class="wikitable"

| -1

| -2

|[[File:accidental sharp up.png]]

|[[File:accidental sharp.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.  

| -1

| -2

| -3

| -4

|}

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.  

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.  

|[[File:accidental doubleflat.png]]

 

{| class="wikitable"

|}