43edo: Difference between revisions

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Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A♯ and B♭ are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use "third-sharps", "two-thirds-sharps", "third-flats", and "two-thirds-flats" to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly.

=== ~~Ups and downs~~ notation ===

=== Stein–Zimmermann–Gould notation ===

In [[~~ups and downs~~ notation]]~~, the "third-sharp" becomes an up and the "two-thirds-sharp" becomes a downsharp.~~

[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:

~~Note that downsharp can be respelled as dup (double-up), and upflat as dud.~~

~~{{Ups and downs sharpness}}~~

~~Or one can use the [[Alternative symbols for ups and downs notation#Sharp-3|alternative ups and downs]]. They use~~ sharps and flats with arrows~~, borrowed from extended [[Helmholtz-Ellis notation|Helmholtz–Ellis]] notation~~:

The notes between A and B can then be notated as A, A{{naturalup}}, A{{sharpdown}}, A♯, B♭, B{{flatup}}, B{{naturaldown}}, B. Note that A♯ is enharmonic to B{{flatdown}}, and B♭ is enharmonic to A{{sharpup}}.

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Double or even triple arrows may arise if the arrows are taken to have their own layer of enharmonic spellings.

=== Kite's ups and downs notation ===

In [[Kite's ups and downs notation]], the "third-sharp" becomes an up and the "two-thirds-sharp" becomes a downsharp.

Note that downsharp can be respelled as dup (double-up), and upflat as dud.

=== Sagittal notation ===

This notation uses the same sagittal sequence as [[36edo#Sagittal notation|~~36-EDO~~]].

This notation uses the same sagittal sequence as [[36edo #Sagittal notation|36edo]].

==== Evo flavor ====

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</imagemap>

=== Red-Blue ~~Notation~~ ===

=== Red-Blue notation ===

For people who are not colorblind, a red-note/blue-note system (similar to that proposed for [[36edo]]) can also be used. (Note that this is different ~~than~~ Kite's [[color notation]].~~) Now we~~ have the following sequence of notes, each separated by one meride: {{colored note|A}}, {{colored note|red|A}}, {{colored note|blue|A♯}}, {{colored note|A♯}}, {{colored note|B♭}}, {{colored note|red|B♭}}, {{colored note|blue|B}}, {{colored note|B}}. (Note that red sharps or blue flats are enharmonically equivalent to simpler notes: {{colored note|red|A♯}} is enharmonic to B♭, and {{colored note|blue|B♭}} is actually just A♯).

For people who are not colorblind, a red-note/blue-note system (similar to that proposed for [[36edo]]) can also be used. Note that this is different from [[Kite's color notation]]. We have the following sequence of notes, each separated by one meride: {{colored note|A}}, {{colored note|red|A}}, {{colored note|blue|A♯}}, {{colored note|A♯}}, {{colored note|B♭}}, {{colored note|red|B♭}}, {{colored note|blue|B}}, {{colored note|B}}. (Note that red sharps or blue flats are enharmonically equivalent to simpler notes: {{colored note|red|A♯}} is enharmonic to B♭, and {{colored note|blue|B♭}} is actually just A♯).

The diatonic semitone is four steps, so for the region between B and C, we can use: {{colored note|B}}, {{colored note|C♭}}, {{colored note|blue|B♯}} / {{colored note|red|C♭}} (they are enharmonic equivalents), {{colored note|B♯}}, and {{colored note|C}}. All of the notes in 43edo therefore have only one name except for {{colored note|blue|B♯}} / {{colored note|red|C♭}}, and {{colored note|blue|E♯}} / {{colored note|red|F♭}}. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter).

@@ Line 352: / Line 352: @@
 Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A♯ and B♭ are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use "third-sharps", "two-thirds-sharps", "third-flats", and "two-thirds-flats" to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly.
-=== Ups and downs notation ===
+=== Stein–Zimmermann–Gould notation ===
-In [[ups and downs notation]], the "third-sharp" becomes an up and the "two-thirds-sharp" becomes a downsharp.
+[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
-Note that downsharp can be respelled as dup (double-up), and upflat as dud.
+{{Sharpness-sharp3-szg}}
-{{Ups and downs sharpness}}
-Or one can use the [[Alternative symbols for ups and downs notation#Sharp-3|alternative ups and downs]]. They use sharps and flats with arrows, borrowed from extended [[Helmholtz-Ellis notation|Helmholtz&ndash;Ellis]] notation:
-{{Sharpness-sharp3}}
 The notes between A and B can then be notated as A, A{{naturalup}}, A{{sharpdown}}, A♯, B♭, B{{flatup}}, B{{naturaldown}}, B. Note that A♯ is enharmonic to B{{flatdown}}, and B♭ is enharmonic to A{{sharpup}}.
@@ Line 365: / Line 361: @@
 Double or even triple arrows may arise if the arrows are taken to have their own layer of enharmonic spellings.
+=== Kite's ups and downs notation ===
+In [[Kite's ups and downs notation]], the "third-sharp" becomes an up and the "two-thirds-sharp" becomes a downsharp.
+Note that downsharp can be respelled as dup (double-up), and upflat as dud.
+{{Ups and downs sharpness}}
 === Sagittal notation ===
-This notation uses the same sagittal sequence as [[36edo#Sagittal notation|36-EDO]].
+This notation uses the same sagittal sequence as [[36edo #Sagittal notation|36edo]].
 ==== Evo flavor ====
@@ Line 389: / Line 390: @@
 </imagemap>
-=== Red-Blue Notation ===
+=== Red-Blue notation ===
-For people who are not colorblind, a red-note/blue-note system (similar to that proposed for [[36edo]]) can also be used. (Note that this is different than Kite's [[color notation]].) Now we have the following sequence of notes, each separated by one meride: {{colored note|A}}, {{colored note|red|A}}, {{colored note|blue|A♯}}, {{colored note|A♯}}, {{colored note|B♭}}, {{colored note|red|B♭}}, {{colored note|blue|B}}, {{colored note|B}}. (Note that red sharps or blue flats are enharmonically equivalent to simpler notes: {{colored note|red|A♯}} is enharmonic to B♭, and {{colored note|blue|B♭}} is actually just A♯).
+For people who are not colorblind, a red-note/blue-note system (similar to that proposed for [[36edo]]) can also be used. Note that this is different from [[Kite's color notation]]. We have the following sequence of notes, each separated by one meride: {{colored note|A}}, {{colored note|red|A}}, {{colored note|blue|A♯}}, {{colored note|A♯}}, {{colored note|B♭}}, {{colored note|red|B♭}}, {{colored note|blue|B}}, {{colored note|B}}. (Note that red sharps or blue flats are enharmonically equivalent to simpler notes: {{colored note|red|A♯}} is enharmonic to B♭, and {{colored note|blue|B♭}} is actually just A♯).
 The diatonic semitone is four steps, so for the region between B and C, we can use: {{colored note|B}}, {{colored note|C♭}}, {{colored note|blue|B♯}}&nbsp;/&nbsp;{{colored note|red|C♭}} (they are enharmonic equivalents), {{colored note|B♯}}, and {{colored note|C}}. All of the notes in 43edo therefore have only one name except for {{colored note|blue|B♯}}&nbsp;/&nbsp;{{colored note|red|C♭}}, and {{colored note|blue|E♯}}&nbsp;/&nbsp;{{colored note|red|F♭}}. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter).