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.

For people who aren't colorblind, a red-note/blue-note system (similar to that proposed for ~~sixth-tones/~~[[36edo]]) can be used. (~~This~~ is a different ~~use of color~~ than Kite's [[color notation]].) Now we have the following sequence of notes, each separated by one meride: A, ~~red~~ A, ~~blue~~ A♯, A♯, B♭, ~~red~~ B♭, ~~blue~~ B, B. (Note that ~~there are red flats and blue sharps, but no~~ red sharps or blue flats~~, because the latter~~ are enharmonically equivalent to simpler notes: ~~blue~~ B♭ is actually just A♯, for instance).

For people who aren't colorblind, a red-note/blue-note system (similar to that proposed for [[36edo]]) can 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: A, A, A♯, A♯, B♭, B♭, B, B. (Note that red sharps or blue flats are somewhat redundant since they are enharmonically equivalent to simpler notes: B♭ is actually just A♯, for instance).

The diatonic semitone is four steps, so for the region between B and C ~~(or, E and F)~~, we can use: B, C♭, ~~red~~ C♭/~~blue B♯~~ (''they are enharmonic equivalents''), B♯, and C. All of the notes in 43edo therefore have unambiguous names except for ~~two~~: ~~red~~ C♭/~~blue B♯~~, and ~~red~~ F♭/~~blue E♯~~. 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).

The diatonic semitone is four steps, so for the region between B and C, we can use: B, C♭, B♯ / C♭ (they are enharmonic equivalents), B♯, and C. All of the notes in 43edo therefore have unambiguous names except for B♯/C♭, and E♯/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).

If ~~red~~ C♭ and ~~blue~~ B♯ (and ~~red~~ F♭/~~blue~~ E♯) are instead forced to be distinct, but the requirement that all notes be equally spaced is maintained, then we end up with a ''completely'' unambiguous red-note/blue-note notation for [[45edo]], which is another meantone (actually, a [[flattone]]) system.

If C♭ and B♯ (and F♭/E♯) are instead forced to be distinct, but the requirement that all notes be equally spaced is maintained, then we end up with a ''completely'' unambiguous red-note/blue-note notation for [[45edo]], which is another meantone (actually, a [[flattone]]) system.

=== Ups and downs notation ===

The ~~following shows how~~ [[ups and downs notation]] ~~can notate the third-sharps~~ and ~~third-flats through~~ extended [[Helmholtz-Ellis notation|Helmholtz–Ellis]] ~~symbols~~:

The third-sharps and third-flats can also be notated using [[ups and downs notation]] and extended [[Helmholtz-Ellis notation|Helmholtz–Ellis]] accidentals:

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}}.

The notes from B to C are B, C♭, B{{sharpdown}} / C{{flatup}}, B♯, and C. Similarily, the notes from E to F are E, F♭, E{{sharpdown}} / F{{flatup}}, E♯, and F. As with the red/blue note system described above, all notes in 43edo therefore have unambiguous names except for the note halfway between B and C and the note halfway between E and F.

=== Sagittal ===

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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.
-For people who aren't colorblind, a red-note/blue-note system (similar to that proposed for sixth-tones/[[36edo]]) can be used. (This is a different use of color than Kite's [[color notation]].) Now we have the following sequence of notes, each separated by one meride: A, red A, blue A♯, A♯, B♭, red B♭, blue B, B. (Note that there are red flats and blue sharps, but no red sharps or blue flats, because the latter are enharmonically equivalent to simpler notes: blue B♭ is actually just A♯, for instance).
+For people who aren't colorblind, a red-note/blue-note system (similar to that proposed for [[36edo]]) can 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: A, <span style="background-color: #eda2a2; color: #ff0000;">A</span>, <span style="background-color: #6ee8e8; color: #071ac7;">A♯</span>, A♯, B♭, <span style="background-color: #eda2a2; color: #ff0000;">B♭</span>, <span style="background-color: #6ee8e8; color: #071ac7;">B</span>, B. (Note that red sharps or blue flats are somewhat redundant since they are enharmonically equivalent to simpler notes: <span style="background-color: #6ee8e8; color: #071ac7;">B♭</span> is actually just A♯, for instance).
-The diatonic semitone is four steps, so for the region between B and C (or, E and F), we can use: B, C♭, red C♭/blue B♯ (''they are enharmonic equivalents''), B♯, and C. All of the notes in 43edo therefore have unambiguous names except for two: red C♭/blue B♯, and red F♭/blue E♯. 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).
+The diatonic semitone is four steps, so for the region between B and C, we can use: B, C♭, <span style="background-color: #6ee8e8; color: #071ac7;">B♯</span> / <span style="background-color: #eda2a2; color: #ff0000;">C♭</span> (they are enharmonic equivalents), B♯, and C. All of the notes in 43edo therefore have unambiguous names except for <span style="background-color: #6ee8e8; color: #071ac7;">B♯</span>/<span style="background-color: #eda2a2; color: #ff0000;">C♭</span>, and <span style="background-color: #6ee8e8; color: #071ac7;">E♯</span>/<span style="background-color: #eda2a2; color: #ff0000;">F♭</span>. 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).
-If red C♭ and blue B♯ (and red F♭/blue E♯) are instead forced to be distinct, but the requirement that all notes be equally spaced is maintained, then we end up with a ''completely'' unambiguous red-note/blue-note notation for [[45edo]], which is another meantone (actually, a [[flattone]]) system.
+If <span style="background-color: #eda2a2; color: #ff0000;">C♭</span> and <span style="background-color: #6ee8e8; color: #071ac7;">B♯</span> (and <span style="background-color: #eda2a2; color: #ff0000;">F♭</span>/<span style="background-color: #6ee8e8; color: #071ac7;">E♯</span>) are instead forced to be distinct, but the requirement that all notes be equally spaced is maintained, then we end up with a ''completely'' unambiguous red-note/blue-note notation for [[45edo]], which is another meantone (actually, a [[flattone]]) system.
 === Ups and downs notation ===
-The following shows how [[ups and downs notation]] can notate the third-sharps and third-flats through extended [[Helmholtz-Ellis notation|Helmholtz&ndash;Ellis]] symbols:
+The third-sharps and third-flats can also be notated using [[ups and downs notation]] and extended [[Helmholtz-Ellis notation|Helmholtz&ndash;Ellis]] accidentals:
 {{Sharpness-sharp3-extended}}
+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}}.
+The notes from B to C are B, C♭, B{{sharpdown}} / C{{flatup}}, B♯, and C. Similarily, the notes from E to F are E, F♭, E{{sharpdown}} / F{{flatup}}, E♯, and F. As with the red/blue note system described above, all notes in 43edo therefore have unambiguous names except for the note halfway between B and C and the note halfway between E and F.
 === Sagittal ===