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 [[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~~).

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 enharmonically equivalent to simpler notes: '''A♯''' is enharmonic to B♭, and '''B♭''' is actually just A♯).

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).

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 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.

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 ===

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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 [[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).
+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 enharmonically equivalent to simpler notes: '''<span style="background-color: #eda2a2; color: #ff0000;">A♯</span>''' is enharmonic to B♭, and '''<span style="background-color: #6ee8e8; color: #071ac7;">B♭</span>''' is actually just A♯).
-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).
+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>'''&nbsp;/&nbsp;'''<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>'''&nbsp;/&nbsp;'''<span style="background-color: #eda2a2; color: #ff0000;">C♭</span>''', and '''<span style="background-color: #6ee8e8; color: #071ac7;">E♯</span>'''&nbsp;/&nbsp;'''<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 <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.
+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>'''&nbsp;/&nbsp;'''<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 ===