Fractional sharp notation: Difference between revisions

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VERY WIP (I'll move it to the main namespace if it's finished.)

The '''fractional sharp notation''' (FSN) is a notation developed by [[User:CompactStar|CompactStar]] that is an extension of [[chain-of-fifths notation]], supporting a wide range of [[EDO]] and [[rank-2 temperament]] systems. It represents all intervals with conventional accidentals, but with sharps and flats extended to have an arbitrary rational amount, denoted by a superscript, such as #<sup>1/2</sup> for half-sharp, except for in the case of single and double accidentals. If ASCII compatibility is required, superscripts can be substituted for carets–in this case, #^(a/b) is ~~usually~~ preferred over #^a/b for clarity.

The '''fractional sharp notation''' (FSN) is a notation developed by [[User:CompactStar|CompactStar]] that is an extension of [[chain-of-fifths notation]], supporting a wide range of [[EDO]] and [[rank-2 temperament]] systems. It represents all intervals with conventional accidentals, but with sharps and flats extended to have an arbitrary rational amount, denoted by a superscript, such as #<sup>1/2</sup> for half-sharp, except for in the case of single and double accidentals. If ASCII compatibility is required, superscripts can be substituted for carets–in this case, #^(a/b) is preferred over #^a/b for clarity.

The sharp and flat accidentals are always taken to raise and lower by an augmented union or chromatic semitone. In interval naming, x-augmented (x-A) ~~is x~~ chromatic ~~semitones~~ above a major or perfect interval, x-diminished (x-d) ~~is x~~ chromatic ~~semitones~~ below a minor or ~~perfect~~ interval. ~~Additionally, for~~ intervals between major ~~and minor~~, "x-augmented minor" ~~(x-Am)~~ is x chromatic semitones above minor and "x-diminished major" ~~(x-dM)~~ is x chromatic semitones below major~~. For example "1/3-augmented minor 3rd" (1/3-Am3) means a minor 3rd raised by 1/3 of a chromatic semitone~~ (~~formerly, these were described as a "fraction of major" like 1/3-major, the updated version~~ was suggested by [[User:Frostburn|Frostburn]]). ~~Since~~ 1/2-augmented minor and 1/2-diminished major ~~mean the same thing~~, ~~they~~ are replaced with the more conventional term "neutral" (n).

The sharp and flat accidentals are always taken to raise and lower by an augmented union or chromatic semitone. In interval naming, "a/b-augmented" (abbreviated as a/b-A) means a/b of a chromatic semitone above a major or perfect interval, and "a/b-diminished" (abbreviated as a/b-D) means a/b of a chromatic semitone below a minor or diminished interval. To address intervals which are between minor and major, "a/b-augmented minor" is used for a/b chromatic semitones above a minor interval, and "a/b-diminished major" is used for a/b chromatic semitones below a major interval (this was suggested by [[User:Frostburn|Frostburn]]). 1/2-augmented minor and 1/2-diminished major are identical, corresponding to halfway between minor and major, so both are replaced with the more conventional term "neutral" (n).

== For EDOs ==

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 VERY WIP (I'll move it to the main namespace if it's finished.)
-The '''fractional sharp notation''' (FSN) is a notation developed by [[User:CompactStar|CompactStar]] that is an extension of [[chain-of-fifths notation]], supporting a wide range of [[EDO]] and [[rank-2 temperament]] systems. It represents all intervals with conventional accidentals, but with sharps and flats extended to have an arbitrary rational amount, denoted by a superscript, such as #<sup>1/2</sup> for half-sharp, except for in the case of single and double accidentals. If ASCII compatibility is required, superscripts can be substituted for carets–in this case, #^(a/b) is usually preferred over #^a/b for clarity.
+The '''fractional sharp notation''' (FSN) is a notation developed by [[User:CompactStar|CompactStar]] that is an extension of [[chain-of-fifths notation]], supporting a wide range of [[EDO]] and [[rank-2 temperament]] systems. It represents all intervals with conventional accidentals, but with sharps and flats extended to have an arbitrary rational amount, denoted by a superscript, such as #<sup>1/2</sup> for half-sharp, except for in the case of single and double accidentals. If ASCII compatibility is required, superscripts can be substituted for carets–in this case, #^(a/b) is preferred over #^a/b for clarity.
-The sharp and flat accidentals are always taken to raise and lower by an augmented union or chromatic semitone. In interval naming, x-augmented (x-A) is x chromatic semitones above a major or perfect interval, x-diminished (x-d) is x chromatic semitones below a minor or perfect interval. Additionally, for intervals between major and minor, "x-augmented minor" (x-Am) is x chromatic semitones above minor and "x-diminished major" (x-dM) is x chromatic semitones below major. For example "1/3-augmented minor 3rd" (1/3-Am3) means a minor 3rd raised by 1/3 of a chromatic semitone (formerly, these were described as a "fraction of major" like 1/3-major, the updated version was suggested by [[User:Frostburn|Frostburn]]). Since 1/2-augmented minor and 1/2-diminished major mean the same thing, they are replaced with the more conventional term "neutral" (n).
+The sharp and flat accidentals are always taken to raise and lower by an augmented union or chromatic semitone. In interval naming, "a/b-augmented" (abbreviated as a/b-A) means a/b of a chromatic semitone above a major or perfect interval, and "a/b-diminished" (abbreviated as a/b-D) means a/b of a chromatic semitone below a minor or diminished interval. To address intervals which are between minor and major, "a/b-augmented minor" is used for a/b chromatic semitones above a minor interval, and "a/b-diminished major" is used for a/b chromatic semitones below a major interval (this was suggested by [[User:Frostburn|Frostburn]]). 1/2-augmented minor and 1/2-diminished major are identical, corresponding to halfway between minor and major, so both are replaced with the more conventional term "neutral" (n).
 == For EDOs ==