Fractional sharp notation: Difference between revisions

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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, "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 perfect 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" (abbreviated as lowercase n).

The sharp and flat accidentals are always taken to raise and lower by an augmented union or chromatic semitone. Interval naming is accomplished by augmented and diminished to fractional values–"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 perfect 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" (abbreviated as lowercase n).

== For EDOs ==

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 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, "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 perfect 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" (abbreviated as lowercase n).
+The sharp and flat accidentals are always taken to raise and lower by an augmented union or chromatic semitone. Interval naming is accomplished by augmented and diminished to fractional values–"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 perfect 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" (abbreviated as lowercase n).
 == For EDOs ==