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 almost all [[EDO]]s and several [[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 #1/2 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.

<nowiki>#</nowiki>a/b (can be spoken as "a over b sharp") is always taken to raise by a/b chromatic semitones, and ba/b is always taken to lower by a/b chromatic semitones. The "augmented" and "diminished" qualifiers are also extended to arbitrary rational amounts, where a/b-augmented (~~A~~a/b~~~~) widens the interval by a/b chromatic semitones and a/b-diminished (~~d~~a/b~~~~) narrows the interval by a/b chromatic semitones. Intervals between minor and major are expressed as a/b-augmented minor or a/b-diminished major (this was suggested by [[User:Frostburn]]). For example, 1/3 of the way from a minor third to a major third is a 1/3-augmented minor third, while 2/3 of the way from a minor third to a major third is a 1/3-diminished major third. Because 1/2-augmented ~~major~~ and 1/2-diminished ~~minor~~ are identical, they are instead referred to by the more conventional "neutral" (n).

<nowiki>#</nowiki>a/b (can be spoken as "a over b sharp") is always taken to raise by a/b chromatic semitones, and ba/b is always taken to lower by a/b chromatic semitones. The "augmented" and "diminished" qualifiers for interval names are also extended to arbitrary rational amounts, where a/b-augmented (a/b-A) widens the interval by a/b chromatic semitones and a/b-diminished (a/b-d) narrows the interval by a/b chromatic semitones. Intervals between minor and major are expressed as a/b-augmented minor or a/b-diminished major (this was suggested by [[User:Frostburn]]). For example, 1/3 of the way from a minor third to a major third is a 1/3-augmented minor third, while 2/3 of the way from a minor third to a major third is a 1/3-diminished major third. Because 1/2-augmented minor and 1/2-diminished major are identical, they are instead referred to by the more conventional "neutral" (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 almost all [[EDO]]s and several [[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.
-<nowiki>#</nowiki><sup>a/b</sup> (can be spoken as "a over b sharp") is always taken to raise by a/b chromatic semitones, and b<sup>a/b</sup> is always taken to lower by a/b chromatic semitones. The "augmented" and "diminished" qualifiers are also extended to arbitrary rational amounts, where a/b-augmented (A<sup>a/b</sup>) widens the interval by a/b chromatic semitones and a/b-diminished (d<sup>a/b</sup>) narrows the interval by a/b chromatic semitones. Intervals between minor and major are expressed as a/b-augmented minor or a/b-diminished major (this was suggested by [[User:Frostburn]]). For example, 1/3 of the way from a minor third to a major third is a 1/3-augmented minor third, while 2/3 of the way from a minor third to a major third is a 1/3-diminished major third. Because 1/2-augmented major and 1/2-diminished minor are identical, they are instead referred to by the more conventional "neutral" (n).
+<nowiki>#</nowiki><sup>a/b</sup> (can be spoken as "a over b sharp") is always taken to raise by a/b chromatic semitones, and b<sup>a/b</sup> is always taken to lower by a/b chromatic semitones. The "augmented" and "diminished" qualifiers for interval names are also extended to arbitrary rational amounts, where a/b-augmented (a/b-A) widens the interval by a/b chromatic semitones and a/b-diminished (a/b-d) narrows the interval by a/b chromatic semitones. Intervals between minor and major are expressed as a/b-augmented minor or a/b-diminished major (this was suggested by [[User:Frostburn]]). For example, 1/3 of the way from a minor third to a major third is a 1/3-augmented minor third, while 2/3 of the way from a minor third to a major third is a 1/3-diminished major third. Because 1/2-augmented minor and 1/2-diminished major are identical, they are instead referred to by the more conventional "neutral" (n).
 == For EDOs ==
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+{{Navbox notation}}
 [[Category:Notation]]