Fractional sharp notation: Difference between revisions

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 b^a/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).