Fractional sharp notation: Difference between revisions

The '''fractional sharp notation''' (FSN) is a notation developed by [[User:CompactStar|CompactStar]] that is largely an extension of [[circle-of-fifths notation]], which can be used for [[EDO]]s, and secondarily for [[temperament]]s and [[just intonation]] subgroups of [[rank]] 3. It represents all intervals with conventional accidentals, but with sharps and flats extended to have an arbitrary rational amount, denoted by a superscript (like #^1/2 for half-sharp) except for in the case of single and double accidentals. This means that there is support for not only half-sharps and half-flats, but third-sharps, third-flats and so on, supporting almost all equal tunings. Multiples of [[7edo]] up to [[35edo]], and excluding [[7edo]] itself, are not supported, but these are possible to be notated as subsets of larger EDOs. In particular, [[14edo]] and [[21edo]] can be notated as subsets of  [[42edo]] and [[28edo]] as a subset of [[56edo]].

The sharp and flat accidentals are always taken to raise and lower by an augmented union. In a given EDO system, the step size is 1 over the [[sharpness]] of a sharp. In interval naming, x-major represents x of the way from minor to major (0-major is minor and 1-major is major), x-augmented represents x of the way from perfect/major to augmented, and x-diminished represents x of the way from perfect/minor to diminished. 1/2-major is essentially the same as "neutral". Augmented and diminished can be stacked more than once, such as doubly augmented, and with fractions as well like 3/2-augmented.