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 largely an extension of [[circle-of-fifths notation]], which can be used for [[EDO]]s and secondarily for [[just intonation]]. It represents all intervals with conventional accidentals, but with sharps and flats extended to have an arbitrary rational amount, denoted by a superscript (like #<sup>1/2</sup> 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]] are not supported, but these are possible to be notated as subsets of larger EDOs, ~~with~~ [[14edo]] and [[21edo]] ~~in particular~~ as ~~both~~ subsets of [[42edo]].

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 #<sup>1/2</sup> 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, 1/2-major is aliased as "neutral" for compatibility), 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. Augmented and diminished can be stacked more than once, such as doubly augmented, and with fractions as well like 3/2-augmented.

~~any accident~~

~~== Just intonation ==~~

~~(this part of the notation is the most likely to be scrapped/changed)~~

=== Accidentals ===

{|class="wikitable"

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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 largely an extension of [[circle-of-fifths notation]], which can be used for [[EDO]]s and secondarily for [[just intonation]]. It represents all intervals with conventional accidentals, but with sharps and flats extended to have an arbitrary rational amount, denoted by a superscript (like #<sup>1/2</sup> 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]] are not supported, but these are possible to be notated as subsets of larger EDOs, with [[14edo]] and [[21edo]] in particular as both subsets of [[42edo]].
+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 #<sup>1/2</sup> 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, 1/2-major is aliased as "neutral" for compatibility), 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. Augmented and diminished can be stacked more than once, such as doubly augmented, and with fractions as well like 3/2-augmented.
-any accident
-== Just intonation ==
-(this part of the notation is the most likely to be scrapped/changed)
 === Accidentals ===
 {|class="wikitable"