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 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 '''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 | 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. | ||
Revision as of 04:43, 1 March 2024
VERY WIP (I'll move it to the main namespace if it's finished.)
The fractional sharp notation (FSN) is a notation developed by CompactStar that is largely an extension of circle-of-fifths notation, which can be used for EDOs, and secondarily for temperaments 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.
Accidentals
| Prime limit | Comma | Sharps |
|---|---|---|
| 5 | 81/80 | 1/5 |
| 7 | 64/63 | 1/4 |
| 11 | 33/32 | 1/2 |
| 13 | 1053/1024 | 1/2 |
| 17 | 4131/4096 | 1/8 |
| 19 | 513/512 | 1/34 |
| 23 | 736/729 | 1/7 |