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Following Frostburn's suggestion here for aug minor and dim major, since it's unintuitive to call minor intervals "x-major"
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VERY WIP (I'll move it to the main namespace if it's finished.)
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 [[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 EDO systems. 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]], [[28edo]] as a subset of [[56edo]], and [[35edo]] as a subset of [[70edo]] or using the alternative fifth from [[5edo]]. [[1edo]] to [[4edo]] are obviously notated as subsets, and [[8edo]] is also required to be notated as a subset of [[16edo]], [[24edo]], or [[32edo]] with no fifth except for 750 cents. [[2L 5s|Antidiatonic]] fifths may be notated using both the "major wider than minor" and "minor wider than major" systems, depending on what is needed.
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 or caret (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 EDO systems. 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]], [[28edo]] as a subset of [[56edo]], and [[35edo]] as a subset of [[70edo]] or using the alternative fifth from [[5edo]]. [[1edo]] to [[4edo]] are obviously notated as subsets, and [[8edo]] is also required to be notated as a subset of [[16edo]], [[24edo]], or [[32edo]] with no fifth except for 750 cents. [[2L 5s|Antidiatonic]] fifths may be notated using both the "major wider than minor" and "minor wider than major" systems, depending on what is needed.


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:
The sharp and flat accidentals are always taken to raise and lower by an augmented union or apotome. In a given EDO system, the step size is 1 over the [[sharpness]] of a sharp. In interval naming, x-augmented and x-diminished raise and lower by x times a chromatic semitone. These are used in the same way as augmented and diminished normally are, but additionally, "augmented minor" and "diminished major" are used for constructions like "1/3-augmented minor", meaning a minor third raised by 1/3 of an apotome (formerly these were described as a "fraction of major" like 1/3-major, the updated version was suggested by [[User:Frostburn|Frostburn]]). Since 1/2-augmented minor and 1/2-diminished major mean the same thing, they are replaced with the more conventional term "neutral".
* x-major represents x of the way from minor to major (1/2-major is the same as "neutral" essentially).
* x-augmented represents x of the way from perfect/major to augmented.
* x-diminished represents x of the way from perfect/minor to diminished.
* Augmented and diminished can be stacked more than once if needed, such as doubly augmented, and with fractional amounts as well like 3/2-augmented.


Here is an example for [[22edo]]:
Here is an example for [[22edo]]:
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| 2
| 2
| 109.091
| 109.091
| 1/3-major 2nd
| 1/3-aug minor 2nd
| 1/3-M2
| 1/3-AM2
| Eb<sup>2/3</sup>
| Eb<sup>2/3</sup>
|-
|-
| 3
| 3
| 163.636
| 163.636
| 2/3-major 2nd
| 1/3-dim major 2nd
| 2/3-M2
| 1/3-dM2
| Eb<sup>1/3</sup>
| Eb<sup>1/3</sup>
|-
|-
Line 56: Line 52:
| 6
| 6
| 327.273
| 327.273
| 1/3-major 3rd
| 1/3-aug minor 3rd
| 1/3-M3
| 1/3-Am3
| F#<sup>1/3</sup>
| F#<sup>1/3</sup>
|-
|-
| 7
| 7
| 381.818
| 381.818
| 2/3-major 3rd
| 1/3-aug dim 3rd
| 2/3-M3
| 1/3-dM3
| F#<sup>2/3</sup>
| F#<sup>2/3</sup>
|-
|-
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| 15
| 15
| 818.182
| 818.182
| 1/3-major 6th
| 1/3-aug minor 6th
| 1/3-M6
| 1/3-Am6
| Bb<sup>2/3</sup>
| Bb<sup>2/3</sup>
|-
|-
| 16
| 16
| 872.727
| 872.727
| 2/3-major 6th
| 1/3-dim major 6th
| 2/3-M6
| 1/3-dM6
| Bb<sup>1/3</sup>
| Bb<sup>1/3</sup>
|-
|-
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| 19
| 19
| 1036.364
| 1036.364
| 1/3-major 7th
| 1/3-aug minor 7th
| 1/3-M7
| 1/3-Am7
| C#<sup>1/3</sup>
| C#<sup>1/3</sup>
|-
|-
| 20
| 20
| 1090.909
| 1090.909
| 2/3-major 7th
| 1/3-dim major 7th
| 2/3-M7
| 1/3-dM7
| C#<sup>2/3</sup>
| C#<sup>2/3</sup>
|-
|-
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