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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 an extension of [[chain-of-fifths notation]], supporting a wide range of [[EDO]] and [[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 {{sharp}}<sup>1/2</sup> for half-sharp. If ASCII compatibility is required, superscripts can be substituted for carets–in this case, #^(a/b) is preferred over #^a/b for clarity.
The '''fractional sharp notation''' (FSN) is a notation developed by [[User:CompactStar|CompactStar]] that is an extension of [[chain-of-fifths notation]], supporting a wide range of [[EDO]] and [[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 {{sharp}}<sup>1/2</sup> for half-sharp. If ASCII compatibility is required, superscripts can be substituted for carets–in this case, #^(a/b) is preferred over #^a/b for clarity.


As in the original chain-of-fifths notation, the sharp and flat accidentals are always taken to raise and lower by an augmented union or chromatic semitone. For interval naming, augmented and diminished are expanded to fractional values: a/b-augmented (abbreviated as A<sup>a/b</sup>) is a/b of a chromatic semitone above a major or perfect interval, and a/b-diminished (abbreviated as a/b-d) is a/b of a chromatic semitone below a minor or perfect interval. Additionally, for intervals between minor and major, a/b-augmented minor is used for a/b chromatic semitones above a minor interval, and a/b-diminished major is used for a/b chromatic semitones below a major interval (this was suggested by [[User:Frostburn|Frostburn]]). 1/2-augmented minor and 1/2-diminished major are identical, corresponding to halfway between minor and major, so both are replaced with the more conventional term "neutral" (abbreviated as lowercase n).
As in the original chain-of-fifths notation, the sharp and flat accidentals are always taken to raise and lower by an augmented union or chromatic semitone. {{shar}}<sup>x</sup> and .


== For EDOs ==
== For EDOs ==
Line 27: Line 27:
| 1/2-aug unison, minor 2nd
| 1/2-aug unison, minor 2nd
| 1/2-A1, m2
| 1/2-A1, m2
| D#<sup>1/2</sup>, Eb
| D{{sharp}}<sup>1/2</sup>, Eb
|-
|-
| 2
| 2
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| aug unison, neutral 2nd
| aug unison, neutral 2nd
| A1, n2
| A1, n2
| D#, Eb<sup>1/2</sup>
| D{{sharp}}, Eb<sup>1/2</sup>
|-
|-
| 3
| 3
Line 51: Line 51:
| neutral 3rd
| neutral 3rd
| n3
| n3
| F#<sup>1/2</sup>
| F{{sharp}}<sup>1/2</sup>
|-
|-
| 6
| 6
Line 57: Line 57:
| major 3rd
| major 3rd
| M3
| M3
| F#
| F{{sharp}}
|-
|-
| 7
| 7
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| 1/2-aug 4th, dim 5th
| 1/2-aug 4th, dim 5th
| 1/2-A4, d5
| 1/2-A4, d5
| G#<sup>1/2</sup>, Ab
| G{{sharp}}<sup>1/2</sup>, Ab
|-
|-
| 9
| 9
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| aug 4th, 1/2-dim 5th
| aug 4th, 1/2-dim 5th
| A4, 1/2-d5
| A4, 1/2-d5
| G#, Ab<sup>1/2</sup>  
| G{{sharp}}, Ab<sup>1/2</sup>  
|-
|-
| 10
| 10
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| neutral 7th, dim octave
| neutral 7th, dim octave
| n7, d8
| n7, d8
| C#<sup>1/2</sup>, Db
| C{{sharp}}<sup>1/2</sup>, Db
|-
|-
| 16
| 16
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| major 7th, 1/2-dim octave
| major 7th, 1/2-dim octave
| M7, 1/2-d8
| M7, 1/2-d8
| C#, Db<sup>1/2</sup>
| C{{sharp}}, Db<sup>1/2</sup>
|-
|-
| 17
| 17
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| 1/3-aug unison, minor 2nd
| 1/3-aug unison, minor 2nd
| 1/3-A1, m2
| 1/3-A1, m2
| D#<sup>1/3</sup>, Eb
| D{{sharp}}<sup>1/3</sup>, Eb
|-
|-
| 2
| 2
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| 2/3-aug unison, 1/3-aug minor 2nd
| 2/3-aug unison, 1/3-aug minor 2nd
| 2/3-A1, 1/3-AM2
| 2/3-A1, 1/3-AM2
| D#<sup>2/3</sup>, Eb<sup>2/3</sup>
| D{{sharp}}<sup>2/3</sup>, Eb<sup>2/3</sup>
|-
|-
| 3
| 3
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| aug unison, 1/3-dim major 2nd
| aug unison, 1/3-dim major 2nd
| A1, 1/3-dM2
| A1, 1/3-dM2
| D#, Eb<sup>1/3</sup>
| D{{sharp}}, Eb<sup>1/3</sup>
|-
|-
| 4
| 4
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| 1/3-aug minor 3rd
| 1/3-aug minor 3rd
| 1/3-Am3
| 1/3-Am3
| F#<sup>1/3</sup>
| F{{sharp}}<sup>1/3</sup>
|-
|-
| 7
| 7
Line 180: Line 180:
| 1/3-dim major 3rd
| 1/3-dim major 3rd
| 1/3-dM3
| 1/3-dM3
| F#<sup>2/3</sup>
| F{{sharp}}<sup>2/3</sup>
|-
|-
| 8
| 8
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| major 3rd
| major 3rd
| M3
| M3
| F#
| F{{sharp}}
|-
|-
| 9
| 9
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| 1/3-aug 4th, dim 5th
| 1/3-aug 4th, dim 5th
| 1/3-A4, d5
| 1/3-A4, d5
| G#<sup>1/3</sup>, Ab
| G{{sharp}}<sup>1/3</sup>, Ab
|-
|-
| 11
| 11
Line 204: Line 204:
| 2/3-aug 4th, 2/3-dim 5th
| 2/3-aug 4th, 2/3-dim 5th
| 2/3-A4, 2/3-d5
| 2/3-A4, 2/3-d5
| G#<sup>2/3</sup>, Ab<sup>2/3</sup>
| G{{sharp}}<sup>2/3</sup>, Ab<sup>2/3</sup>
|-
|-
| 12
| 12
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| aug 4th, 1/3-dim 5th
| aug 4th, 1/3-dim 5th
| A4, 1/3-d5
| A4, 1/3-d5
| G#, Ab<sup>1/3</sup>
| G{{sharp}}, Ab<sup>1/3</sup>
|-
|-
| 13
| 13
Line 252: Line 252:
| 1/3-aug minor 7th
| 1/3-aug minor 7th
| 1/3-Am7
| 1/3-Am7
| C#<sup>1/3</sup>
| C{{sharp}}<sup>1/3</sup>
|-
|-
| 20
| 20
Line 258: Line 258:
| 1/3-dim major 7th
| 1/3-dim major 7th
| 1/3-dM7
| 1/3-dM7
| C#<sup>2/3</sup>
| C{{sharp}}<sup>2/3</sup>
|-
|-
| 21
| 21
Line 264: Line 264:
| major 7th
| major 7th
| M7
| M7
| C#
| C{{sharp}}
|-
|-
| 22
| 22
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