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 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 ~~or caret (like~~ #<sup>1/2</sup> for half-sharp) except for in the case of single and double accidentals.~~The sharp and flat accidentals are always taken to raise and lower by an augmented union or apotome. 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 3rd"~~, ~~meaning a minor 3rd 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"~~.

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 #<sup>1/2</sup> for half-sharp, except for in the case of single and double accidentals. If ASCII compatibility is required, superscripts can be substituted for carets–in this case, #^(a/b) is usually preferred over #^a/b for clarity.

The sharp and flat accidentals are always taken to raise and lower by an augmented union or chromatic semitone. In interval naming, x-augmented (x-A) is x chromatic semitones above a major or perfect interval, x-diminished (x-d) is x chromatic semitones below a minor or perfect interval. Additionally, for intervals between major and minor, "x-augmented minor" (x-Am) is x chromatic semitones above minor and "x-diminished major" (x-dM) is x chromatic semitones below major. For example "1/3-augmented minor 3rd" (1/3-Am3) means a minor 3rd raised by 1/3 of a chromatic semitone (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" (n).

==For EDOs ==

== For EDOs ==

~~Fractional sharp notes by~~ using a ~~[[3~~-~~limit]] mapping~~. Excluding [[1edo]]-[[4edo]] and [[8edo]], there are four EDOs (all multiples of [[7edo]]) that cannot be notated using the native fifth: [[14edo]], [[21edo]], [[28edo]] and [[35edo]]. However, it is still possible to notate them with [[subset notation]], using [[42edo]]'s notation for 14edo and 21edo, [[56edo]]'s notation for 28edo, and [[70edo]]'s notation for 35edo. [[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~~. Accidentals do not stack for large EDOs because of the superscript notation, but the amount of sharps can often be a complicated rational number.

By using a tempered fifth, almost all EDO tunings are supported, since there is support for not only half-sharps and half-flats, but third-sharps, third-flats and so on. Excluding [[1edo]]-[[4edo]] and [[8edo]], there are four EDOs (all multiples of [[7edo]]) that cannot be notated using the native fifth: [[14edo]], [[21edo]], [[28edo]] and [[35edo]]. However, it is still possible to notate them with [[subset notation]], using [[42edo]]'s notation for 14edo and 21edo, [[56edo]]'s notation for 28edo, and [[70edo]]'s notation for 35edo. [[2L 5s|Antidiatonic]] fifths may be notated using both the "major wider than minor" and "minor wider than major" systems. Accidentals do not stack for large EDOs because of the superscript notation, but the amount of sharps can often be a complicated rational number.

== Examples ==

@@ Line 1: / Line 1: @@
 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 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 or caret (like #<sup>1/2</sup> for half-sharp) except for in the case of single and double accidentals.The sharp and flat accidentals are always taken to raise and lower by an augmented union or apotome. 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 3rd", meaning a minor 3rd 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".
+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 #<sup>1/2</sup> for half-sharp, except for in the case of single and double accidentals. If ASCII compatibility is required, superscripts can be substituted for carets–in this case, #^(a/b) is usually preferred over #^a/b for clarity.
+The sharp and flat accidentals are always taken to raise and lower by an augmented union or chromatic semitone. In interval naming, x-augmented (x-A) is x chromatic semitones above a major or perfect interval, x-diminished (x-d) is x chromatic semitones below a minor or perfect interval. Additionally, for intervals between major and minor, "x-augmented minor" (x-Am) is x chromatic semitones above minor and "x-diminished major" (x-dM) is x chromatic semitones below major. For example "1/3-augmented minor 3rd" (1/3-Am3) means a minor 3rd raised by 1/3 of a chromatic semitone (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" (n).
-==For EDOs ==
+== For EDOs ==
-Fractional sharp notes by using a [[3-limit]] mapping. Excluding [[1edo]]-[[4edo]] and [[8edo]], there are four EDOs (all multiples of [[7edo]]) that cannot be notated using the native fifth: [[14edo]], [[21edo]], [[28edo]] and [[35edo]]. However, it is still possible to notate them with [[subset notation]], using [[42edo]]'s notation for 14edo and 21edo, [[56edo]]'s notation for 28edo, and [[70edo]]'s notation for 35edo. [[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.  Accidentals do not stack for large EDOs because of the superscript notation, but the amount of sharps can often be a complicated rational number.
+By using a tempered fifth, almost all EDO tunings are supported, since there is support for not only half-sharps and half-flats, but third-sharps, third-flats and so on. Excluding [[1edo]]-[[4edo]] and [[8edo]], there are four EDOs (all multiples of [[7edo]]) that cannot be notated using the native fifth: [[14edo]], [[21edo]], [[28edo]] and [[35edo]]. However, it is still possible to notate them with [[subset notation]], using [[42edo]]'s notation for 14edo and 21edo, [[56edo]]'s notation for 28edo, and [[70edo]]'s notation for 35edo. [[2L 5s|Antidiatonic]] fifths may be notated using both the "major wider than minor" and "minor wider than major" systems. Accidentals do not stack for large EDOs because of the superscript notation, but the amount of sharps can often be a complicated rational number.
 == Examples ==