Fractional sharp notation: Difference between revisions

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}}^1/2 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. {{shar}}^x and .

A few [[rank-2 temperament]]s can be notated, but only ones which have a period of an unsplit octave, and in which the [[generator]] can be expressed as an FSN interval category.  For example, [[neutral]] temperament can have the generator notated as n3, and [[porcupine]] temperament can have the generator notated as 1/3-dM2, because the difference between the generator and [[9/8]] (represented by [[81/80]]) is equated to 1/3 of an [[2187/2048|apotome]] in porcupine. [[Semaphore]] is an example of a temperament which does not qualify, because there is no FSN category that implies a semifourth.  

| D{{sharp}}^1/2, Eb

| D{{sharp}}, Eb^1/2

| F{{sharp}}^1/2

| F{{sharp}}

| G{{sharp}}^1/2, Ab

| G{{sharp}}, Ab^1/2  

| C{{sharp}}^1/2, Db

| C{{sharp}}, Db^1/2

| D{{sharp}}^1/3, Eb

| D{{sharp}}^2/3, Eb^2/3

| D{{sharp}}, Eb^1/3

| F{{sharp}}^1/3

| F{{sharp}}^2/3

| F{{sharp}}

| G{{sharp}}^1/3, Ab

| G{{sharp}}^2/3, Ab^2/3

| G{{sharp}}, Ab^1/3

| C{{sharp}}^1/3

| C{{sharp}}^2/3

| C{{sharp}}