Extended bra–ket notation: Difference between revisions

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===Variant including curly and square brackets===

Dave Keenan and Douglas Blumeyer propose that it may be helpful to distinguish objects with distinctive shapes, such as GC-vectors and [[generator tuning map]]s, by using curly ~~brackets~~ in place of angle ~~brackets~~, wherever the height or width of a vector or matrix is equal to the [[rank]] of the temperament, <math>r</math>.

Dave Keenan and Douglas Blumeyer propose that it may be helpful to distinguish objects with distinctive shapes, such as GC-vectors and [[generator tuning map]]s, by using a curly bracket [...} in place of an angle bracket [..⟩, wherever the height or width of a vector or matrix is equal to the [[rank]] of the temperament, <math>r</math>.

For ~~examples~~, while the PC-vector representing 5/4 would be written {{vector|-2 0 1}}, the mapped version of this in meantone could be written {{rket|-2 4}}. And while the tuning map for quarter-comma meantone might be written {{map|1200.000 1896.578 2786.314}}, the generator tuning map could be written {{rbra|1200.000 696.578}}.

For example, while the PC-vector representing 5/4 would be written {{vector|-2 0 1}}, the mapped version of this in meantone could be written {{rket|-2 4}}. And while the tuning map for quarter-comma meantone might be written {{map|1200.000 1896.578 2786.314}}, the generator tuning map could be written {{rbra|1200.000 696.578}}.

We considered using a round bracket for this, [...), however it is sometimes necessary to include parenthesized expressions as entries in the bra or ket, which would be ~~very~~ difficult to parse if we had round bra or ket brackets. A mnemonic for the curly bracket is that it resembles the tilde (~) which is commonly used to mark approximated or tempered intervals, e.g. ~3/2 is an approximation of 3/2.

We considered using a round bracket for this, [...), however it is sometimes necessary to include parenthesized expressions as entries in the bra or ket, which would be difficult to parse if we had round bra or ket brackets. A mnemonic for the curly bracket is that it resembles the tilde (~) which is commonly used to mark approximated or tempered intervals, e.g. ~3/2 is an approximation of 3/2.

~~Furthermore,~~ the use of the normal angle bracket could be restricted to matrix widths and heights equal only to the [[dimensionality]] of the temperament, <math>d</math>, and any other width or height besides <math>d</math> and <math>r</math> would be given with plain square brackets. So, for example, a comma basis could be written [{{vector|4 -4 1}} {{vector|7 0 -3}}].

We further propose that the use of the normal angle bracket could be restricted to matrix widths and heights equal only to the [[dimensionality]] of the temperament, <math>d</math>, and any other width or height besides <math>d</math> and <math>r</math> would be given with plain square brackets [...]. So, for example, a comma basis could be written [{{vector|4 -4 1}} {{vector|7 0 -3}}] because its width is equal to the [[nullity]] <math>n</math> of the temperament.

==Notes==

@@ Line 141: / Line 141: @@
 ===Variant including curly and square brackets===
-Dave Keenan and Douglas Blumeyer propose that it may be helpful to distinguish objects with distinctive shapes, such as GC-vectors and [[generator tuning map]]s, by using curly brackets in place of angle brackets, wherever the height or width of a vector or matrix is equal to the [[rank]] of the temperament, <math>r</math>.
+Dave Keenan and Douglas Blumeyer propose that it may be helpful to distinguish objects with distinctive shapes, such as GC-vectors and [[generator tuning map]]s, by using a curly bracket [...} in place of an angle bracket [..⟩, wherever the height or width of a vector or matrix is equal to the [[rank]] of the temperament, <math>r</math>.
-For examples, while the PC-vector representing 5/4 would be written {{vector|-2 0 1}}, the mapped version of this in meantone could be written {{rket|-2 4}}. And while the tuning map for quarter-comma meantone might be written {{map|1200.000 1896.578 2786.314}}, the generator tuning map could be written {{rbra|1200.000 696.578}}.
+For example, while the PC-vector representing 5/4 would be written {{vector|-2 0 1}}, the mapped version of this in meantone could be written {{rket|-2 4}}. And while the tuning map for quarter-comma meantone might be written {{map|1200.000 1896.578 2786.314}}, the generator tuning map could be written {{rbra|1200.000 696.578}}.
-We considered using a round bracket for this, [...), however it is sometimes necessary to include parenthesized expressions as entries in the bra or ket, which would be very difficult to parse if we had round bra or ket brackets. A mnemonic for the curly bracket is that it resembles the tilde (~) which is commonly used to mark approximated or tempered intervals, e.g. ~3/2 is an approximation of 3/2.
+We considered using a round bracket for this, [...), however it is sometimes necessary to include parenthesized expressions as entries in the bra or ket, which would be difficult to parse if we had round bra or ket brackets. A mnemonic for the curly bracket is that it resembles the tilde (~) which is commonly used to mark approximated or tempered intervals, e.g. ~3/2 is an approximation of 3/2.
-Furthermore, the use of the normal angle bracket could be restricted to matrix widths and heights equal only to the [[dimensionality]] of the temperament, <math>d</math>, and any other width or height besides <math>d</math> and <math>r</math> would be given with plain square brackets. So, for example, a comma basis could be written [{{vector|4 -4 1}} {{vector|7 0 -3}}].
+We further propose that the use of the normal angle bracket could be restricted to matrix widths and heights equal only to the [[dimensionality]] of the temperament, <math>d</math>, and any other width or height besides <math>d</math> and <math>r</math> would be given with plain square brackets [...]. So, for example, a comma basis could be written [{{vector|4 -4 1}} {{vector|7 0 -3}}] because its width is equal to the [[nullity]] <math>n</math> of the temperament.
 ==Notes==