Extended bra–ket notation: Difference between revisions

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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 {{bra| 1200.000 1896.578 2786.314 }}, the generator tuning map could be written {{rbra| 1200.000 696.578 }}.

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 [{{ket| 4 -4 1 }} {{ket| 7 0 -3 }}] because its width is equal to the [[nullity]] of the temperament, <math>n</math>. This is consistent with the fact that it is common for linear algebra texts to treat a nullspace basis not as a matrix but as a mere list of vectors.

They 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 [{{ket| 4 -4 1 }} {{ket| 7 0 -3 }}] because its width is equal to the [[nullity]] of the temperament, <math>n</math>. This is consistent with the fact that it is common for linear algebra texts to treat a nullspace basis not as a matrix but as a mere list of vectors.

Instead of curly brackets, we considered using round brackets (parentheses), (…] […), 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.

Instead of curly brackets, they considered using round brackets (parentheses), (…] […), 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.

We also considered using curved angle brackets ⧼…] […⧽, (Unicode U+29FC and U+29FD), however in some fonts these are almost indistinguishable from ordinary angle brackets. If you see distinctly-curved angle brackets in the preceding sentence, it may only be because we specified ~~that they~~ be shown in one of the fonts 'STIXGeneral', 'Cambria Math' (Windows) or 'STIX Two Math' (Mac). Here's an ordinary angle bracket followed by a curved angle bracket without special treatment: ⟩⧽. If this situation should change in future, a mnemonic for the curved angle brackets is that they can also be called "rounded" angle brackets, and a rounded number is an approximate number in the same way that a tempered interval is an approximation of a just interval. Curly brackets would still be used as a substitute in ASCII-only environments.

They also considered using curved angle brackets ⧼…] […⧽, (Unicode U+29FC and U+29FD), however in some fonts these are almost indistinguishable from ordinary angle brackets. If you see distinctly-curved angle brackets in the preceding sentence, it may only be because they have been specified to be shown in one of the fonts 'STIXGeneral', 'Cambria Math' (Windows) or 'STIX Two Math' (Mac). Here's an ordinary angle bracket followed by a curved angle bracket without special treatment: ⟩⧽. If this situation should change in future, a mnemonic for the curved angle brackets is that they can also be called "rounded" angle brackets, and a rounded number is an approximate number in the same way that a tempered interval is an approximation of a just interval. Curly brackets would still be used as a substitute in ASCII-only environments.

== Notes ==

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 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 {{bra| 1200.000 1896.578 2786.314 }}, the generator tuning map could be written {{rbra| 1200.000 696.578 }}.
-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 [{{ket| 4 -4 1 }} {{ket| 7 0 -3 }}] because its width is equal to the [[nullity]] of the temperament, <math>n</math>. This is consistent with the fact that it is common for linear algebra texts to treat a nullspace basis not as a matrix but as a mere list of vectors.
+They 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 [{{ket| 4 -4 1 }} {{ket| 7 0 -3 }}] because its width is equal to the [[nullity]] of the temperament, <math>n</math>. This is consistent with the fact that it is common for linear algebra texts to treat a nullspace basis not as a matrix but as a mere list of vectors.
-Instead of curly brackets, we considered using round brackets (parentheses), (…] […), 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.
+Instead of curly brackets, they considered using round brackets (parentheses), (…] […), 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.
-We also considered using curved angle brackets <span style="font-family: STIXGeneral, 'Cambria Math', 'STIX Two Math', serif">⧼</span>…] […<span style="font-family: STIXGeneral, 'Cambria Math', 'STIX Two Math', serif">⧽</span>, (Unicode U+29FC and U+29FD), however in some fonts these are almost indistinguishable from ordinary angle brackets. If you see distinctly-curved angle brackets in the preceding sentence, it may only be because we specified that they be shown in one of the fonts 'STIXGeneral', 'Cambria Math' (Windows) or 'STIX Two Math' (Mac). Here's an ordinary angle bracket followed by a curved angle bracket without special treatment: ⟩⧽. If this situation should change in future, a mnemonic for the curved angle brackets is that they can also be called "rounded" angle brackets, and a rounded number is an approximate number in the same way that a tempered interval is an approximation of a just interval. Curly brackets would still be used as a substitute in ASCII-only environments.
+They also considered using curved angle brackets <span style="font-family: STIXGeneral, 'Cambria Math', 'STIX Two Math', serif">⧼</span>…] […<span style="font-family: STIXGeneral, 'Cambria Math', 'STIX Two Math', serif">⧽</span>, (Unicode U+29FC and U+29FD), however in some fonts these are almost indistinguishable from ordinary angle brackets. If you see distinctly-curved angle brackets in the preceding sentence, it may only be because they have been specified to be shown in one of the fonts 'STIXGeneral', 'Cambria Math' (Windows) or 'STIX Two Math' (Mac). Here's an ordinary angle bracket followed by a curved angle bracket without special treatment: ⟩⧽. If this situation should change in future, a mnemonic for the curved angle brackets is that they can also be called "rounded" angle brackets, and a rounded number is an approximate number in the same way that a tempered interval is an approximation of a just interval. Curly brackets would still be used as a substitute in ASCII-only environments.
 == Notes ==