Extended bra–ket notation: Difference between revisions

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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}}.

~~The stylistic reasoning~~ is that the curly bracket 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 in teaching this subject it is often desirable to include parenthesized expressions as entries in the bra or ket, which would be very difficult to read. A mnemonic is that the curly bracket 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}}].

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 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}}.
-The stylistic reasoning is that the curly bracket 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 in teaching this subject it is often desirable to include parenthesized expressions as entries in the bra or ket, which would be very difficult to read. A mnemonic is that the curly bracket 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}}].