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}}.

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.

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.

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}}.
-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.
+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.
 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}}].