Extended bra–ket notation: Difference between revisions
Dave Keenan (talk | contribs) Added "where <math>g</math> is the grade". |
Dave Keenan (talk | contribs) →Extensions: Changed "nesting" to "alternating", since "repeating" is a kind of nesting too. |
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==Extensions== | ==Extensions== | ||
EBK extends standard bra-ket notation | EBK extends standard bra-ket notation using two different kinds of nesting: | ||
# '' | # ''alternating'', to allow for notating matrices, and | ||
# ''repeating'', to allow for notating multivectors. | # ''repeating'', to allow for notating multivectors. | ||
=== | ===Alternating, for matrices=== | ||
Vectors (including covectors) are used to represent musical objects of various dimensionality. For example, the PC-vector {{vector|1 -2 1}} represents the interval 10/9, which would be found as a point in the ''three''-dimensional space of 5-limit JI lattice, while the PC-vector {{vector|0 -1 1 1 -1}} represents the interval 35/33, which would be found as a point in the ''five''-dimensional space of the 11-limit JI lattice. However, regardless of the dimensionality of the musical object represented, a vector itself will always be a ''one''-dimensional structure, in the sense that it is a simple list of numbers. Due to this, vectors are always fairly easy to embed in similarly one-dimensional strings of text or data cells of tables. | Vectors (including covectors) are used to represent musical objects of various dimensionality. For example, the PC-vector {{vector|1 -2 1}} represents the interval 10/9, which would be found as a point in the ''three''-dimensional space of 5-limit JI lattice, while the PC-vector {{vector|0 -1 1 1 -1}} represents the interval 35/33, which would be found as a point in the ''five''-dimensional space of the 11-limit JI lattice. However, regardless of the dimensionality of the musical object represented, a vector itself will always be a ''one''-dimensional structure, in the sense that it is a simple list of numbers. Due to this, vectors are always fairly easy to embed in similarly one-dimensional strings of text or data cells of tables. | ||
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====History==== | ====History==== | ||
The | The alternating-for-matrices extension was contributed by [[Graham Breed]], dating at least from March 2008 when he used it in his paper "Provably Complete Rank 2 Temperament Searches"<ref>http://x31eq.com/complete.pdf, beginning on page 4</ref>. | ||
====Usage==== | ====Usage==== | ||
The | The alternating-for-matrices extension is used in Graham Breed's writings and web app, as well as the writings on the wiki of [[Douglas Blumeyer]] and [[Dave Keenan]]. | ||
====Alternatives==== | ====Alternatives==== | ||