Extended bra–ket notation: Difference between revisions

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The second extension of EBK from standard bra-ket notation is the repetition of brackets, allowing for the representation of [[multivector]]s.

Some advanced practitioners of RTT use multivectors, such as [[wedgie]]s, as an alternative way to represent temperaments (besides mappings and comma bases). These multivectors come in various grades, such as 2-vectors and 3-vectors. In fact, ordinary vectors are simply 1-vectors. In order to distinguish a <math>g</math>-vector from a 1-vector ~~other~~, the brackets that would normally be used can be repeated <math>g</math> times.

Some advanced practitioners of RTT use multivectors, such as [[wedgie]]s, as an alternative way to represent temperaments (besides mappings and comma bases). These multivectors come in various grades, such as 2-vectors and 3-vectors. In fact, ordinary vectors are simply 1-vectors. In order to distinguish a <math>g</math>-vector from a 1-vector, the brackets that would normally be used can be repeated <math>g</math> times.

For example, the 2-vector (bivector) representing meantone temperament uses two sets of brackets: {{multivector|1 4 4}}. The 3-covector representing 7-limit 31-ET {{multicovector|grade=3|-87 72 -49 31}}.

For example, the 2-vector (bivector) representing meantone temperament uses two sets of brackets: {{multivector|1 4 4}}. The 3-covector representing 7-limit 31-ET ⟨{{multicovector|grade=3|-87 72 -49 31}}].

The repetition-for-multivectors extension was developed in November of 2003 by Dave Keenan<ref>https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_7525#7749</ref>.

@@ Line 90: / Line 90: @@
 The second extension of EBK from standard bra-ket notation is the repetition of brackets, allowing for the representation of [[multivector]]s.
-Some advanced practitioners of RTT use multivectors, such as [[wedgie]]s, as an alternative way to represent temperaments (besides mappings and comma bases). These multivectors come in various grades, such as 2-vectors and 3-vectors. In fact, ordinary vectors are simply 1-vectors. In order to distinguish a <math>g</math>-vector from a 1-vector other, the brackets that would normally be used can be repeated <math>g</math> times.
+Some advanced practitioners of RTT use multivectors, such as [[wedgie]]s, as an alternative way to represent temperaments (besides mappings and comma bases). These multivectors come in various grades, such as 2-vectors and 3-vectors. In fact, ordinary vectors are simply 1-vectors. In order to distinguish a <math>g</math>-vector from a 1-vector, the brackets that would normally be used can be repeated <math>g</math> times.
-For example, the 2-vector (bivector) representing meantone temperament uses two sets of brackets: {{multivector|1 4 4}}. The 3-covector representing 7-limit 31-ET {{multicovector|grade=3|-87 72 -49 31}}.
+For example, the 2-vector (bivector) representing meantone temperament uses two sets of brackets: {{multivector|1 4 4}}. The 3-covector representing 7-limit 31-ET ⟨{{multicovector|grade=3|-87 72 -49 31}}].
 The repetition-for-multivectors extension was developed in November of 2003 by Dave Keenan<ref>https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_7525#7749</ref>.