Mapping: Difference between revisions

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=== Notation ===

In regular temperament theory there is a special notation for this kind of JI mapping. We notate the 3-limit 12edo temperament described above as "{{val| 12 19 }}", because the first prime (2) is mapped to 12 steps, and the second prime (3) is mapped to 19 steps. This mathematical object is known as a "mapping matrix" and it summarizes all the information in the mapping in a very compact form. Since this is an equal temperament, the mapping matrix contains only one row, and since it's a 3-limit temperament, the mapping matrix contains two columns, representing the primes 2 and 3. Such mapping with one row ~~in [[Extended bra-ket notation|bra notation]]~~ is called [[val]]~~. And~~ mapping matrix in multiple vals (described below) is called '''val list'''.

In regular temperament theory there is a special notation for this kind of JI mapping. We notate the 3-limit 12edo temperament described above as "{{val| 12 19 }}"<ref group="note">Known as [[extended bra-ket notation]].</ref>, because the first prime (2) is mapped to 12 steps, and the second prime (3) is mapped to 19 steps. This mathematical object is known as a "mapping matrix" and it summarizes all the information in the mapping in a very compact form. Since this is an equal temperament, the mapping matrix contains only one row, and since it's a 3-limit temperament, the mapping matrix contains two columns, representing the primes 2 and 3. Such mapping with one row is called a [[val]], and a mapping matrix in multiple vals (described below) is also called a '''val list'''.

=== Many 12edo temperaments ===

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* [[Reduced mapping]]

* [[Dave Keenan %26 Douglas Blumeyer%27s guide to RTT/Mappings]] – for a step-by-step textbook tutorial style introduction to this topic

== Notes ==

[[Category:Regular temperament theory]]

@@ Line 27: / Line 27: @@
 === Notation ===
-In regular temperament theory there is a special notation for this kind of JI mapping. We notate the 3-limit 12edo temperament described above as "{{val| 12 19 }}", because the first prime (2) is mapped to 12 steps, and the second prime (3) is mapped to 19 steps. This mathematical object is known as a "mapping matrix" and it summarizes all the information in the mapping in a very compact form. Since this is an equal temperament, the mapping matrix contains only one row, and since it's a 3-limit temperament, the mapping matrix contains two columns, representing the primes 2 and 3. Such mapping with one row in [[Extended bra-ket notation|bra notation]] is called [[val]]. And mapping matrix in multiple vals (described below) is called '''val list'''.
+In regular temperament theory there is a special notation for this kind of JI mapping. We notate the 3-limit 12edo temperament described above as "{{val| 12 19 }}"<ref group="note">Known as [[extended bra-ket notation]].</ref>, because the first prime (2) is mapped to 12 steps, and the second prime (3) is mapped to 19 steps. This mathematical object is known as a "mapping matrix" and it summarizes all the information in the mapping in a very compact form. Since this is an equal temperament, the mapping matrix contains only one row, and since it's a 3-limit temperament, the mapping matrix contains two columns, representing the primes 2 and 3. Such mapping with one row is called a [[val]], and a mapping matrix in multiple vals (described below) is also called a '''val list'''.
 === Many 12edo temperaments ===
@@ Line 114: / Line 114: @@
 * [[Reduced mapping]]
 * [[Dave Keenan %26 Douglas Blumeyer%27s guide to RTT/Mappings]] – for a step-by-step textbook tutorial style introduction to this topic
+== Notes ==
+<references group="note"/>
 [[Category:Regular temperament theory]]