Val: Difference between revisions

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In practice, most single-row mappings in RTT are vals, because we usually deal with integer entries, and the other specifications only mean anything to advanced mathematicians.

== Generalizations ==

=== Mapping matrix ===

''Main article: [[Temperament mapping matrix]]''

A mapping matrix is the most common generalization of a val, for a rank-2 or higher temperament. As a result, it has more than one row, To be precise, there is one row for each generator of the temperament.

=== Tuning map ===

''Main article: [[Tuning map]]''

A tuning map generalizes a val in a different way. Instead of treating the entries of a val as equal temperament steps, it treats them as a logarithmic interval size measure (usually cents). Thus, the entries of a tuning map may be any real number. ⟨1200 1901.955] is the tuning map for the justly-tuned 3-limit, and ⟨1200 1896.8 2787.1] is the tuning map for the 5-limit tuned to meantone (specifically, 31edo).

=== Subgroup val ===

''Main article: [[Subgroup monzos and vals]]''

A subgroup val specifies the tunings of an arbitrary set of intervals, which can be stacked to form all the intervals in a subgroup. For example, the subgroup val 2.3.7 ⟨5 8 14] tells you that prime 2 is mapped to 5 steps, prime 3 is mapped to 8 steps, and prime 7 is mapped to 14 steps, without specifying a mapping for 5.

=== Tempered val ===

''Main article: [[Tempered monzos and vals]]''

A tempered val specifies the mappings of [[Mapped interval|tempered intervals]] (that is, intervals in the space of intervals generated by a temperament). For example, ⟨15 2] is the tval for porcupine (with generators ~2 and ~10/9) in 15edo. There are also tempered tuning maps.

== See also ==

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* [[Monzos and interval space]]

* [[Patent val]]

* [[Smonzos and svals]]

* Definition on Tonalsoft's encyclopedia of microtonal music theory: http://tonalsoft.com/enc/v/val.aspx

@@ Line 171: / Line 171: @@
 In practice, most single-row mappings in RTT are vals, because we usually deal with integer entries, and the other specifications only mean anything to advanced mathematicians.
+== Generalizations ==
+=== Mapping matrix ===
+''Main article: [[Temperament mapping matrix]]''
+A mapping matrix is the most common generalization of a val, for a rank-2 or higher temperament. As a result, it has more than one row, To be precise, there is one row for each generator of the temperament.
+=== Tuning map ===
+''Main article: [[Tuning map]]''
+A tuning map generalizes a val in a different way. Instead of treating the entries of a val as equal temperament steps, it treats them as a logarithmic interval size measure (usually cents). Thus, the entries of a tuning map may be any real number. ⟨1200 1901.955] is the tuning map for the justly-tuned 3-limit, and ⟨1200 1896.8 2787.1] is the tuning map for the 5-limit tuned to meantone (specifically, 31edo).
+=== Subgroup val ===
+''Main article: [[Subgroup monzos and vals]]''
+A subgroup val specifies the tunings of an arbitrary set of intervals, which can be stacked to form all the intervals in a subgroup. For example, the subgroup val 2.3.7 ⟨5 8 14] tells you that prime 2 is mapped to 5 steps, prime 3 is mapped to 8 steps, and prime 7 is mapped to 14 steps, without specifying a mapping for 5.
+=== Tempered val ===
+''Main article: [[Tempered monzos and vals]]''
+A tempered val specifies the mappings of [[Mapped interval|tempered intervals]] (that is, intervals in the space of intervals generated by a temperament). For example, ⟨15 2] is the tval for porcupine (with generators ~2 and ~10/9) in 15edo. There are also tempered tuning maps.
 == See also ==
@@ Line 178: / Line 200: @@
 * [[Monzos and interval space]]
 * [[Patent val]]
-* [[Smonzos and svals]]
 * Definition on Tonalsoft's encyclopedia of microtonal music theory: http://tonalsoft.com/enc/v/val.aspx