Val: Difference between revisions

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* A wart letter may ''prefix'' the number, in which case it specifies the corresponding prime as the [[interval of equivalence]] to be divided by the following number. For example, b13 refers to the patent val of [[13edt|13ed3]]. The octave is assumed, so "a" is typically not written out.

* In Graham Breed's temperament finder, the wart letter "q" and after refers each non-prime basis of composite/fractional subgroup, respectively and temporarily.

=== Sparse Offset Val notation ===

In 2022 [[User:Mike Battaglia|Mike Battaglia]] proposed '''SOV notation''' as a way to be explicit about which primes are being affected and in which direction. In 2024 it was further refined by him and [[User:Frostburn|Lumi Pakkanen]] to be more analogous to [[Ups and downs notation]].

Generalized patent vals are notated using the number of divisions followed by square brackets e.g. 17[] for {{val| 17 27 39 }}.

To indicate a wider mapping for a prime it is prefixed with a carret (^) e.g. 17[^5] for {{val| 17 27 40 }}.

To indicate a narrower mapping for a prime it is prefixed with a vee (v) e.g. 17[v5] for {{val| 17 27 38 }}.

The prefixes stack e.g. 17[^^5] corresponds to {{val| 17 27 41 }}.

Multiple modifications are separated by commas (and optionally spaces) e.g. 17[v3, ^5] for {{val| 17 26 40 }}.

The interval of equivalence may be prefixed in square brackets e.g. [3]13[] for {{val| 8 13 19 }} (subgroup 2.3.5).

The subgroup may be made explicit separated by an "at" sign (@) at the end e.g. 46[]@2.3.7.13/5 for {{val| 46 73 129 63 }} (subgroup 2.3.7.13/5).

Formal primes are treated the same way as actual primes e.g. 46[^13/5]@2.3.7.13/5 for {{val| 46 73 129 64 }} (subgroup 2.3.7.13/5)

For patent vals the empty square brackets are optional when using an "at" sign. The subgroup itself is optional if its obvious from context e.g. 12@ for {{val|12 19 28 }} (subgroup 2.3.5).

The 2022 version used a plus sign (+) in place of the caret and a minus sign (-) in place of the vee.

== Vals in JI subgroups ==

@@ Line 43: / Line 43: @@
 * A wart letter may ''prefix'' the number, in which case it specifies the corresponding prime as the [[interval of equivalence]] to be divided by the following number. For example, b13 refers to the patent val of [[13edt|13ed3]]. The octave is assumed, so "a" is typically not written out.
 * In Graham Breed's temperament finder, the wart letter "q" and after refers each non-prime basis of composite/fractional subgroup, respectively and temporarily.
+=== Sparse Offset Val notation ===
+In 2022 [[User:Mike Battaglia|Mike Battaglia]] proposed '''SOV notation''' as a way to be explicit about which primes are being affected and in which direction. In 2024 it was further refined by him and [[User:Frostburn|Lumi Pakkanen]] to be more analogous to [[Ups and downs notation]].
+Generalized patent vals are notated using the number of divisions followed by square brackets e.g. 17[] for {{val| 17 27 39 }}.
+To indicate a wider mapping for a prime it is prefixed with a carret (^) e.g. 17[^5] for {{val| 17 27 40 }}.
+To indicate a narrower mapping for a prime it is prefixed with a vee (v) e.g. 17[v5] for {{val| 17 27 38 }}.
+The prefixes stack e.g. 17[^^5] corresponds to {{val| 17 27 41 }}.
+Multiple modifications are separated by commas (and optionally spaces) e.g. 17[v3, ^5] for {{val| 17 26 40 }}.
+The interval of equivalence may be prefixed in square brackets e.g. [3]13[] for {{val| 8 13 19 }} (subgroup 2.3.5).
+The subgroup may be made explicit separated by an "at" sign (@) at the end e.g. 46[]@2.3.7.13/5 for {{val| 46 73 129 63 }} (subgroup 2.3.7.13/5).
+Formal primes are treated the same way as actual primes e.g. 46[^13/5]@2.3.7.13/5 for {{val| 46 73 129 64 }} (subgroup 2.3.7.13/5)
+For patent vals the empty square brackets are optional when using an "at" sign. The subgroup itself is optional if its obvious from context e.g. 12@ for {{val|12 19 28 }} (subgroup 2.3.5).
+The 2022 version used a plus sign (+) in place of the caret and a minus sign (-) in place of the vee.
 == Vals in JI subgroups ==