Wedgie: Difference between revisions

Line 1:

A '''wedgie''' is an object that uniquely characterizes a [[regular temperament]] regardless of choice of [[period]] vs. [[generator]] or of [[equave]], which can therefore provide some illuminating information beyond the [[mapping|mapping matrix]], which specifies a particular equave. A wedgie takes the form ⟨⟨…⟨ ''w''1 ''w''2 … ''w''''n'' ]]…], with ''n'' entries listed in between multiple [[val]] brackets (double brackets for rank-2, triple brackets for rank-3, and so on). Wedgies can be thought of as a generalization of vals, called ''multivals'', so that a val is a wedgie for a rank-1 temperament. Each element conveys information about the structure of a set of primes in the temperament, containing a number of primes equivalent to the temperament's rank.

A '''wedgie''' is a primarily mathematical object that uniquely characterizes a [[regular temperament]] regardless of choice of [[period]] vs. [[generator]] or of [[equave]], which can therefore provide some illuminating information beyond the [[mapping|mapping matrix]], which specifies a particular equave. A wedgie takes the form ⟨⟨…⟨ ''w''1 ''w''2 … ''w''''n'' ]]…], with ''n'' entries listed in between multiple [[val]] brackets (double brackets for rank-2, triple brackets for rank-3, and so on). Wedgies can be thought of as a generalization of vals, called ''multivals'', so that a val is a wedgie for a rank-1 temperament. Each element conveys information about the structure of a set of primes in the temperament, containing a number of primes equivalent to the temperament's rank.

While wedgies historically served as the canonical way to represent temperaments mathematically due to their equave-agnostic nature, and are nowadays a fairly common way to do so, they are of limited musical utility - [[Mapping|mappings]] would often be of more immediate use to musicians.

== How to read a wedgie ==

@@ Line 1: / Line 1: @@
 {{Beginner|Plücker coordinates}}
-A '''wedgie''' is an object that uniquely characterizes a [[regular temperament]] regardless of choice of [[period]] vs. [[generator]] or of [[equave]], which can therefore provide some illuminating information beyond the [[mapping|mapping matrix]], which specifies a particular equave. A wedgie takes the form ⟨⟨…⟨ ''w''<sub>1</sub> ''w''<sub>2</sub> … ''w''<sub>''n''</sub> ]]…], with ''n'' entries listed in between multiple [[val]] brackets (double brackets for rank-2, triple brackets for rank-3, and so on). Wedgies can be thought of as a generalization of vals, called ''multivals'', so that a val is a wedgie for a rank-1 temperament. Each element conveys information about the structure of a set of primes in the temperament, containing a number of primes equivalent to the temperament's rank.
+A '''wedgie''' is a primarily mathematical object that uniquely characterizes a [[regular temperament]] regardless of choice of [[period]] vs. [[generator]] or of [[equave]], which can therefore provide some illuminating information beyond the [[mapping|mapping matrix]], which specifies a particular equave. A wedgie takes the form ⟨⟨…⟨ ''w''<sub>1</sub> ''w''<sub>2</sub> … ''w''<sub>''n''</sub> ]]…], with ''n'' entries listed in between multiple [[val]] brackets (double brackets for rank-2, triple brackets for rank-3, and so on). Wedgies can be thought of as a generalization of vals, called ''multivals'', so that a val is a wedgie for a rank-1 temperament. Each element conveys information about the structure of a set of primes in the temperament, containing a number of primes equivalent to the temperament's rank.
+While wedgies historically served as the canonical way to represent temperaments mathematically due to their equave-agnostic nature, and are nowadays a fairly common way to do so, they are of limited musical utility - [[Mapping|mappings]] would often be of more immediate use to musicians.
 == How to read a wedgie ==