Temperament merging: Difference between revisions
Cmloegcmluin (talk | contribs) →Cross-interval-basis merges: add link |
Cmloegcmluin (talk | contribs) →Parallel intersections: format diagrams better |
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== Parallel intersections == | == Parallel intersections == | ||
Every temperament mapping has a dual comma basis, and every comma basis has a dual mapping. Because of this duality, a special parallelism exists. | Every temperament mapping has a dual comma basis, and every comma basis has a dual mapping. Because of this duality, a special parallelism exists. | ||
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In this sense, map-merging and comma-merging should be understood not truly as operations on matrices, but as operations on [[basis|bases]]. Another way to describe these such intersections would be as bases for the [[linear dependence]] of the given temperaments, as described here: [[Linear dependence#For a given set of basis matrices, how to compute a basis for their linearly dependent vectors]]. | In this sense, map-merging and comma-merging should be understood not truly as operations on matrices, but as operations on [[basis|bases]]. Another way to describe these such intersections would be as bases for the [[linear dependence]] of the given temperaments, as described here: [[Linear dependence#For a given set of basis matrices, how to compute a basis for their linearly dependent vectors]]. | ||
<gallery heights=450px widths=450px> | |||
File:Map-merge.png|A map-merge gives a comma-intersection (for purposes of illustrating this concept, the results are not being canonicalized). | |||
File:Comma-merge.png|A comma-merge gives a map-intersection (for purposes of illustrating this concept, the results are not being canonicalized). | |||
</gallery> | |||
== Example system of temperaments related by merging == | == Example system of temperaments related by merging == | ||