Scale diversity: Difference between revisions
m Xenwolf moved page Scale Diversity to Scale diversity: rule (for normal terms): only first letter should be capitalized for easy linking |
m recat, todo |
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Properties: | Properties: | ||
* Degenerate scales (scales with no intervals smaller than an octave and larger than a unison) have a diversity of 0. | |||
* EDOs have a diversity of 1. | |||
* Div(S) ≥ 0 since there are no intervals larger than an octave. | |||
=Definition:= | =Definition:= | ||
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N is the cardinality of S. | N is the cardinality of S. | ||
dia(S) is the [[ | dia(S) is the [[diamond function]]. | ||
sort(S) returns a tuple with all of the elements of S in non-decreasing order. | sort(S) returns a tuple with all of the elements of S in non-decreasing order. | ||
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steps(T) returns a multiset whose elements are the consecutive differences of elements in a tuple T | steps(T) returns a multiset whose elements are the consecutive differences of elements in a tuple T | ||
The scale diversity measure was proposed by [[ | The scale diversity measure was proposed by [[Ryan Avella]]. | ||
[[Category: | [[Category:Math]] | ||
[[Category:theory]] | [[Category:Scale theory]] | ||
{{todo|clarify}} | |||