Cross-set scale: Difference between revisions
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Cited Narushima's book which apparently attributes the term "cross-set" to Wilson. |
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In combinatorics, this operation is called a [[wikipedia:Sumset|sumset]]. | In combinatorics, this operation is called a [[wikipedia:Sumset|sumset]]. | ||
The term ''cross-set'' goes back to [[Erv Wilson]].<ref name="Narushima 2017">Narushima, T. (2017). Microtonality and the tuning systems of Erv Wilson. Routledge.</ref> | |||
== Examples == | == Examples == | ||
The 4:5:6:7 cross-set scale is generated by multiplying every pair of intervals from the 4:5:6:7 tetrad ([[1/1]] - [[5/4]] - [[3/2]] - [[7/4]]), including an interval with itself, and [[Octave reduction|octave-reducing]] as necessary. It contains 10 distinct pitches out of 16 combinations. | The 4:5:6:7 cross-set scale is generated by multiplying every pair of intervals from the 4:5:6:7 tetrad ([[1/1]] - [[5/4]] - [[3/2]] - [[7/4]]), including an interval with itself, and [[Octave reduction|octave-reducing]] as necessary. It contains 10 distinct pitches out of 16 combinations. | ||
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== See also == | == See also == | ||
* [[Tonality diamond]] | * [[Tonality diamond]] | ||
== References == | |||
[[Category:Scale]] | [[Category:Scale]] | ||