Hexany: Difference between revisions
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{{Wikipedia|Hexany}} | {{Wikipedia|Hexany}} | ||
A '''hexany''' is a 6-note [[scale]] built using all the possible combinations of 2 [[interval]]s from a given set of 4 intervals. It is the simplest case of a [[combination product set]]. | A '''hexany''' is a 6-note [[scale]] built using all the possible combinations of 2 [[interval]]s from a given set of 4 intervals. It is the simplest non-trivial case of a [[combination product set]]. | ||
A '''stellated hexany''' is a 14-tone scale and is also called a '''dekatesserany'''. | |||
== Example == | == Example == | ||
Here is a step-by-step construction of the canonical 1-3-5-7 hexany (i.e. using [[1/1]], [[3/1]], [[5/1]], and [[7/1]] with the smallest product as the root): | Here is a step-by-step construction of the canonical 1-3-5-7 hexany (i.e. using [[1/1]], [[3/1]], [[5/1]], and [[7/1]] with the smallest product as the root): | ||
# Multiply together each pair of intervals (to find the combinations):<br>{1 × 3, 1 × 5, 1 × 7, 3 × 5, 3 × 7, 5 × 7}<br> = {3, 5, 7, 15, 21, 35}; | # Multiply together each pair of intervals (to find the combinations):<br>{1 × 3, 1 × 5, 1 × 7, 3 × 5, 3 × 7, 5 × 7}<br> = {3, 5, 7, 15, 21, 35}; | ||
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# Sort the elements in ascending order:<br>{1/1, 7/6, 5/4, 35/24, 5/3, 7/4}; | # Sort the elements in ascending order:<br>{1/1, 7/6, 5/4, 35/24, 5/3, 7/4}; | ||
# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{7/6, 5/4, 35/24, 5/3, 7/4, 2/1}. | # Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{7/6, 5/4, 35/24, 5/3, 7/4, 2/1}. | ||
== Pages for individual hexanies == | |||
''See [[:Category:Hexanies]].'' | |||
== External links == | == External links == | ||
* [http://anaphoria.com/grady1-1.pdf ''Ervin Wilson's Hexany''] by Kraig Grady | * [http://anaphoria.com/grady1-1.pdf ''Ervin Wilson's Hexany''] by Kraig Grady | ||
* [https://www.youtube.com/watch?v=-GeR8XbFxvI The Tonality Cube] Demonstration video by 12tone music. | |||
* [[Paul Erlich]]. [https://sethares.engr.wisc.edu/paperspdf/Erlich-Forms.pdf The Forms of Tonality]. | |||
{{todo|add examples|add illustration|expand}} | {{todo|add examples|add illustration|expand}} | ||
[[Category:Hexanies| ]] <!-- main article --> | [[Category:Hexanies| ]] <!-- main article --> | ||
[[Category:6-tone scales]] | [[Category:6-tone scales]] | ||