Hexany: Difference between revisions
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A '''hexany''' is a 6-note scale built using all the possible combinations of 2 intervals 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 intervals from a given set of 4 intervals. It is the simplest case of a [[combination product set]]. | ||
== Example == | == Example == | ||
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* [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 | ||
[[Category: | [[Category:Hexanies| ]] <!-- main article --> | ||
[[Category:6-tone scales]] | [[Category:6-tone scales]] | ||
[[Category:todo:expand]] | [[Category:todo:expand]] | ||
Revision as of 21:28, 7 August 2021
A hexany is a 6-note scale built using all the possible combinations of 2 intervals from a given set of 4 intervals. It is the simplest case of a combination product set.
Example
Here is a step-by-step construction of the 1-3-5-7 hexany (i.e. using 1/1, 3/1, 5/1, and 7/1):
- Multiply together each pair of intervals (to find the combinations):
{1 × 3, 1 × 5, 1 × 7, 3 × 5, 3 × 7, 5 × 7}
= {3, 5, 7, 15, 21, 35}; - Divide each product by the smallest element of the previous set (to base the scale on 1/1):
{3/3, 5/3, 7/3, 15/3, 21/3, 35/3}
= {1/1, 5/3, 7/3, 5/1, 7/1, 35/3}; - Octave-reduce each element:
{1/1, 5/3, 7/6, 5/4, 7/4, 35/24}; - Sort the elements in ascending order:
{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:
{7/6, 5/4, 35/24, 5/3, 7/4, 2/1}.
External links
- Wikipedia: Hexany
- Ervin Wilson's Hexany by Kraig Grady