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{{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 non-trivial case of a [[combination product set]]. | |||
[[ | A '''stellated hexany''' is a 14-tone scale and is also called a '''dekatesserany'''. | ||
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== 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): | |||
# 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}; | |||
# Divide each product by the smallest element of the previous set (to base the scale on 1/1):<br>{3/3, 5/3, 7/3, 15/3, 21/3, 35/3}<br>= {1/1, 5/3, 7/3, 5/1, 7/1, 35/3}; | |||
# [[Octave reduction|Octave-reduce]] each element:<br>{1/1, 5/3, 7/6, 5/4, 7/4, 35/24}; | |||
# 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}. | |||
== Pages for individual hexanies == | |||
''See [[:Category:Hexanies]].'' | |||
== External links == | |||
* [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}} | |||
[[Category:Hexanies| ]] <!-- main article --> | |||
[[Category:6-tone scales]] | |||
Latest revision as of 20:56, 17 August 2025
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 non-trivial case of a combination product set.
A stellated hexany is a 14-tone scale and is also called a dekatesserany.
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):
- 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}.
Pages for individual hexanies
See Category:Hexanies.
External links
- Ervin Wilson's Hexany by Kraig Grady
- The Tonality Cube Demonstration video by 12tone music.
- Paul Erlich. The Forms of Tonality.