# Hexany

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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.

## 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}.

## External links

*Ervin Wilson's Hexany*by Kraig Grady