What is "hexany"

In music theory, the hexany is a six-note just intonation structure, with the notes placed on the vertices of an octahedron, equivalently the faces of a cube. The notes are arranged so that every edge of the octahedron joins together notes that make a consonant dyad, and every face joins together the notes of a consonant triad.

This makes a "musical geometry" with the geometrical form of the octahedron. It has eight just intonation triads in a scale of only six notes, and each triad has two notes in common with three of the other chords, arranged in a musically symmetrical fashion due to the symmetry of the octahedron on which it is based.

The Hexany is the invention of Erv Wilson and represents one of the simplest structures found in his Combination Product Sets. The numbers of vertices follow the numbers in Pascal's triangle. The hexany is the third cross section. "Hexany is the name that Erv Wilson gave to the six notes in the 2-out-of-4 combination product set (abbreviated as 2)4 CPS)."