Image Octahedron.svg thumb Regular Octahedron. Listen filename Hexany 1 3 5 7.mid title Hexany 1 3 5 7 description 7 limit hexany scale filename2 Hexany 1 3 5 9.mid title2 Hexany 1 3 5 9 description2 9 limit music limit hexany scale without 7 In music theory , the hexany is a six note just intonation scale, with the notes placed on the vertices of an octahedron , equivalently the faces of a cube . The notes are arranged so that every edge geometry edge of the octahedron joins together notes that make a Consonance and dissonance consonant dyad music dyad , and every face geometry face joins together ... due to the symmetry of the octahedron it is based on. The Hexany is the invention of Erv Wilson ... . The hexany is the third cross section of the hypercube four dimensional cube . Hexany is the name ... by 2 using octave equivalence . For example, for a 2 3 5 7 hexany, assign 2 3 5 7, to the four ... and one step in the 7 dimension and so would be tuned as 5× 7. So, to make the complete hexany ... the context in 4D. Image Hexany.png In this picture of a hypercube, the six hexany vertices ..., 6 vertices for the yellow octahedron hexany , 4 for the purple tetrahedron and 1 more vertex to make ... hertz, and so forth. This figure shows the hexany in its more usual 3D representation Image with unknown ... tetrad , 6 hexany , 4 another tetrad , 1. The idea generalises to other numbers of dimensions ... br 1100 1010 1001 0110 0101 0011 hexany octahedron br 1110 1101 1011 0111 tetrad br 1111 br The octahedron ... Wilson s Hexany periodical Just Intonation volume 7 issue 1 pages 8 11 year 1991 Citation last Schiemer ... date June 2010 see the Background section External links http www.anaphoria.com hex.PDF Some Hexany and Hexany Diamond Lattices and Blanks , http www.anaphoria.com wilson.html The Wilson Archives . Original Hexany papers showing different facets and configurations, not assembled by Erv Wilson 1967 ... software Hexany hexany.htm Hexany , RobertInventor.com . With a hexany you can turn around and click ... more details
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