Click and drag to rotate.

Click on red spheres to hear the triads, or blue spheres to hear diads.

Click on the corners (vertices) for single notes.

The edge joining two of the corners play both notes. Also each face (red sphere) plays the triad of all three notes around that face.

So this is a pattern of eight triads. Each triad shares a pair of notes with each its three neighbours - so there's lots of shared harmony, and the chords fit together in exactly the same way as the faces fit together in the geometrical shape.

This remarkable idea is a discovery by Erv Wilson. He called them CPS - Combination Product Set. This geometrical pattern of pitches, consisting as it does of six notes, he called the hexany. The geometrical shape itself is an octahedron.

You can use Virtual Flower to make more musical geometries like this. You need to install Fractal Tune Smithy as well, which is a music program able to make the notes for the chords.

To find this feature in Virtual Flower, go to Output | Musical Geometries. Select a musical geometry from the drop list, then click the button Make model and Clips... Fractal Tune Smithy will start up to make the clips. Once it is done, use Show Model... to see the result. Techy users can edit the VRML templates or add new ones, and if familiar with CPS sets as well, can make new models of their own for other CPS sets.

The drop list at present includes some versions of the hexany (six notes), the octony (eight notes) and dekany (musical geometry with ten notes and with tetrads as well as triads, actually a three dimensional projection of a four dimensional shape) and another musical geometry called the double tie circular mirroring (twelve notes, eight tetrads). You can vary the choice of factors for each model - which changes the chords that get played.

You can try out other versions of this hexany - this one is opaque:

Opague hexany (opens in new window)

hexany.wrl (opens in new window, will show in your VRML browser)

To explore more about the idea of using triangular faces of geometrical shapes for triads, with more example CPS sets to try out as well, see Musical Geometry (opens in new window)

Freeware / Shareware status: This feature is free. If you wish to show your appreciation, use the Donations page.

To read more about Virtual Flower, go on to:

Musical e-cards

To get the program, download and install Virtual Flower.

Download Virtual Flower

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