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Here is the hexany, an example of a musical geometry (NB The musical notes may take a while to load if you are on a slow connection - about half a MB - on broadband it will be pretty quick.)

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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.

You can also try the Opague hexany (opens in new window)

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.

For more about it see Hexany.

You can use Virtual Flower to make this model, and several other musical geometries.

So far it has:

Versions of the hexany (six notes)
Octony (eight notes)
Dekany (ten notes and with tetrads as well as triads, actually a three dimensional projection of a four dimensional shape)
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. To make the audio clips for the model, you need to install Fractal Tune Smithy as well. If it is installed, Virtual Flower can then find it and run it invisibly to make the clips.

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 to can make new models of their own for other musical geometries. If you make any more models yourself, and would like your model to be included with Virtual flower, let me know.

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.

The program comes with a generous Free Test drive with all the features completely unlocked (start the test drive at any time):

Download Virtual Flower