Inspired by the cyclical nature of octaves and helical structure of a scale (Shepard, '82 and '83), we prepared a model of a piano-style keyboard (prototyped in Mathematica), which was then geometrically warped into a left-handed helical configuration, one octave/revolution, pitch mapped to height. The natural orientation of upper frequency keys higher on the helix suggests a parsimonious left-handed chirality, so that ascending notes cross in front of a typical listener left->right. Our model is being imported (via the dxf file format) into (Open Inventor/)VRML, where it can be driven by MIDI events, realtime or sequenced, which stream is both synthesized (by a Roland Sound Module), and spatialized by a heterogeneous spatial sound backend (including the Crystal River Engineering Acoustetron II and the Pioneer Sound Field Control speaker-array System), so that the sound of the respective notes is directionalized with respect to sinks, avatars of the human user, by default in the tube of the helix. This is a work-in-progress which we hope to be fully functional within the next few months.

Alternative coloring schemes:

Discontinuous (spiraling) color wheel (color-complementing traditionally black keys)	Chromastereoptic rendering

Octave normalization through multiple sinks:

Perhaps the most exotic feature of the helical keyboard is the ability to fork one's presence (Cohen, '95; Cohen and Koizumi, '95), replicating subject instead of object, by installing multiple sinks at arbitrary places around the virtual scene so that, for example, harmony and melody can be separately directionalized, using two heads to normalize the octave; such a technique effectively doubles the helix from the perspective of a single listener. Rather than a symmetric arrangement of the individual helices, we perceptually superimpose them in-phase, coextensively, so that corresponding notes in different octaves are at the same azimuth. (For instance, a c4 melodic note and a collapsed c major chord (c2 + e2 + f2) would both be at 12 o'clock.)

References:

• Michael Cohen. Besides immersion: Overlaid points of view and frames of reference; using audio windows to analyze audio scenes. In Proc. ICAT/VRST: Int. Conf. Artificial Reality and Tele-Existence/Conf. on Virtual Reality Software and Technology, pages 29-38, Makuhari, Chiba; Japan, November 1995.
• Michael Cohen and Nobuo Koizumi. Audio Windows for Virtual Concerts II: Sonic Cubism. In Video Proc. ICAT/VRST: Int. Conf. Artificial Reality and Tele-Existence/Conf. on Virtual Reality Software and Technology, page 254, Makuhari, Chiba; Japan, November 1995.
• Diana Deutsch. Paradoxes of musical pitch. Scientific American, pages 70-75, August 1992.
• Roger N. Shepard. The Psychology of Music, Structural Representations of Musical Pitch, pages 343-390. Academic Press, December 1982.
• Roger N. Shepard. Demonstrations of circular components of pitch. J. Aud. Eng. Soc., 31(9):641-649, September 1983.

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