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            Compositions with Magic Squares


I have written several works that belong to an original series of experimental music compositions that incorporate

planetary magic squares, ancient Chinese magic squares and feng shui as compositional models. My approach to

composition combines the use of magic squares with elements of classical art, popular culture and Chinese history.

A magic square consists of a series of numbers arranged so that the sum of each row, column, and diagonal is the

same amount. Routes through the square are mapped onto a musical structure that uses the properties of the square

as a compositional model. The unique position of each number within the square is paralled in the musical score by a

particular style, rhythm, density, timbre and orchestration. Of the enormous number of magic squares it is possible

to form, seven have been associated with the seven planets of the Ptolemaic universe (Saturn, Jupiter, Mars, the

Sun, Venus, Mercury, and the Moon).  These¡°planetary magic squares¡± appear in De Occulta Philosophia, a book on

magic by the renaissance polymath Heinrich Cornelius Agrippa von Nettesheim published in 1531. The rotations of

the 3x3 Lo Shu Square as dictated by the Flying Star System of feng shui have also been used to generate

compositional structures.


Compositions that incorporate computer-generated sounds were produced using the original computer music

software GACSS (Genetic Algorithms in Composition and Sound Synthesis).  GACSS was developed by Benjamin

Grosser in 1994 using funds I received from a research board grant from the University of Illinois. The software has

received a distinguished Arnold O. Beckman Research Award.  Sound generation algorithms, or Waveform Synthesis

Procedures (WSP) are of an original design, and provide procedures by which to build periods in a manner based on

graphical representations of acoustic waveforms.