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.
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