THE HARMONIC MATRIX: EXPLORING THE GEOMETRY OF PITCH
Daryn Bond · University of Michigan Library Repository · 2011
Harmonic matrix theory is a comprehensive synthesis of just intonation and Pythagorean tuning systems related to, but extending the classical lambdoma of the ancient Greeks.Extrapolated to n-dimensional structures, cubes, hyper-planes, hyper-cubes, and so on, the approach is completed by the logical inclusion of additional special matrices such as the 'iterative power' and 'golden' matrix.The harmonic matrix describes a geometry that exposes the fractal nature of the integer set and the significance of the prime numbers to the human perception of harmony.Applications include compositions not restricted to fixed-tone systems and traditional time structures, various instrument/interface adaptations, and audiovisual representations demonstrating a well-defined link between position, color and pitch.