Mathews' Diagram and Euclid's Line: Fifty Years Ago

Making the science and technology of computer music comprehensible to musicians and composers who had little or no background therein was a part of Max Mathews’ genius. In this presentation I will show how a simple diagram led to the essential understanding of Claude Shannon’s sampling theorem, which in turn opened up a conceptual path to composing music for loudspeakers that had nothing to do with wires, cables and electronic devices, but led to learning how to program a computer—to write code. The change from device-determined output (analog) to program-determined output (digital) was a major change in paradigm that led to my realization of an integral sound spatialization system that would have been impossible for me to achieve in any other medium. Along the way, the discovery of FM Synthesis provided not only a means of creating diverse spectra but coupled with a ratio from Euclid’s Elements produced an unusual and productive connection between spectral space and pitch space and a path that leads ...?