Musimathics, by Gareth Loy

Volume one of Gareth Loy’s book Musimathics (Loy 2006) is a concise description of the properties of music and composition from the perspective of a composer with a mathematical approach to the science of music. Loy gives clear explanations of key music concepts. In chapter one he uses his explanation of simple harmonic motion to explain the sinusoidal character of sound and the movement of pressure as a waveform. Loy’s approach throughout this book is to refer to natural systems as starting points for elucidation of complex musical concepts. The illustration of a pendulum is used to help the reader visualise the steady perpetual motion of a system in equilibrium. The summary for the first chapter includes a simple explanation of the physics of sound relative to music.

Frequency, onset, and duration are time-based aspects of sound, and intensity is a measure of the energy in a sound. These physical properties of frequency and intensity correspond to the perceptual cues of pitch and loudness. Onset and duration largely determine musical rhythm. (Loy 2006 p.9)

Loy moves on to describe forms of musical notation with western common music notation as a starting point. He explains the diatonic scale and compares different modes within a historical context. His definitions of Pentatonic, Hungarian Minor and Whole-tone scales are clearly illustrated with notation. Chapter three defines scales in terms of their frequencies and describes the use of ratios within tuning. Loy offers a strong historical foundation and clearly illustrates the mechanics of tempered tuning, European microtonal and Hindustani tuning. There is a description of late twentieth century music research including the work of Heinz Bohlen and John Pierce. Bohlen-Pierce tuning is described in detail as it contains a very high degree of internal order. In chapter four Loy explains duration in music with reference to Sir Isaac Newton’s theories on time and returns to a visualisation of the waveform by describing it’s kinetic energy. Tangential velocity and circular motion are compared in the chapter focused on geometry. Loy returns to a comparison of harmonic motion in time and the sinusoidal wave. The book closes on an analysis of human perception of sound and music. The clarity of Loy’s explanation throughout this book suggests that it is a useful companion to understanding the complex tuning executed by La Monte Young and his contemporaries. The book can also be used to place some more cellular minimalist music, like that of Tony Conrad or Steve Reich, within a mathematical framework.

LOY, D. G. (2006). Musimathics the mathematical foundations of music. Vol. 1. Cambridge, Mass, MIT Press.