Musimathics: The Mathematical Foundations of Music

Mathematics can be as effortless as humming a tune, if you know thetune, writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing afriendly and spirited tour of the mathematics of music–a commonsense, self-contained introduction for the nonspecialist reader.Volume 2 of Musimathicscontinues the story of music engineering begun in volume 1, focusing on the digitaland computational domain. Loy goes deeper into the mathematics of music and sound, beginning with digital audio, sampling, and binary numbers, as well as complexnumbers and how they simplify representation of musical signals. Chapters cover theFourier transform, convolution, filtering, resonance, the wave equation, acousticalsystems, sound synthesis, the short time Fourier transform, and the wavelettransform. These subjects provide the theoretical underpinnings of today’s musictechnology. The material in volume 1 is all preparatory to the subjects presented inthis volume, although either volume can be read independently. Cross-references tovolume 1 are provided for concepts introduced in the earlier volume, and additionalmathematical orientation is offered where necessary. The topics are all subjectsthat contemporary composers, musicians, and music engineers have found to beimportant. The examples given are all practical problems in music and audio. Thelevel of scholarship and the pedagogical approach also make Musimathics ideal forclassroom use. Additional material can be found at a companion web site.