Musimathics, Volume 2

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"Mathematics can be as effortless as humming a tune, if you know the tune," writes Gareth Loy, who provides a spirited tour of the mathematics of music in this engaging volume. The second installment continues the exploration of music engineering, focusing on the digital and computational aspects. Loy delves into the mathematics of music and sound, starting with digital audio, sampling, and binary numbers, and introduces complex numbers to simplify the representation of musical signals. Key topics include the Fourier transform, convolution, filtering, resonance, the wave equation, acoustical systems, sound synthesis, the short time Fourier transform, and the wavelet transform, all of which form the theoretical foundation of modern music technology. While volume 1 serves as preparatory material, each volume can stand alone, with cross-references to earlier concepts and additional mathematical orientation provided as needed. The subjects covered are essential for contemporary composers, musicians, and music engineers, with practical examples addressing real-world problems in music and audio. The scholarly approach and pedagogical style also make this work suitable for classroom use, complemented by additional resources available on a companion website.