Musimathics: The Mathematical Foundations of Music, Volume 1
"Mathematics can be as effortless as humming a tune, if you know the tune," writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music—a commonsense, self-contained introduction for the nonspecialist reader. It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science.
In this volume, Loy presents the materials of music (notes, intervals, and scales); the physical properties of music (frequency, amplitude, duration, and timbre); the perception of music and sound (how we hear); and music composition. Musimathics is carefully structured so that new topics depend strictly on topics already presented, carrying the reader progressively from basic subjects to more advanced ones. Cross-references point to related topics and an extensive glossary defines commonly used terms. The book explains the mathematics and physics of music for the reader whose mathematics may not have gone beyond the early undergraduate level. Calling himself "a composer seduced into mathematics," Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously. The topics are all subjects that contemporary composers, musicians, and musical engineers have found to be important. The examples given are all practical problems in music and audio. The level of scholarship and the pedagogical approach also make Musimathics ideal for classroom use. Additional material can be found at a companion web site.
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Musical Scales Tuning and Intonation
Physical Basis of Sound
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acceleration acoustical amplitude angle bandwidth basilar membrane Bohlen-Pierce Bohlen-Pierce scale called chromatic scale composer composition consonance constant corresponding create critical bands decibel defined degrees diatonic scale diffraction displacement dissonant distance duration elastic equal equal-tempered equal-tempered scale equation example fifth force frequency function hearing hidden units increases input Integer IntegerList interval order length linear loudness major third Markov mass mathematics measure melody membrane method microtonal minor scale modes MusiMAt object octave Oh Susanna output pattern piano pitch classes play position pressure Pythagorean random range Real RealList reflected resonant result reverberation rotation rules semitone sequence shown in figure shows signal simple harmonic motion sinusoid sound intensity sound source spectral spectrum speed of sound step string tempered theory timbre tone transition transpose triad tuning variable vibrating system wave waveform zero