2nd Edition

Mathematics and Music Composition, Perception, and Performance

By James S. Walker, Gary Don Copyright 2020
    398 Pages 87 Color & 319 B/W Illustrations
    by Chapman & Hall

    398 Pages 87 Color & 319 B/W Illustrations
    by Chapman & Hall

    398 Pages 87 Color & 319 B/W Illustrations
    by Chapman & Hall

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    Mathematics and Music: Composition, Perception, and Performance, Second Edition includes many new sections and more consistent expectations of a student’s experience. The new edition of this popular text is more accessible for students with limited musical backgrounds and only high school mathematics is required.

    The new edition includes more illustrations than the previous one and the added sections deal with the XronoMorph rhythm generator, musical composition, and analyzing personal performance.

    The text teaches the basics of reading music, explaining how various patterns in music can be described with mathematics, providing mathematical explanations for musical scales, harmony, and rhythm. The book gives students a deeper appreciation showing how music is informed by both its mathematical and aesthetic structures.

    Highlights of the Second Edition:

    • Now updated for more consistent expectations of students’ backgrounds
    • More accessible for students with limited musical backgrounds
    • Full-color presentation
    • Includes more thorough coverage of spectrograms for analyzing recorded music
    • Provides a basic introduction to reading music
    • Features new coverage of building and evaluating rhythms

    Pitch, Frequency, and Musical Scales

    Pitch and Frequency

    Overtones, Pitch Equivalence, and Musical Scales

    The 12-Tone Equal Tempered Scale

    Musical Scales within the Chromatic Scale


    Basic Musical NotationStaff Notation, Clefs, and Note Positions

    Time Signatures and Tempo

    Key Signatures and the Circle of Fifths

    Some Music Theory Interval and Chords

    Diatonic Music

    Diatonic Transformations – Scale Shifts

    Diatonic Transformations – Inversions, Retrograde

    Chromatic Transformation

    Composing Your Own Music

    Web Resources

    Spectrograms and Musical TonesMusical Gestures in Spectrograms

    Mathematical Model for Musical Tones

    Modeling Instrumental Tones

    Beating and Dissonance

    Estimating Amplitude and Frequency

    Windowing the Waveform: Spectrograms

    A Deeper Study of Amplitude Estimation

    Spectrograms and Music

    Evaluating Personal Performance

    Analyzing Pitch and Rhythm

    Geometry of Pitch Organization and Transpositions

    Geometry of Chromatic Inversions

    Cyclic Rhythms

    Rhythmic Inversion

    A Case Study in Rhythm: Bruch’s Lok Nidrei

    Construction of Scales and Cyclic Rhythms

    Perfectly Balanced Rhythms, XronoMorph

    XronoMoprh, Well-formed Rhythms
    Comparing Musical Scales and Cyclic Rhythms


    Composing Your Own Music II

    A Geometry of Harmony

    Riemann’s Chromatic Inversions

    A Network of Triadic Chords

    Embedding Pitch Classes with the Tonnetz

    Other Chordal Transformations

    Tonnetz Patterns in Music

    Audio Synthesis in Music

    Creating New Music from Spectrograms

    Phase Vocoding

    How Auto-Tune Works

    Time Stretching and Time Shrinking

    MIDI Synthesis

    Software and Other Resources

    Exercise Solutions

    Amplitude and Frequency Results

    Complex Numbers

    Autocorrelation and Periodicity

    Music Software



    James S. Walker holds a doctorate from the University of Illinois at Chicago, advised by Louis L. Pennisi. He is a Professor and teaches in the Mathematics Department at the University of Wisconsin-Eau Claire. He has published papers on topics in Fourier analysis, wavelet analysis, logic, image compression, image denoising, and mathematics & music.

    Gary W. Don is a professor of music theory at the University of Wisconsin-Eau Claire. He teaches freshman and sophomore theory and aural skills, and upper-division theory courses. Additionally, he holds a doctorate in music theory from the University of Washington, and taught theory and aural skills at Skidmore College in New York before joining the UWEC faculty.