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Mathematics and Music: Composition, Perception, and Performance

Mathematics and Music: Composition, Perception, and Performance


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About the Book

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

Table of Contents:
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 Logarithms 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 Singing Instrumentals Compositions Evaluating Personal Performance Essay 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 Serialism 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 Glossary

About the Author :
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.


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Product Details
  • ISBN-13: 9780429013546
  • Publisher: Taylor & Francis Ltd
  • Publisher Imprint: Routledge Cavendish
  • Language: English
  • No of Pages: 398
  • ISBN-10: 042901354X
  • Publisher Date: 24 Sep 2019
  • Binding: Digital (delivered electronically)
  • No of Pages: 398
  • Sub Title: Composition, Perception, and Performance


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