Mathematics and music : composition, perception, and performance
- Walker, James S.
- Boca Raton, FL : CRC Press, 
- Physical description
- 318 pages : illustrations ; 26 cm
ML3805 .W25 2013
- Unknown ML3805 .W25 2013
- Don, Gary W.
- Includes bibliographical references and index.
- Pitch, Frequency, 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 Notation Staff Notation, Clefs, Note Positions Time Signatures and Tempo Key Signatures and The Circle of Fifths Some Music Theory Intervals and Chords Diatonic Music Diatonic Transformations-Scale Shifts Diatonic Transformations-Inversions, Retrograde Chromatic Transformations Web Resources Spectrograms and Musical Tones Musical 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 Analyzing Pitch and Rhythm Geometry of Pitch Organization and Transpositions Geometry of Chromatic Inversions Cyclic Rhythms Rhythmic Inversion Construction of Scales and Cyclic Rhythms Comparing Musical Scales and Cyclic Rhythms Serialism A Geometry of Harmony Riemann's Chromatic Inversions A Network of Triadic Chords Embedding Pitch Classes within the Tonnetz Other Chordal Transformations Audio Synthesis in Music Creating New Music from Spectrograms Phase Vocoding Time Stretching and Time Shrinking MIDI Synthesis A Exercise Solutions B Music Software C Amplitude and Frequency Results D Glossary E Permissions Bibliography Index.
- (source: Nielsen Book Data)
- Publisher's Summary
- At first glance, mathematics and music seem to be from separate worlds-one from science, one from art. But in fact, the connections between the two go back thousands of years, such as Pythagoras's ideas about how to quantify changes of pitch for musical tones (musical intervals). Mathematics and Music: Composition, Perception, and Performance explores the many links between mathematics and different genres of music, deepening students' understanding of music through mathematics. In an accessible way, the text teaches the basics of reading music and explains how various patterns in music can be described with mathematics. The authors extensively use the powerful time-frequency method of spectrograms to analyze the sounds created in musical performance. Numerous examples of music notation assist students in understanding basic musical scores. The text also provides mathematical explanations for musical scales, harmony, and rhythm and includes a concise introduction to digital audio synthesis. Along with helping students master some fundamental mathematics, this book gives them a deeper appreciation of music by showing how music is informed by both its mathematical and aesthetic structures. Web Resource On the book's CRC Press web page, students can access videos of many of the spectrograms discussed in the text as well as musical scores playable with the free music software MuseScore. An online bibliography offers many links to free downloadable articles on math and music. The web page also provides links to other websites related to math and music, including all the sites mentioned in the book.
(source: Nielsen Book Data)
- Publication date
- James S. Walker, Gary W. Don.