The connections between mathematics and music to back thousands of years. This text explores the many links between mathematics and different genres of music. It requires only high school mathematics. The new edition offers many updates, including several new sections. The authors offer much for mathematics and music students alike.
The connections between mathematics and music to back thousands of years. This text explores the many links between mathematics and different genres of music. It requires only high school mathematics. The new edition offers many updates, including several new sections. The authors offer much for mathematics and music students alike.
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.
Inhaltsangabe
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
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
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