Mathematics and Music : Composition, Perception, and Performance (Paperback, 2 ed)

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 SingingInstrumentalsCompositionsEvaluating Personal PerformanceEssay 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 RhythmsComparing 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