Mathematics and Music

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.

• Pitch, Frequency, and Musical ScalesPitch and FrequencyOvertones, Pitch Equivalence, and Musical ScalesThe 12-Tone Equal Tempered ScaleMusical Scales within the Chromatic Scale LogarithmsBasic Musical NotationStaff Notation, Clefs, and Note PositionsTime Signatures and TempoKey Signatures and the Circle of FifthsSome Music Theory Interval and ChordsDiatonic MusicDiatonic Transformations – Scale ShiftsDiatonic Transformations – Inversions, RetrogradeChromatic TransformationComposing Your Own MusicWeb ResourcesSpectrograms and Musical TonesMusical Gestures in SpectrogramsMathematical Model for Musical TonesModeling Instrumental TonesBeating and DissonanceEstimating Amplitude and FrequencyWindowing the Waveform: SpectrogramsA Deeper Study of Amplitude EstimationSpectrograms and MusicSingingInstrumentalsCompositionsEvaluating Personal PerformanceEssayAnalyzing Pitch and RhythmGeometry of Pitch Organization and TranspositionsGeometry of Chromatic InversionsCyclic RhythmsRhythmic InversionA Case Study in Rhythm: Bruch’s Lok NidreiConstruction of Scales and Cyclic RhythmsPerfectly Balanced Rhythms, XronoMorphXronoMoprh, Well-formed RhythmsComparing Musical Scales and Cyclic RhythmsSerialismComposing Your Own Music IIA Geometry of HarmonyRiemann’s Chromatic InversionsA Network of Triadic ChordsEmbedding Pitch Classes with the TonnetzOther Chordal TransformationsTonnetz Patterns in MusicAudio Synthesis in MusicCreating New Music from SpectrogramsPhase VocodingHow Auto-Tune WorksTime Stretching and Time ShrinkingMIDI SynthesisSoftware and Other ResourcesExercise SolutionsAmplitude and Frequency ResultsComplex Numbers Autocorrelation and PeriodicityMusic SoftwareGlossary