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Full Description
Mathematics and MusicEdition includes many new sections and more consistent expectations of 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 presentationIncludes more thorough coverage of spectrograms for analyzing recorded musicProvides a basic introduction to reading musicFeatures new coverage of building and evaluating rhythms
Contents
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
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