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Seminar Notes: The Mathematics of Music - Yale University

Seminar Notes: The Mathematics of MusicZhou FanSeptember 1, 20102 ContentsPrefaceiii1 Understanding Musical Sound, the human ear, and the sinusoidal wave .. waves and musical notation .. human ear and the sinusoidal wave .. Timbre and resonance harmonics .. Fourier series and frequency analysis .. Further topics .. instruments .. phenomena ..82 Chords, Scales, and the Fundamentals of Western Consonance and dissonance .. Scales and temperament .. fractions and the twelve-tone scale .. intonation, Euclidean lattices, and the fundamental domain .. , irregular, and equal temperament .. The Javanese gamelan ..173 Musical Structure and Musical symmetries and transformations.

corresponding to higher frequencies and lower pitches corresponding to lower frequencies. The marking mp is a dynamic marking to indicate the volume of the sound, which corresponds to the amplitude of the sound wave. Finally, the stems and heads of the notes indicate the duration of each note, which is the amount of

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