Music and Mathematics: From Pythagoras to Fractals
From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authorized by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional and...
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From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authorized by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional and analytical relationships between mathematics and music are unfolded and explored with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques.
Music and mathematics: an overview1Pt. IMusic and mathematic through history111Tuning and temperament: closing the spiral132Musical cosmology: Kepler and his readers29Pt. IIThe mathematics of musical sound453The science of musical sound474Faggot's fretful fiasco615Helmholtz: combinational tones and consonance77Pt. IIIMathematical structure in music896The geometry of music917Ringing the changes: bells and mathematics1138Composing with numbers: sets, rows and magic squares131Pt. IVThe composer speaks1479Microtomes and projective planes14910Composing with fractals163Notes on contributors173Notes, references, and further reading177Acknowledgements183Index187
