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, authored 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.

CONTENIDO:

Preface
Susan Wollenberg: Music and mathematics: an overview
Part I: Music and mathematics through history
1: Neil Bibby: Tuning and temperament: closing the spiral
2: J.V. Field: Musical cosmology: Kepler and his readers
Part II: The mathematics of musical sound
3: Charles Taylor: The science of musical sound
4: Ian Stewart: Faggot's fretful blunder
5: David Fowler: Helmholtz: combinational tones and consonance
Part III: Mathematical structure in music
6: Wilfrid Hodges: Musical frieze patterns
7: Dermot Roaf and Arthur White: Ringing the changes: bells and mathematics
8: Jonathan Cross: Composing with numbers: sets, rows and magic squares
Part IV: The composer speaks
9: Carlton Gamer & Robin Wilson: Microtones and projective planes
10: Robert Sherlaw Johnson: Composing with fractals
Notes on contributors
Notes, references, and further reading
Acknowledgements
Index