Music and Mathematics: From Pythagoras to FractalsJohn Fauvel, Raymond Flood, Robin J. Wilson 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. |
Contents
an overview | 1 |
closing the spiral | 13 |
Kepler and his readers | 29 |
The science of musical sound | 47 |
Faggots fretful fiasco | 61 |
combinational tones and consonance | 77 |
The geometry of music | 91 |
bells and mathematics | 113 |
sets rows | 131 |
Microtones and projective planes | 149 |
Composing with fractals | 163 |
Notes on contributors | 173 |
Acknowledgements | 183 |
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Common terms and phrases
angle appear approximation Athanasius Kircher basic beginning bells called century changes channel Chapter close composer composition consonance construction corresponding described developed diagram double effect equal exactly example exchange explain fact fifth Figure five follows four frequency geometrical given gives harmonics hear Helmholtz ideas integer interest interval involved Kepler kinds known leads length London major mathematical mathematicians means method minor modulo move movement natural notes obtained octave original Oxford pairs particular pattern piano piece pitch Plain plane played points position possible problem produce published Pythagorean range ratio reflection represent result ringing scale semitone sequence shown shows simple single sound space square starting string structure successive symmetry tempered theory third tion tones transformations transposition tuning University values vibrations whole
References to this book
Bibliographic information
| Title | Music and Mathematics: From Pythagoras to Fractals |
| Editors | John Fauvel, Raymond Flood, Robin J. Wilson |
| Edition | illustrated, reprint |
| Publisher | Oxford University Press, 2006 |
| ISBN | 0199298939, 9780199298938 |
| Length | 189 pages |
| Export Citation | BiBTeX EndNote RefMan |