Mathematics and Music: A Diderot Mathematical Forum

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Springer Science & Business Media, Jul 10, 2002 - Mathematics - 288 pages
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In Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition to sound production by traditional instruments or by digital means. Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music.
  

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Contents

Proportions in Ancient and Medieval Music
1
LateMedieval France
18
Epilogue
47
Conclusion
62
Lagrange Working Mathematician
65
Musical Patterns
79
Variations on the Logical in Music
93
The Formalization of Logic and the Issue of Meaning
113
Ethnomusicology Ethnomathematics
161
References
181
References
198
References
211
Composition of Textures
224
References
240
References
254
References
284

Conclusion
134
Musical Analysis Using Mathematical Proceedings
139

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