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The Topos of Music: Geometric Logic of Concepts, Theory, and Performance [With CDROM]

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The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der T ne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der T ne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der T ne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der T ne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory of musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples.


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The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der T ne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der T ne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der T ne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der T ne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory of musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples.

33 review for The Topos of Music: Geometric Logic of Concepts, Theory, and Performance [With CDROM]

  1. 4 out of 5

    J C

    Honestly speaking, I have no idea what this is about, but I became interested in algebraic geometry after reading about a series of papers developing an inscrutably abstract reformulation of algebraic geometry, dubbed 'inter-universal Teichmüller theory' by its creator, Shinichi Mochizuki, who later quite audaciously (but perhaps justifiably) compared the mathematical world's bewilderment at his work with the general public's own bewilderment with mathematics. I love a good abstraction, which is Honestly speaking, I have no idea what this is about, but I became interested in algebraic geometry after reading about a series of papers developing an inscrutably abstract reformulation of algebraic geometry, dubbed 'inter-universal Teichmüller theory' by its creator, Shinichi Mochizuki, who later quite audaciously (but perhaps justifiably) compared the mathematical world's bewilderment at his work with the general public's own bewilderment with mathematics. I love a good abstraction, which is why I hate linear algebra proofs, and was pleased to find out that the whole field of algebraic geometry was apparently built around highly abstract notions, largely due to an fiery, irreverent and brilliant young mathematician named Grothendieck, so much so that these notions in some sense are more primal than sets (or something like that). Which is why these notions could be applied in fields like logic, and thus computer science. Apparently 'Homotopy Type Theory' is such an application, which is a reformulation of the foundations of mathematics, borrowing language from algebraic geometry and category theory and skirting around the notion of 'sets'. I got the impression that it was a variant of intuitionism, a movement to make mathematics more rigorous by allowing only constructive proofs, (i.e. forbidding the 'excluded middle', the notion that things, if not true, must be false, and vice versa) which fell out of favour with the mathematical community by the 1930s or so. Apparently, this way of formulating mathematics lends all theorems to a purely computational method of proof. I love fundamentals, of anything, because one can truly approach it as a beginner and ask (and even start answering) expert questions immediately. There isn't prerequisite knowledge to make you feel inexperienced or stupid. On the other hand, fundamentals are both fun and important; fun because you get to see how things unravel from psychological and philosophical roots into a rich formal system; important because where you begin limits where you can end up. I have also been interested, since before I can remember, in what music IS. No matter how many rather experienced musicians I've asked about what harmony IS (well just nice ratios of waves whose lack of discordance your brain likes) they've just looked at me with puzzlement... I'm sure there are many other questions about music that've occurred to me which have very interesting answers. So when I was looking for something interesting to read, I was suprised that this book popped up on my google search 'mathematics of music' uniting, apparently, all these interesting intellectual activities. I guess I want to read it, but only after I've done enough algebraic geometry, which is only after I've done commutative algebra, after I've done abstract algebra, complex analysis, analytical geometry... Plus it costs ~200$, weighs in at 1500 pages (normally that wouldn't stop me) and I can't get it second-hand. So it will have to wait a while I guess...

  2. 4 out of 5

    Mark

  3. 5 out of 5

    Sergey

  4. 4 out of 5

    Sønder

  5. 4 out of 5

    dwmasten

  6. 4 out of 5

    S

  7. 4 out of 5

    Veaceslav Molodiuc

  8. 5 out of 5

    Archimedes

  9. 4 out of 5

    Paul

  10. 5 out of 5

    Sha

  11. 5 out of 5

    Jens

  12. 5 out of 5

    Darrin Tisdale

  13. 5 out of 5

    Loreno

  14. 5 out of 5

    Brian33

  15. 4 out of 5

    Nancy

  16. 4 out of 5

    Wqe23

  17. 4 out of 5

    Nomegor

  18. 5 out of 5

    seafirefly

  19. 4 out of 5

    Cyrta

  20. 5 out of 5

    Mark Moon

  21. 5 out of 5

    James Tauber

  22. 5 out of 5

    J.

  23. 4 out of 5

    Ronald Lett

  24. 4 out of 5

    Kilano Dey

  25. 4 out of 5

    Will Nalls

  26. 5 out of 5

    Tim Schafer

  27. 4 out of 5

    Risto Saarelma

  28. 5 out of 5

    Alicja Paw

  29. 4 out of 5

    Filip

  30. 5 out of 5

    Sean

  31. 5 out of 5

    K.

  32. 4 out of 5

    John

  33. 5 out of 5

    Cameron Smith

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