These software were also used to compose music, see mazzola’s homepage , and go to CV there. Best, Guerino. Guerino Mazzola (born ) is a Swiss mathematician, musicologist, jazz pianist as well as The Topos of Music, Geometric Logic of Concepts, Theory, and Performance. Birkhäuser () ISBN Perspectives in Mathematical. PDF | On Sep 1, , Guerino Mazzola and others published The Topos of Music: Geometric Logic of Concepts, Theory, and Performance.
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Open Preview See a Problem? Thanks for telling us about the problem. Return to Book Page. The Topos of Music: It reflects the dramatic progress of mathematical music theory and its operationalization by information if since the publication of Geometrie der T ne in 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.
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.
Hardcoverpages. Published January 17th by Birkhauser first published Geometric Logic of Concepts, Theory, and Performance.
The Topos of Music: Geometric Logic of Concepts, Theory, and Performance [With CDROM]
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Nov 24, Jonathan Chuang marked it as to-read. 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.
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.
What is Mazzola’s “Topos of Music” about? – Mathematics Stack Exchange
No matter how many rather experienced musicians I’ve asked about what harmony IS well just nice ratios of maszola whose lack of discordance your brain likes they’ve just looked nusic 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 guetino 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 So it will have to wait a while I guess Mark rated it it was amazing May 04, Sergey rated it really liked it Sep 14, Stephen Lavelle rated it really liked it May 25, David rated it liked it May 31, Paul mazola it as to-read Apr 08, Sha marked topoa as to-read Mar 26, Jens marked it as to-read Aug 09, Darrin Tisdale added it Feb 06, Loreno added it Apr 16, Brian33 added it Jun 08, Nancy marked it as to-read Oct 07, Wqe23 marked it as to-read Nov 10, Nomegor marked it mksic to-read Jan 20, Cyrta marked it as to-read Apr 19, Mark Gomer marked it as to-read May 31, James Tauber added it Toposs 03, Ronald Lett marked it as to-read Jan 05, Kilano Dey marked it as to-read Mar 31, Will Nalls marked it as to-read Apr 09, Tim Schafer marked it as to-read May 12, Risto Saarelma toos it Aug 16, Alicja Paw added it Sep 17, Filip marked it as to-read Jun 29, Sean marked it as to-read Jul 06, Akira marked it as to-read Jan 20, John Davis marked it as to-read Feb 08, Cameron Smith marked it as to-read Feb 11, Cooper marked it as to-read Apr 24, Gianpietro added it Jun 25, BookDB marked it as to-read Oct 23, There are no discussion topics on this book yet.
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