LEADER 04456nam 22007335 450 001 9910255019303321 005 20200704025339.0 010 $a3-319-42937-X 024 7 $a10.1007/978-3-319-42937-3 035 $a(CKB)3710000000926199 035 $a(DE-He213)978-3-319-42937-3 035 $a(MiAaPQ)EBC6311986 035 $a(MiAaPQ)EBC5588879 035 $a(Au-PeEL)EBL5588879 035 $a(OCoLC)962016766 035 $a(PPN)196324122 035 $a(EXLCZ)993710000000926199 100 $a20161026d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCool Math for Hot Music $eA First Introduction to Mathematics for Music Theorists /$fby Guerino Mazzola, Maria Mannone, Yan Pang 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XV, 323 p. 179 illus., 112 illus. in color.) 225 1 $aComputational Music Science,$x1868-0305 311 $a3-319-42935-3 320 $aIncludes bibliographical references and index. 327 $aPart I: Introduction and Short History -- The ?Counterpoint? of Mathematics and Music -- Short History of the Relationship Between Mathematics and Music -- Part II: Sets and Functions -- The Architecture of Sets -- Functions and Relations -- Universal Properties -- Part III: Numbers -- Natural Numbers -- Recursion -- Natural Arithmetic -- Euclid and Normal Forms -- Integers -- Rationals -- Real Numbers -- Roots, Logarithms, and Normal Forms -- Complex Numbers -- Part IV: Graphs and Nerves -- Directed and Undirected Graphs -- Nerves -- Part V: Monoids and Groups -- Monoids -- Groups -- Group Actions, Subgroups, Quotients, and Products -- Permutation Groups -- The Third Torus and Counterpoint -- Coltrane?s Giant Steps -- Modulation Theory -- Part VI: Rings and Modules -- Rings and Fields -- Primes -- Matrices -- Modules -- Just Tuning -- Categories -- Part VII: Continuity and Calculus -- Continuity -- Differentiability -- Performance -- Gestures -- Part VIII: Solutions, References, Index -- Solutions of Exercises -- References -- Index. 330 $aThis textbook is a first introduction to mathematics for music theorists, covering basic topics such as sets and functions, universal properties, numbers and recursion, graphs, groups, rings, matrices and modules, continuity, calculus, and gestures. It approaches these abstract themes in a new way: Every concept or theorem is motivated and illustrated by examples from music theory (such as harmony, counterpoint, tuning), composition (e.g., classical combinatorics, dodecaphonic composition), and gestural performance. The book includes many illustrations, and exercises with solutions. 410 0$aComputational Music Science,$x1868-0305 606 $aApplication software 606 $aMusic 606 $aMathematics 606 $aComputer science?Mathematics 606 $aArtificial intelligence 606 $aComputer Appl. in Arts and Humanities$3https://scigraph.springernature.com/ontologies/product-market-codes/I23036 606 $aMusic$3https://scigraph.springernature.com/ontologies/product-market-codes/417000 606 $aMathematics in Music$3https://scigraph.springernature.com/ontologies/product-market-codes/M33000 606 $aMathematics of Computing$3https://scigraph.springernature.com/ontologies/product-market-codes/I17001 606 $aArtificial Intelligence$3https://scigraph.springernature.com/ontologies/product-market-codes/I21000 615 0$aApplication software. 615 0$aMusic. 615 0$aMathematics. 615 0$aComputer science?Mathematics. 615 0$aArtificial intelligence. 615 14$aComputer Appl. in Arts and Humanities. 615 24$aMusic. 615 24$aMathematics in Music. 615 24$aMathematics of Computing. 615 24$aArtificial Intelligence. 676 $a781.0151 700 $aMazzola$b Guerino$4aut$4http://id.loc.gov/vocabulary/relators/aut$0283272 702 $aMannone$b Maria$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPang$b Yan$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910255019303321 996 $aCool Math for Hot Music$92273112 997 $aUNINA