04456nam 22007335 450 991025501930332120200704025339.03-319-42937-X10.1007/978-3-319-42937-3(CKB)3710000000926199(DE-He213)978-3-319-42937-3(MiAaPQ)EBC6311986(MiAaPQ)EBC5588879(Au-PeEL)EBL5588879(OCoLC)962016766(PPN)196324122(EXLCZ)99371000000092619920161026d2016 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierCool Math for Hot Music A First Introduction to Mathematics for Music Theorists /by Guerino Mazzola, Maria Mannone, Yan Pang1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (XV, 323 p. 179 illus., 112 illus. in color.)Computational Music Science,1868-03053-319-42935-3 Includes bibliographical references and index.Part 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.This 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.Computational Music Science,1868-0305Application softwareMusicMathematicsComputer science—MathematicsArtificial intelligenceComputer Appl. in Arts and Humanitieshttps://scigraph.springernature.com/ontologies/product-market-codes/I23036Musichttps://scigraph.springernature.com/ontologies/product-market-codes/417000Mathematics in Musichttps://scigraph.springernature.com/ontologies/product-market-codes/M33000Mathematics of Computinghttps://scigraph.springernature.com/ontologies/product-market-codes/I17001Artificial Intelligencehttps://scigraph.springernature.com/ontologies/product-market-codes/I21000Application software.Music.Mathematics.Computer science—Mathematics.Artificial intelligence.Computer Appl. in Arts and Humanities.Music.Mathematics in Music.Mathematics of Computing.Artificial Intelligence.781.0151Mazzola Guerinoauthttp://id.loc.gov/vocabulary/relators/aut283272Mannone Mariaauthttp://id.loc.gov/vocabulary/relators/autPang Yanauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910255019303321Cool Math for Hot Music2273112UNINA