000 03625nam a22005895i 4500
001 978-3-319-42937-3
003 DE-He213
005 20200421112042.0
007 cr nn 008mamaa
008 161026s2016 gw | s |||| 0|eng d
020 _a9783319429373
_9978-3-319-42937-3
024 7 _a10.1007/978-3-319-42937-3
_2doi
050 4 _aNX260
072 7 _aH
_2bicssc
072 7 _aUB
_2bicssc
072 7 _aCOM018000
_2bisacsh
072 7 _aART000000
_2bisacsh
082 0 4 _a004
_223
100 1 _aMazzola, Guerino.
_eauthor.
245 1 0 _aCool Math for Hot Music
_h[electronic resource] :
_bA First Introduction to Mathematics for Music Theorists /
_cby Guerino Mazzola, Maria Mannone, Yan Pang.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aXV, 323 p. 179 illus., 112 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aComputational Music Science,
_x1868-0305
505 0 _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.
520 _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.
650 0 _aComputer science.
650 0 _aMusic.
650 0 _aComputer science
_xMathematics.
650 0 _aArtificial intelligence.
650 0 _aApplication software.
650 0 _aMathematics.
650 1 4 _aComputer Science.
650 2 4 _aComputer Appl. in Arts and Humanities.
650 2 4 _aMusic.
650 2 4 _aMathematics in Music.
650 2 4 _aMathematics of Computing.
650 2 4 _aArtificial Intelligence (incl. Robotics).
700 1 _aMannone, Maria.
_eauthor.
700 1 _aPang, Yan.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319429359
830 0 _aComputational Music Science,
_x1868-0305
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-42937-3
912 _aZDB-2-SCS
942 _cEBK
999 _c56679
_d56679