The Topos of Music II: Performance

, 208, 210 action, 518 literal -, 210 theorem, 208 complete category, 1425 harmony, 827 quiver, 1375 uniform space, 1450 completeness, 36, 42, 49 finite -, 138 completion, semantic -, 49 complex analysis, 1465 cell -, 325 chain -, 1475 cochain -, 1477 derivative, 1465 gesture, 1042 module -, 288 number, 948 numbers, 1385 of affine functions, 288 quotient -, 289 set -, 314 simplicial -, 779, 1445 simplicial cochain -, 1447 time, 1186, 1218 complexity, 165 degree of -, 162 formal -, 383 measure, 254 of performance, 548 component aleatoric -, 198 alteration, 107 idempotent -, 1377 irreducible -, 269 metrical -, 267 reduced -, 107 semiotic -, 854 composed frame, 802 composer, 12, 895, 1263 perspective of the -, 246 composition, 162, 1372 t-fold tangent -, 551 global standard -, 293 commutative local -, 105 computer assisted -, 801 computer-aided -, 774, 791 concept, 571 dodecaphonic -, 124 functorial -, 1180 functorial local -, 101 generic, 174 global -, 41, 140, 831, 987, 1466 N -formed -, 291 oriented -, 291 resolution of a -, 323 global functorial -, 256 global objective -, 252 interpretable -, 304 local -, 41, 75, 89, 90 embedded -, 106 dimension of a -, 178 generating -, 106 projecting -, 178 standard -, 293 local objective -, 90 locally free local -, 175 modular -, 251 musical -, 30 non-interpretable -, 305, 308 non-interpretable global -, 990 tangent -, 551 tools, fractal -, 115 compositional design, 209 idea, 322 space, 204 compositions commutative global -, 285 local category of -, 89 computation symbolic -, 801 computational musicology, 21 computer assisted composition, 801 science, 6, 156 computer-aided anthropology, 765 composition, 774, 791 computer-assisted performance research, 629, 701 conativity, 212 concatenation, 132, 1372 principle, 133, 512 concept, 9, 35 architecture, 152 composition -, 571 construction history, 47 critical -, 1072 denotator -, 665 form -, 665 format, 42 framework, 3, 5, 9 abstraction -, 385 dynamic -, 329 fuzzy -, 164 grouping -, 250

[1]  E. B. Cowley Examen des différentes méthodes employées pour résoudre les problémes de géométrie , 1928, Nature.

[2]  S. Lane,et al.  Sheaves In Geometry And Logic , 1992 .

[3]  R. Douady Jeux de cadres et dialectique outil-objet , 2009 .

[4]  Shlomo Dubnov,et al.  Using Factor Oracles for Machine Improvisation , 2004, Soft Comput..

[5]  J. L. Coolidge,et al.  The Origin of Polar Coordinates , 1952 .

[6]  Anders Friberg,et al.  Performance Rules for Computer-Controlled Contemporary Keyboard Music , 1991 .

[7]  F. Patras La pensée mathématique contemporaine , 2001 .

[8]  Roman Jakobson,et al.  Language in Relation to Other Communication Systems , 1971 .

[9]  Guerino Mazzola,et al.  Gestural Shaping And Transformation In A Universal Space Of Structure And Sound , 2010, ICMC.

[10]  Nicolas Bourbaki,et al.  Foundations of mathematics for the working mathematician , 1949, Journal of Symbolic Logic.

[11]  L. Munari How the body shapes the way we think — a new view of intelligence , 2009 .

[12]  G. Grisey Tempus ex Machina: A composer's reflections on musical time , 1987 .

[13]  H. Wieser,et al.  Improved multipolar foramen ovale electrode monitoring , 1988 .

[14]  R. Guitart Bachelard et la pulsation mathématique , 2015 .

[15]  M. Corballis,et al.  From manual gesture to speech: A gradual transition , 2006, Neuroscience & Biobehavioral Reviews.

[16]  G. Mazzola Categorical gestures, the diamond conjecture, Lewin's question, and the Hammerklavier Sonata , 2009 .

[17]  Alan C. Evans,et al.  Emotional responses to pleasant and unpleasant music correlate with activity in paralimbic brain regions , 1999, Nature Neuroscience.

[18]  Milton Babbitt,et al.  TWELVE-TONE INVARIANTS AS COMPOSITIONAL DETERMINANTS , 1960 .

[19]  Youichi Horry A graphical user interface for MIDI Signal Generation and sound synthesis , 1994, ICMC.

[20]  L. Isenman The Brain and Perception , 2018 .

[21]  Hirnelektrische Vorgänge im limbischen System bei konsonanten und dissonanten Klängen , 1989 .

[22]  K. Popper,et al.  The Open Society and Its Enemies , 1946 .

[24]  Erwin Ratz,et al.  Einführung in die musikalische Formenlehre : über Formprinzipien in den Inventionen und Fugen J.S. Bachs und ihre Bedeutung für die Kompositionstechnik Beethovens , 1953 .

[25]  Counterpoint in 2k-tone equal temperament , 2009 .

[26]  Hideo Miyahara,et al.  Hyperscore: A design of a hypertext model for musical expression and structure* , 1995 .

[27]  Johan Sundberg,et al.  Recent musical performance research at KTH , 1994 .

[28]  Gérard Milmeister,et al.  The Rubato Composer Music Software - Component-Based Implementation of a Functorial Concept Architecture , 2009, Computational Music Science.

[29]  Guerino Mazzola Musical Performance - A Comprehensive Approach: Theory, Analytical Tools, and Case Studies , 2011, Computational Music Science.

[30]  R. Guitart Cohomological Emergence of Sense in Discourses (As Living Systems Following Ehresmann and Vanbremeersch) , 2009 .

[31]  Dominik Hörnel,et al.  Learning Musical Structure and Style by Recognition, Prediction and Evolution , 1996, ICMC.

[32]  R. C. Bose,et al.  Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler's Conjecture , 1960, Canadian Journal of Mathematics.

[33]  K. Reidemeister Elementare Begründung der Knotentheorie , 1927 .

[34]  Matti Karjalainen,et al.  DSP Approach to Multichannel Audio Mixing , 1996, ICMC.

[35]  Carl Dahlhaus Untersuchungen über die Entstehung der harmonischen Tonalität , 1967 .

[36]  N. Todd A Model of Expressive Timing in Tonal Music , 1985 .

[37]  R. Florida The Rise of the Creative Class , 2002 .

[38]  David Cooper,et al.  Handwritten Music Manuscript Recognition , 1996, ICMC.

[39]  Œuvres scientifiques , 1931, Nature.

[40]  C. Cadoz,et al.  Le geste canal de communication homme/machine: la communication "instrumentale" , 1994 .

[41]  Yongmiao Hong Testing for independence between two covariance stationary time series , 1996 .

[42]  A. Forte The Structure of Atonal Music , 1973 .

[43]  Mathematical Pulsation at the root of invention , 2008 .

[44]  S. Gottwald,et al.  Fuzzy sets, fuzzy logic, fuzzy methods with applications , 1995 .

[45]  Thomas Noll Fractal Depth Structure of Tonal Harmony , 1995, ICMC.

[46]  Philipp Ackermann Developing Object-Oriented Multimedia Software , 1997 .

[47]  Ian M. Wanless,et al.  On the Number of Latin Squares , 2005, 0909.2101.

[48]  J. Assmann Schöpfungsmythen und Kreativitätskonzepte im Alten Ägypten , 2000 .

[49]  G. Mazzola,et al.  A harmonic analysis network , 2015 .

[50]  Guerino Mazzola,et al.  The BigBang Rubette: gestural Music Composition with Rubato Composer , 2008, ICMC.

[51]  Mark A. Runco,et al.  A History of Research on Creativity , 1998 .

[52]  Guy L. Steele,et al.  Common LISP: the language, 2nd Edition , 1990 .

[53]  Petri Toiviainen,et al.  Perception of Expression in Conductors' Gestures: A Continuous Response Study , 2010 .

[54]  Dika Newlin Fundamentals of Musical Composition , 1968 .

[55]  G. Mazzola Singular homology on hypergestures , 2012 .

[56]  C. Losada Isography and structure in the music of Boulez , 2008 .

[57]  M. Leyton Symmetry, Causality, Mind , 1999 .

[58]  R. Sternberg The Nature of creativity : contemporary psychological perspectives , 1988 .

[59]  Neil P. McAngus Todd,et al.  Towards a cognitive theory of expression: The performance and perception of rubato , 1989 .

[60]  H. John Maxwell,et al.  An expert system for harmonizing analysis of tonal music , 1992 .

[61]  Henkjan Honing Expresso, a Strong and Small Editor for Expression , 1992, ICMC.

[62]  R. Hatten,et al.  Interpreting Musical Gestures, Topics, and Tropes: Mozart, Beethoven, Schubert , 2004 .

[63]  C. Bacchilega The Passeggiata and Popular Culture in an Italian Town: Folklore and the Performance of Modernity , 2006 .

[64]  Gerald Teschl,et al.  Mathematical Methods in Quantum Mechanics , 2009 .

[65]  David Henderson Words About Music , 1997 .

[66]  Brian Cabral,et al.  Imaging vector fields using line integral convolution , 1993, SIGGRAPH.

[67]  Kofi Agawu,et al.  Playing with Signs , 1994 .

[68]  B. Mansouri Normes internationales élargies et dépassement du calcul de la valeur , 2015 .

[69]  Daniel G. Bobrow,et al.  Book review: The Art of the MetaObject Protocol By Gregor Kiczales, Jim des Rivieres, Daniel G. and Bobrow(MIT Press, 1991) , 1991, SGAR.

[70]  J. Sloboda The Musical Mind: The Cognitive Psychology of Music , 1987 .

[71]  Insook Choi Cognitive engineering of gestural primitives for multi-modal interaction in a virtual environment , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[72]  David W. Galenson Old Masters and Young Geniuses: The Two Life Cycles of Human Creativity , 2009 .

[73]  D. Lieberman,et al.  Fourier analysis , 2004, Journal of cataract and refractive surgery.

[74]  Nell P. McAngusTodd,et al.  The dynamics of dynamics: A model of musical expression , 1992 .

[75]  E. Goffman Behavior in Public Places , 1963 .

[76]  Richard Cohn Introduction to Neo-Riemannian Theory: A Survey and a Historical Perspective , 1998 .

[77]  C. Osgood The nature and measurement of meaning. , 1952, Psychological bulletin.

[78]  David Lewin,et al.  Re: Intervallic Relations between Two Collections of Notes , 1959 .

[79]  Barry Vercoe,et al.  The Synthetic Performer in The Context of Live Performance , 1984, International Conference on Mathematics and Computing.

[80]  Guerino Mazzola Inverse Performance Theory , 1995, ICMC.

[81]  Madelle Becker,et al.  Nineteenth-Century Foundations of Creativity Research , 1995 .

[82]  Donald Martino,et al.  The Source Set and Its Aggregate Formations , 1961 .

[83]  H. Lane,et al.  A Pilot Study of the Expressive Gestures Used by Classical Orchestra Conductors: Penny Boyes Braem and Thüring Bräm , 2013 .

[84]  Nicholas Wolterstorff,et al.  A History of Six Ideas: An Essay in Aesthetics. , 1980 .

[85]  Ian Quinn,et al.  Fuzzy Extensions to the Theory of Contour , 1997 .

[86]  George Perle Serial Composition and Atonality; An Introduction to the Music of Schoenberg, Berg, and Webern , 1968 .

[87]  Paul E. Utgoff,et al.  Detecting Motives and Recurring Patterns in PolyphonicMusic , 2006, ICMC.

[88]  Gregory H. Wakefield,et al.  A Modal Distribution Approach to Piano Analysis and Synthesis , 1996, ICMC.

[89]  F. Gomes Teixeira Traité des courbes spéciales remarquables : planes et gauches , 1908 .

[90]  P. Guillaume La Psychologie de la forme , 2009 .

[91]  Milton Babbitt,et al.  Set Structure as a Compositional Determinant , 1961 .

[92]  Jeremy L. Leach Towards a Universal Algorithmic System for Composition of Music and Audio-Visual Works , 1996, ICMC.

[93]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[94]  J. Bach,et al.  Generative Rules for Music Performance: A Formal Description of a Rule System , 2008 .

[95]  L. Henry Shaffer,et al.  Musical Performance as Interpretation , 1995 .

[96]  Roger B. Dannenberg,et al.  An On-Line Algorithm for Real-Time Accompaniment , 1984, ICMC.

[97]  Guerino Mazzola,et al.  A symmetry-oriented mathematical model of classical counterpoint and related neurophysiological investigations by depth EEG , 1989 .

[98]  Dmitri Tymoczko,et al.  Mazzola's Model of Fuxian Counterpoint , 2011, MCM.

[99]  Maurice Merleau-Ponty Phenomenology of Perception , 1964 .

[100]  Jacqueline A. Jones,et al.  Connectionist Models for Tonal Analysis , 1989 .

[101]  Elmar Holenstein,et al.  Semiotik : ausgewählte Texte, 1919-1982 , 1988 .

[102]  Roland Posner,et al.  Semiotic aspects of musicology: Semiotics of music Semiotische Aspekte der Musikwissenschaft: Musiksemiotik , 2003 .

[103]  Guerino Mazzola,et al.  Towards a Categorical Theory of Creativity for Music, Discourse, and Cognition , 2013, MCM.

[104]  D. Cope Virtual Music: Computer Synthesis of Musical Style , 2001 .

[105]  John Mitchell Foundations of object-oriented programming (abstract) , 1992 .

[106]  Eric Clarke,et al.  Imitating and Evaluating Real and Transformed Musical Performances , 1993 .

[107]  Alf Gabrielsson,et al.  Expressive Intention and Performance , 1995 .

[108]  Lisa B. Fiore,et al.  Understanding Creativity: The Interplay of Biological, Psychological, and Social Factors , 1998 .

[109]  Herbert Bruhn,et al.  Harmonielehre als Grammatik der Musik : propositionale Schemata in Musik und Sprache , 1988 .

[110]  Richard Parncutt,et al.  Interdependence of Right and Left Hands in Sight‐Read, Written, and Rehearsed Fingerings of Parallel Melodic Piano Music , 1999 .

[111]  Richard Kronland-Martinet,et al.  Estimation of Parameters Corresponding to A Propagative Synthesis Model Through the Analysis of Real Sounds , 1996, ICMC.

[112]  Gerhard Widmer,et al.  Modeling the rational basis of musical expression , 1995 .

[113]  S. Lane Categories for the Working Mathematician , 1971 .

[114]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[115]  M. Andreatta On group-theoretical methods applied to music : some compositional and implementational aspects , 2022 .

[116]  Jean-Claude Schmitt,et al.  La raison des gestes dans l'occident medieval. , 1992 .

[117]  Paolo Rossi,et al.  Die Geburt der modernen Wissenschaft in Europa , 1998 .

[118]  Jan Beran,et al.  Statistics in Musicology , 2003 .

[119]  Marta Monteleoni,et al.  Side by side , 1995, Nature.

[120]  A. Lehmann,et al.  Tracking Performance Correlates of Changes in Perceived Intensity of Emotion During Different Interpretations of a Chopin Piano Prelude , 2001 .

[121]  Herbert Eimert Grundlagen der musikalischen Reihentechnik , 1964 .

[122]  S. Chatterjee,et al.  Regression Analysis by Example , 1979 .

[123]  R. Lawson The First Century of Blues: One Hundred Years of Hearing and Interpreting the Music and the Musicians , 2007 .

[124]  Lawrence M. Zbikowski Conceptualizing Music: Cognitive Structure, Theory, and Analysis , 2002 .

[125]  Gerald Myerson,et al.  Variety and Multiplicity in Diatonic Systems , 1985 .

[126]  F. Wegeler,et al.  Biographische Notizen über Ludwig van Beethoven , 1838 .

[127]  J. Cusack Creative Cognition: Theory, Research, and Applications , 1994 .

[128]  B. Repp Diversity and commonality in music performance: an analysis of timing microstructure in Schumann's "Träumerei". , 1992, The Journal of the Acoustical Society of America.

[129]  S. Lane Mathematics, Form and Function , 1985 .

[130]  Hermann Danuser,et al.  Neues Handbuch der Musikwissenschaft , 1996 .

[131]  R. Nadeau Le problème mathématique de l’espace : à propos d’un ouvrage récent de Luciano Boi — présentation , 1997 .

[132]  Michael Leyton,et al.  A generative theory of shape , 2004, Proceedings Shape Modeling Applications, 2004..

[133]  F. S.,et al.  A Mathematician's Apology , 1941, Nature.

[134]  R. Penrose The road to reality. , 1984, Nursing times.

[135]  D. A. Dunnett Classical Electrodynamics , 2020, Nature.

[136]  Guerino Mazzola,et al.  Timing microstructure in Schumann's “Träumerei” as an expression of harmony, rhythm, and motivic structure in music performance☆ , 2000 .

[137]  Louis Hjelmslev,et al.  Prolégomènes a une théorie du langage , 1968 .

[138]  M. Charlton Electroclinical Features of the Psychomotor Seizure , 1984 .

[139]  Relativités et puissances spectrales chez Gaston Bachelard , 1999 .

[140]  Gottfried Vossen,et al.  Datenmodelle, Datenbanksprachen und Datenbank-Management-Systeme , 1990 .

[141]  N. H. C. Yung,et al.  The Analysis and Resynthesis of Sustained Musical Signals in the Time Domain , 1996, ICMC.

[142]  R. Guitart,et al.  Décompositions et Lax-complétions , 1977 .

[143]  Scott J. Simon Computer models of musical creativity , 2007, J. Assoc. Inf. Sci. Technol..

[144]  A. Grothendieck,et al.  Théorie des Topos et Cohomologie Etale des Schémas , 1972 .

[145]  John R. Hayes Cognitive Processes in Creativity. Occasional Paper No. 18. , 1990 .

[146]  Peter Steinbach,et al.  Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition , 1998 .

[148]  R. C. Bose,et al.  On the construction of sets of mutually orthogonal Latin squares and the falsity of a conjecture of Euler , 1960 .

[149]  Dmitri Tymoczko,et al.  The Geometry of Musical Chords , 2006, Science.

[150]  Guerino Mazzola,et al.  Computational Counterpoint Worlds , 2015, Computational Music Science.

[151]  J. Dieudonne Foundations of Modern Analysis , 1969 .

[152]  G. Mazzola,et al.  Creative Analysis of Boulez’s Structures , 2009 .

[153]  Alexander R. Brinkman,et al.  A Unified Set of Software Tools for Computer-Assisted Set-Theoretic and Serial Analysis of Contemporary Music , 1986, ICMC.

[154]  F W Lawvere,et al.  AN ELEMENTARY THEORY OF THE CATEGORY OF SETS. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[155]  Sherman K. Stein,et al.  Algebra and Tiling by Sherman K. Stein , 2009 .

[156]  E. Witten Magic, mystery, and matrix , 1998 .

[157]  Robert B. Cantrick,et al.  A Generative Theory of Tonal Music , 1985 .

[158]  Immanuel Kant Kritik Der Reinen Vernunft , 2004 .

[159]  J. Rufer Die Komposition mit zwölf Tönen , 1952 .

[160]  J. Funke,et al.  Milieus of creativity : an interdisciplinary approach to spatiality of creativity , 2009 .

[161]  J. Tyrrell,et al.  LECTURES ON CURVES ON AN ALGEBRAIC SURFACE , 1968 .

[162]  Jürgen Meyer Akustik und musikalische Aufführungspraxis : Leitfaden für Akustiker, Tonmeister, Musiker, Instrumentenbauer und Architekten , 1972 .

[163]  Dean Keith Simonton,et al.  Thematic fame, melodic originality, and musical zeitgeist: A biographical and transhistorical content analysis. , 1980 .

[164]  F. R. Wilson The Hand: How Its Use Shapes the Brain, Language, and Human Culture , 1998 .

[165]  Guerino Mazzola,et al.  Flow, Gesture, and Spaces in Free Jazz - Towards a Theory of Collaboration , 2008, Computational Music Science.

[166]  Guerino Mazzola,et al.  Hypergestures in Complex Time: Creative Performance Between Symbolic and Physical Reality , 2015, MCM.

[167]  Klaus-Dieter Schewe The Type Concept in OODB Modelling and its Logical Implications , 1999, EJC.

[168]  Guerino Mazzola,et al.  Using the Creative Process for Sound Design Based on Generic Sound Form , 2021, MUME@AIIDE.

[169]  Martin Vogel Die Lehre von den Tonbeziehungen , 1975 .

[170]  Adam Kendon,et al.  How gestures can become like words , 1988 .

[171]  Olivier Messiaen Technique de mon langage musical , 1944 .

[172]  Robert A. Moog MIDI: Musical Instrument Digital Interface , 1986 .

[173]  Roel Vertegaal,et al.  The Sentograph: Input Devices and the Communication of Bodily Expression , 1995, ICMC.

[174]  Douglas R. Stinson,et al.  Combinatorial designs: constructions and analysis , 2003, SIGA.

[175]  Julius O. Smith,et al.  Physical Modeling Synthesis Update , 1996 .

[176]  Suzanne G. Cusick Feminist Theory, Music Theory, and the Mind/Body Problem , 1994 .

[177]  Wolfgang Müller,et al.  Darstellungstheorie von endlichen Gruppen , 1980 .

[178]  B. Repp Expressive Timing in a Debussy Prelude: A Comparison of Student and Expert Pianists , 1997 .

[179]  Henri Lonitz,et al.  Zu Einer Theorie der Musikalischen Reproduktion Aufzeichnungen, Ein Entwurf Und Zwei Schemata , 2001 .

[180]  J. Brooks,et al.  Broca's Area Supports Enhanced Visuospatial Cognition in Orchestral Musicians , 2007, The Journal of Neuroscience.

[181]  Gerald J. Balzano,et al.  The group-theoretic description of 12-fold and microtonal pitch systems , 1980 .

[182]  Itzhak Bars,et al.  Extra Dimensions in Space and Time , 2009 .

[183]  G. Lakoff,et al.  Where mathematics comes from : how the embodied mind brings mathematics into being , 2002 .

[184]  J. Sundberg,et al.  On the anatomy of the retard: A study of timing in music , 1980 .

[185]  Guerino Mazzola,et al.  Constraint-based Shaping of Gestural Performance , 2003, ICMC.

[186]  François Déchelle,et al.  The IRCAM Real-Time Platform and Applications , 1995, ICMC.

[187]  Joseph J. LaViola,et al.  Exploring 3D gestural interfaces for music creation in video games , 2009, FDG.

[188]  A. Wayne Slawson,et al.  The Musical Control of Sound Color , 1982 .

[189]  Arthur H. M. ter Hofstede,et al.  A Category Theory Approach to Conceptual Data Modeling , 1996, RAIRO Theor. Informatics Appl..

[190]  J. W. Bernard,et al.  Music Theory in Concept and Practice , 1997 .

[191]  Carl B. Boyer,et al.  Newton as an Originator of Polar Coördinates , 1949 .

[192]  I. Stravinsky,et al.  SYNTHESIS AND PROCESSING OF THE SINGING VOICE , 2002 .

[193]  Jean Piaget Morphismes et catégories : comparer et transformer , 1990 .

[194]  G. Marino,et al.  The UPIC System: Origins and Innovations , 1993 .

[195]  Enumeration of non-isomorphic canons , 2004 .

[196]  M. Ruggero,et al.  Frequency tuning of basilar membrane and auditory nerve fibers in the same cochleae. , 1998, Science.

[197]  Bertrand Coüasnon,et al.  Using a Grammar for a Reliable Full Score Recognition System , 1995, ICMC.

[198]  David Lewin,et al.  Forte's "Interval Vector, My Interval Function", and Regener's "Common-Note Function" , 1977 .

[199]  A. Hudspeth,et al.  Sensitivity, polarity, and conductance change in the response of vertebrate hair cells to controlled mechanical stimuli. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[200]  Geraint A. Wiggins,et al.  Pattern Induction and matching in polyphonic music and other multidimensional datasets , 2001 .

[201]  Anders Friberg,et al.  A Quantitative Rule System for Musical Performance , 1995 .

[202]  Guerino Mazzola Geometry and Logic of Musical Performance , 1993 .

[203]  Thomas Noll Morphologische Grundlagen der abendländischen Harmonik , 1997 .

[204]  G. Julia Mémoire sur l'itération des fonctions rationnelles , 1918 .

[205]  Lee Kennard How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics , 2008 .

[206]  E. Hehner the Meaning of Mathematics , 2016 .

[207]  G. Langner,et al.  Evidence for neuronal periodicity detection in the auditory system of the Guinea fowl: Implications for pitch analysis in the time domain , 2004, Experimental Brain Research.

[208]  Moreno Andreatta,et al.  aspects théoriques, analytiques et compositionnels , 2003 .

[209]  John Clough Diatonic Interval Cycles and Hierarchical Structure , 1994 .

[210]  R. Sternberg,et al.  The concept of creativity: Prospects and paradigms. , 1998 .

[211]  Alan Purvis,et al.  Acoustic Quanta , 1996, ICMC.

[212]  R. Keith Sawyer,et al.  Improvisation and the creative process : Dewey, collingwood, and the aesthetics of spontaneity , 2000 .

[213]  Jean Cavaillès,et al.  Methode axiomatique et formalisme , 1938 .

[214]  B. Engström Stereocilia of sensory cells in normal and hearing impaired ears. A morphological, physiological and behavioural study. , 1983, Scandinavian audiology. Supplementum.

[215]  Guerino Mazzola,et al.  Musical composition and Performance : statistical decomposition and interpretation , 2001 .

[216]  R. Guitart Deux problèmes en vue d’une épistémologie transitive des mathématiques , 2015, Revue de synthese.

[217]  Robin Hartshorne,et al.  Algebraic geometry , 1977, Graduate texts in mathematics.

[218]  Hubert S. Howe SOME COMBINATIONAL PROPERTIES OF PITCH STRUCTURES , 1965 .

[219]  G. Mazzola The Topos Geometry of Musical Logic , 2002 .

[220]  Richard Shusterman,et al.  Somaesthetics : A disciplinary proposal , 1999 .

[221]  R. Jakobson Linguistics and poetics , 1960 .

[222]  Thomas Noll,et al.  WF Scales, ME Sets, and Christoffel Words , 2007 .

[223]  E. D. Martino,et al.  La terra del rimorso , 1962 .

[224]  Topologien gestalteter Motive in Kompositionen , 2003 .

[225]  J. Locke An Essay concerning Human Understanding , 1924, Nature.

[226]  Gordon Curl The Laban sourcebook , 2012 .

[227]  Manfred Clynes,et al.  Sentics: The touch of emotions , 1977 .

[228]  Nathalie Henrich Bernardoni,et al.  Interplay between harmonics and formants in singing : when vowels become music , 2014 .

[229]  Dan Tudor Vuza Some Mathematical Aspects of David Lewin's Book: Generalized Musical Intervals and Transformations , 1988 .

[230]  S. Hawking A Brief History of Time: From the Big Bang to Black Holes , 1988 .

[231]  Language, Music, and Mind , 1993 .

[232]  Alex Lubet (Paralyzed on One) Sideman: Disability Studies Meets Jazz, through the Hands of Horace Parlan , 2010 .

[233]  Miller Puckette,et al.  Score Following in Practice , 1992, ICMC.

[234]  Takashi Suzuki,et al.  Musical Instrument Database with Multimedia , 1996, ICMC.

[235]  L. Haugh Checking the Independence of Two Covariance-Stationary Time Series: A Univariate Residual Cross-Correlation Approach , 1976 .

[236]  Guerino Mazzola,et al.  Towards Big Science: Geometric Logic of Music and its Technology , 1995 .

[237]  David Lewin,et al.  Klumpenhouwer Networks and Some Isographies that Involve Them , 1990 .

[238]  J. Brust,et al.  Musicophilia. Tales of Music and the Brain. , 2008 .

[239]  Christophe Ramstein,et al.  Analyse, représentation et traitement du geste instrumental : application aux instruments à clavier. (Analysis, representation and processing of the instrumental gesture: application to keyboard instruments) , 1991 .

[240]  R. Ryan Introduction to Tensor Products of Banach Spaces , 2002 .

[241]  John Geweke,et al.  A Comparison of Tests of the Independence of Two Covariance-Stationary Time Series , 1981 .

[242]  Guerino Mazzola,et al.  From Contour Similarity to Motivic Topologies , 2000 .

[243]  Ralph Johnson,et al.  design patterns elements of reusable object oriented software , 2019 .

[244]  A. Badiou Court traité d'ontologie transitoire , 1998 .

[245]  Lothar Ledderose Kreativität und Schrift in China , 2000 .

[246]  George Polya,et al.  Mathematical discovery : on understanding, learning, and teaching problem solving , 1962 .

[247]  H. Riemann,et al.  System der musikalischen Rhythmik und Metrik , 1981 .

[248]  Bruno H. Repp,et al.  Pedal Timing and Tempo in Expressive Piano Performance: A Preliminary Investigation , 1996 .

[249]  Guerino Mazzola,et al.  Musical consonances and dissonances: Are they distinguished independently by the right and left hippocampi? , 1986, Neuropsychologia.

[250]  Peter Desain,et al.  Quantization of musical time: a connectionist approach , 1989 .

[251]  Philipp Ackermann,et al.  Computer und Musik , 1991 .

[252]  Julius O. Smith Synthesis of Bowed Strings , 1982, ICMC.

[253]  P. Gabriel,et al.  Des catégories abéliennes , 1962 .

[254]  Elaine Landry,et al.  Categories in Context: Historical, Foundational, and Philosophical , 2005 .

[255]  P. Zweifel Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach , 1996 .

[256]  Anthony L Bertapelle Spectral Analysis of Time Series. , 1979 .

[257]  Neuronal Response in Limbic and Neocortical Structures During Perception of Consonances and Dissonances , 1995 .

[258]  R. Thom Stabilité structurelle et morphogenèse , 1974 .

[259]  J. Humphreys Introduction to Lie Algebras and Representation Theory , 1973 .

[260]  Guerino Mazzola,et al.  Diagrams, gestures and formulae in music , 2007 .

[261]  Carlton Gamer,et al.  Some Combinational Resources of Equal-Tempered Systems , 1967 .

[262]  Guerino Mazzola,et al.  Rational composition of performance , 1998 .

[263]  J. Lense Über die Hypothesen, welche der Geometrie zu Grunde liegen , 1922 .

[264]  Dan Hosken An Introduction to Music Technology , 2019 .

[265]  Susan Goldin Hearing gesture : how our hands help us think , 2003 .

[266]  Harald Fripertinger,et al.  Enumeration in musical theory. , 1991 .

[267]  Johan Sundberg,et al.  Musical Performance: A Synthesis-by-Rule Approach , 1983 .

[268]  E. Agmon Coherent Tone-Systems: A Study in the Theory of Diatonicism , 1996 .

[269]  Daniel G. Campos Peirce on the Role of Poietic Creation in Mathematical Reasoning , 2007 .

[270]  Gerhard Widmer Learning Expression at Multiple Structural Levels , 1994, ICMC.

[271]  Guerino Mazzola,et al.  Tempo Curves Revisited: Hierarchies of Performance Fields , 1994 .

[272]  C. Moore The Harmonic Structure of Movement, Music, and Dance According to Rudolf Laban: An Examination of His Unpublished Writings and Drawings , 2009 .

[273]  Philip Lambert : Musical Form and Transformation: 4 Analytic Essays . David Lewin. , 1994 .

[274]  Guerino Mazzola,et al.  "Cooking a Canon with RUBATO®": Performance Aspects of J.S. Bach's "Kunst der Fuge" , 1998, ICMC.

[275]  G. Pólya,et al.  Comment poser et résoudre un problème , 1989 .

[276]  Bruno Degazio A Computer-Based Editor for Lerdahl and Jackendoff's Rhythmic Structures , 1996, ICMC.

[277]  A. Kendon Gesture: Visible Action as Utterance , 2004 .

[278]  Guerino Mazzola,et al.  The RUBATO Performance Workstation on NeXTSTEP , 1994, ICMC.

[279]  Oliver Zahorka,et al.  PrediBase - Controlling Semantics of Symbolic Structures in Music , 1995, ICMC.

[280]  Gerhard Widmer,et al.  Computational Models of Expressive Music Performance: The State of the Art , 2004 .

[281]  Costas A. Drossos,et al.  Sets , Categories and Structuralism ∗ , 2005 .

[282]  H. Reeves Patience dans l'azur , 1981 .

[283]  Michael Cherlin Memory and Rhetorical Trope in Schoenberg's String Trio , 1998 .

[284]  Guerino Mazzola,et al.  Analyzing Musical Structure and Performance : A Statistical Approach , 1999 .

[285]  Eduardo Miranda,et al.  You have printed the following article : A Framework for the Evaluation of Music Representation Systems , 2008 .

[286]  J. Bell,et al.  From absolute to local mathematics , 1986, Synthese.

[287]  Maria Mannone,et al.  Comparison of non-Markovianity criteria in a qubit system under random external fields , 2012, 1209.6331.

[288]  Gerald Langner,et al.  Periodicity coding in the auditory system , 1992, Hearing Research.

[289]  R. Guitart Les coordonnées curvilignes de Gabriel Lamé – Représentation des situations physiques et nouveaux objets mathématiques , 2009 .

[290]  Florian Thalmann Gestural composition with arbitrary musical objects and dynamic transformation networks , 2014 .

[291]  Herbert A. Simon,et al.  Scientific discovery: compulalional explorations of the creative process , 1987 .

[292]  Sets, Invariance and Partitions , 1978 .

[293]  Klaus Lucas Grundlagen der Quantenmechanik und der Statistischen Mechanik , 1986 .

[294]  D. McNeill Gesture and Thought , 2005 .

[295]  James Jakób Liszka A general introduction to the semeiotic of Charles Sanders Peirce , 1996 .

[296]  Kacper Miklaszewski,et al.  A Case Study of a Pianist Preparing a Musical Performance , 1989 .

[297]  Alexandra Pierce,et al.  Deepening Musical Performance through Movement: The Theory and Practice of Embodied Interpretation , 2007 .

[298]  Luke Windsor,et al.  Make Me a Match: An Evaluation of Different Approaches to ScorePerformance Matching , 2000, Computer Music Journal.

[299]  Leonhard Euler Tentamen novae theoriae musicae , 1968 .

[300]  Todor Todoroff A Real-Time Analysis and Resynthesis Instrument for Transformation of Sounds in the Frequency Domain , 1996, ICMC.

[301]  Abby Whiteside,et al.  Indispensables of piano playing , 1955 .

[302]  Dirk van Dalen,et al.  Logic and structure , 1980 .

[303]  Ralph Abraham,et al.  Foundations Of Mechanics , 2019 .

[304]  Dard Neuman A house of music : the Hindustani musician and the crafting of traditions , 2004 .

[305]  Martin H. Levinson Creativity: Flow and the Psychology of Discovery and Invention , 1997 .

[306]  Vittorio Gallese,et al.  The Sense of Touch: Embodied Simulation in a Visuotactile Mirroring Mechanism for Observed Animate or Inanimate Touch , 2008, Journal of Cognitive Neuroscience.

[307]  J. Sundberg Music performance research: An overview , 1991 .

[308]  D. Eisenbud Commutative Algebra: with a View Toward Algebraic Geometry , 1995 .

[309]  R. Guitart AN ANABELIAN DEFINITION OF ABELIAN HOMOLOGY , 2007 .

[310]  Amanda Weidman Singing The Classical, Voicing The Modern The Postcolonial Politics of Music in South India , 2006 .

[311]  W. Greub Linear Algebra , 1981 .

[312]  Maria Kuncewicz,et al.  Creativity in Art , 1979 .

[313]  Xavier Rodet,et al.  Xspect: A New X/Motif Signal Visualization and Editing Program , 1996, ICMC.

[314]  Ludwig Wittgenstein Tractatus logico-philosophicus : Logisch-philosophische Abhandlung , 1963 .

[315]  Peter Row,et al.  Intonation in North Indian Music: A Select Comparison of Theories with Contemporary Practices , 1984 .

[316]  Jaime Gomez-Ramirez,et al.  Conciliating neuroscience and phenomenology via category theory. , 2015, Progress in biophysics and molecular biology.

[317]  G. Simondon Du mode d'existence des objets techniques , 1989 .

[318]  Jean-Marie Adrien,et al.  Modal Synthesis Compilation of Mechanical Sub-structures and Acoustical Sub-systems , 1990, ICMC.

[319]  Geoffrey P Hull The Music Business and Recording Industry , 2004 .

[320]  Virginia Hoge Mead More than Mere Movement: Dalcroze Eurhythmics , 1986 .

[321]  M. Violi Violi P., Beyond the body: towards a full embodied semiosis , 2012 .

[322]  Robert Morris,et al.  Composition With Pitch-Classes: A Theory of Compositional Design , 1991 .

[323]  de Ng Dick Bruijn,et al.  On the number of partition patterns of a set , 1974 .

[324]  Reinhard Kopiez,et al.  Handbuch der Musikpsychologie , 1996 .

[325]  K. Douglas,et al.  Amusia is associated with deficits in spatial processing , 2007, Nature Neuroscience.

[326]  A. Grossmann,et al.  Cycle-octave and related transforms in seismic signal analysis , 1984 .

[327]  Guerino Mazzola,et al.  Musical Composition and Gestural Diagrams , 2011, MCM.

[328]  J. Hadamard,et al.  The Psychology of Invention in the Mathematical Field. , 1945 .

[329]  Sally Popkorn,et al.  A Handbook of Categorical Algebra , 2009 .

[330]  Dan Tudor Vuza,et al.  Supplementary Sets and Regular Complementary Unending Canons (Part Four) , 1992 .

[331]  Guerino Mazzola,et al.  Functors for Music: The Rubato Composer System , 2006, ICMC.

[332]  A. Tanaka,et al.  Interaction, Experience and the Future of Music , 2006 .

[333]  E. Goffman The Presentation of Self in Everyday Life , 1959 .

[334]  J. L. Goldstein An optimum processor theory for the central formation of the pitch of complex tones. , 1973, The Journal of the Acoustical Society of America.

[335]  Zadour Khachadourian,et al.  On the homology theory of modules , 1970 .

[336]  David Lewin On Formal Intervals between Time-Spans , 1984 .

[337]  Carlos Agon Openmusic : un langage visuel pour la composition musicale assistee par ordinateur , 1998 .

[338]  Harald Fripertinger,et al.  Enumeration of mosaics , 1999, Discret. Math..

[339]  Fernando Zalamea,et al.  Synthetic Philosophy of Contemporary Mathematics , 2012 .

[340]  David Lewin,et al.  Generalized Musical Intervals and Transformations , 1987 .

[341]  Robert G. Bednarik,et al.  Selfishness and Fairness in Economic and Evolutionary Perspective: An Experimental Economic Study in Papua New Guinea1 , 2003, Current Anthropology.

[342]  Geraint A. Wiggins,et al.  Algorithms for discovering repeated patterns in multidimensional representations of polyphonic music , 2002 .

[343]  Michael Bell,et al.  Mathematical Theory of Switching Circuits and Automata , 1969 .

[344]  B. Repp The Art of Inaccuracy: Why Pianists' Errors Are Difficult to Hear , 1996 .

[345]  John Baer,et al.  The International Handbook of Creativity: Creativity Research in English-Speaking Countries , 2006 .

[346]  Duilio Giannitrapani,et al.  The Electrophysiology of Intellectual Functions , 1984 .

[347]  Haroldo V. Ribeiro,et al.  Universal patterns in sound amplitudes of songs and music genres , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[348]  D. Gorenstein Classifying the finite simple groups , 1986 .

[349]  R. Weisberg Creativity and knowledge: A challenge to theories. , 1998 .

[350]  C. Ginzburg,et al.  À distance : neuf essais sur le point de vue en histoire , 2001 .

[351]  M. Leman,et al.  Musical gestures : sound, movement, and meaning , 2010 .

[352]  Charles van den Borren,et al.  Thesaurus of Scales and Melodic Patterns , 1947 .

[353]  Wolfgang Prinz,et al.  Modes of Linkage Between Perception and Action , 1984 .

[354]  A. Grothendieck,et al.  Éléments de géométrie algébrique , 1960 .

[355]  V. Ramachandran,et al.  Mirror neurons and imitation learning as the driving force behind "the great leap forward" in human evolution , 2010 .

[356]  John M. Lee Introduction to Topological Manifolds , 2000 .

[357]  Joe Harris,et al.  The Geometry Of Schemes , 1992 .

[358]  Milton Babbitt,et al.  Twelve-Tone Rhythmic Structure and the Electronic Medium , 1962 .

[359]  I. Titze,et al.  A theoretical study of the effects of various laryngeal configurations on the acoustics of phonation. , 1979, The Journal of the Acoustical Society of America.

[360]  Richard Kronland-Martinet,et al.  The Wavelet Transform for Analysis, Synthesis, and Processing of Speech and Music Sounds , 1988 .

[361]  Martin Puttke Learning to dance means learning to think , 2010 .

[362]  Terri Gullickson The Creative Mind: Myths and Mechanisms. , 1995 .

[363]  Felix Salzer,et al.  Structural Hearing: Tonal Coherence in Music , 1952 .

[364]  David Lewin,et al.  A Formal Theory of Generalized Tonal Functions , 1982 .

[365]  P. Gabriel,et al.  Representations of Finite-Dimensional Algebras , 1992 .

[366]  John M. Chowning,et al.  The Synthesis of Complex Audio Spectra by Means of Frequency Modulation , 1973 .

[367]  Elon Lages Lima Fundamental Groups and Covering Spaces , 2003 .

[368]  Jean-Pierre Serre Faisceaux algébriques cohérents , 1955 .

[369]  Richard Pamcutt,et al.  Modeling piano performance: Physics and cognition of a virtual pianist , 1997, ICMC.

[370]  S. Langer Feeling and Form , 1953 .

[371]  J. Beran,et al.  Visualizing the Relationship between Two Time Series by Hierarchical Smoothing Models , 1999 .

[372]  Guerino Mazzola,et al.  From a Categorical Point of View: K-nets as Limit Denotators , 2005 .

[373]  W. Marslen-Wilson,et al.  Conjectures and refutations: A reply to Norris , 1982, Cognition.

[374]  Vilém Flusser,et al.  Gesten : Versuch einer Phänomenologie , 1993 .

[375]  W. T. Peake,et al.  Experiments in Hearing , 1963 .

[376]  Reinhard Kopiez,et al.  REALTIME ANALYSIS OF DYNAMIC SHAPING , 2000 .

[377]  B. Repp Patterns of note onset asynchronies in expressive piano performance. , 1996, The Journal of the Acoustical Society of America.

[378]  R. Wille,et al.  Musiktheorie und Mathematik , 1985 .

[379]  Seiji Inokuchi,et al.  Demonstration of Gesture Sensors for the Shakuhachi , 1994, ICMC.

[380]  Hans Kayser Akróasis : die Lehre von der Harmonik der Welt , 1980 .

[381]  Daniel Muzzulini Musical Modulation by Symmetries , 1995 .

[382]  R. Guitart Remarques sur les machines et les structures , 1974 .

[383]  S. Lang Introduction to Differentiable Manifolds , 1964 .

[384]  Neil P. McAngus Todd,et al.  A computational model of rubato , 1989 .

[385]  Peter K. H. Lee,et al.  The Legend of Semimaru: Blind Musician of Japan , 1978 .

[386]  Umberto Eco,et al.  Die Suche nach der vollkommenen Sprache , 1994 .

[387]  Rudolph Reti The Thematic Process in Music , 1978 .

[388]  Guerino Mazzola,et al.  The Extraction of Expressive Shaping in Performance , 2003, Computer Music Journal.

[389]  John Hodgson Mastering Movement: The Life and Work of Rudolf Laban , 2001 .

[390]  E. Prame Measurements of the vibrato rate of ten singers , 1994 .

[391]  K. Gotman Agency and Embodiment: Performing Gestures/Producing Culture , 2012 .

[392]  Stephen Travis Pope,et al.  Music Notations and the Representation of Musical Structure and Knowledge , 1986 .

[393]  R. Guitart TOUTE THEORIE EST ALGEBRIQUE ET TOPOLOGIQUE , 2008 .

[394]  de Ng Dick Bruijn Pólya's theory of counting , 1964 .

[395]  W. Massey A basic course in algebraic topology , 1991 .

[396]  Luca Cardelli,et al.  On understanding types, data abstraction, and polymorphism , 1985, CSUR.

[397]  Guerino Mazzola,et al.  The Composing Hand: Musical Creation with Leap Motion and the BigBang Rubette , 2014, NIME.

[398]  May,et al.  A Concise Course in Algebraic Topology , 1999 .

[399]  Maurice Merleau-Ponty,et al.  Phenomenology of perception , 2016 .

[401]  Michael Holquist,et al.  Toward a Philosophy of the Act , 1995 .

[402]  W. S. Rhode,et al.  Evidence from Mössbauer experiments for nonlinear vibration in the cochlea. , 1974, The Journal of the Acoustical Society of America.

[403]  L. Giard,et al.  L'étranger, ou, L'union dans la différence , 1969 .

[404]  Juan G. Roederer Physikalische und psychoakustische Grundlagen der Musik , 1977 .

[405]  Paul Hudak,et al.  Haskore music notation – An algebra of music – , 1996, Journal of Functional Programming.

[406]  Dominik Hörnel,et al.  Melonet: Neural Networks that Learn Harmony-Based Melodic Variations , 1994, ICMC.