Music and Fuzzy Logic: The Dialectics of Idea and Realizations in the Artwork Process

✍ Scribed by Hanns-Werner Heister

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 745
• Series: Studies in Fuzziness and Soft Computing, 406
• Edition: 1
• Category: Library

✦ Synopsis

This book unfolds the manifold, complex and intertwined relations between Fuzzy Logic and music in a first comprehensive overview on this topic: systematically as an outline, as completely as possible, in the aspects of Fuzzy Logic in this relation, and especially in music as a process with three main phases, five anthropological layers, and thirteen forms of existence of the art work (Classics, Jazz, Pop, Folklore). Being concerned with the ontological, gnoseological, psychological, and (music-) aesthetical status and the relative importance of different phenomena of relationship between music and Fuzzy Logic, the explication follows the four main principles (with five phenotypes) of Fuzzy Logic with respect to music: similarity, sharpening 1 as filtering, sharpening 2 as crystallization, blurring, and variation. The book reports on years of author’s research on topics that have been only little explored so far in the area of Music and Fuzzy Logic. It merges concepts of music analysis with fuzzy logical modes of thinking, in a unique way that is expected to attract both specialists of music and specialists of Fuzzy Logic, and also non-specialists in both fields. The book introduces the concept of dialectic between sharpening and – conscious – “blurring”. In turn, some important aspects of this dialectic are discussed, placing them in an historical dimension, and ending in the postulation of a 'musical turn' in the sciences, with some important reflections concerning a “Philosophy of Fuzzy Logic”. Moreover, a production-oriented thinking is borrowed from fuzzy logic to musicology in this book, opening new perspectives in music, and possibly also in other artistic fields.

✦ Table of Contents

Preface: Subject, Themes and Aims
Double Approach, Hybrid Perspective
Complexity and Priority of Qualitative Questioning
Mutual Benefit for Science of Music and Fuzzy Logic: Tunnel Digging from Two Different Sides
About the Structure of This Book
The Notion of ‘(Art)work’: A structural, Genre-Comprehensive Concept, Not a Concept of Assessment
Towards a ‘Philosophy of Fuzzy Logic’
Acknowledgements
Contents
Bio-Bibliography of the Author
1 Introduction: Fuzzy Logic’s Four Art-Related Principles and Five Phenotypes in the Musical Process
1.1 Realization, ‘Appropriation’. Craftsmanship and Engineering as a Bridge Between Fuzzy Logic and Music
1.2 Logic of Difference and Identity. The Internal and External Interdisciplinary Subjects of Fuzzy Logic
1.2.1 Sources and Elements of Fuzzy Logic as Interdisciplinary Synthesis
1.2.2 Heuristics. Exploring the Uncertain
1.2.3 Realistic Limits of Absolute Precision
1.2.4 “Precise Fuzziness”
1.2.5 Ideology, Illusions, Realities. Vulgar Mathematics and Fuzzy Logic
1.2.6 Abstract Scientific and Concrete Artistic Anticipation
1.3 Modal Logic, Polyvalent Logics and Musical Logic
1.3.1 Possibilities and Reality, Coincidence and Necessity
1.3.2 Infinite Possibilities and Finite Reality. Intermediate Values
1.3.3 Musical Logic
1.4 The Four Principles with Its Five Phenotypes: Similarity, Sharpening (Filtering and Crystallization), Blurring, Variation
References
2 The Structure of the Music Process and the Work’s Thirteen ‘Forms of Existence’. Identity in and as a Process, Against and Through Differences
2.1 The Music Process as Overarching Entirety—The Artwork as Integral and Concentrate. Productive, Reproductive and Receptive Realization of the Idea
2.1.1 Music as Process—and as Result of the Process
2.1.2 Vertical Segmentation: Simultaneity. The Five Anthropological Layers of the Music Process
2.1.3 The Layers Between Physics and Philosophy
2.1.4 Horizontal Segmentation I: Succession. The Arrow of Time
2.1.5 Horizontal Segmentation II: Fanning Out in Various Sensorial Areas
2.1.6 The Three Main Phases: Production/Composition, Reproduction/Interpretation, Reception
2.1.7 Partial Advancement from the More Vague to the More Precise—Tendencies and Countertendencies
2.2 Dialectic—Becoming and Being, Contradictions and Unity, Change and Constancy
2.2.1 Sublation as “Processing Identity”—A New Category for the Entire Process and Result
2.2.2 Difference and Identity: Heraclite’s River Bank, River and Transformations of Object and Subject
2.3 Horizontal Segmentation III. The Sequence of the ‘Forms of Existence’—Progressive Elimination of Fuzziness up to the Score Form
2.3.1 The Concept ‘Forms of Existence’
2.3.2 List of the ‘Forms of Existence’
2.3.3 ‘Segmented Continuum’: Overarching Holistic Process with Cesuras
2.3.4 Processes of Composition and Decomposition, Sharpenings Versus Blurrings
2.3.5 Complete and Incomplete Cycle of ‘Forms of Existence’. Word Form, Picture Form and Quotation Form as Exceptional Cases
2.4 Core and Contours. The Variable and the Relatively Invariable
2.4.1 Dialectic of Variance and “Constancy of Shape” Within and Between the ‘Forms of Existence’
2.4.2 System and Surrounding, Motivations and Functions
References
3 Fundamental Fuzziness: The Imperfect Perfection
3.1 Idea vs. Sound. Fuzziness in Composition and Interpretation
3.1.1 Productive and Receptive Realization
3.1.2 Avoidable “Vagueness” and Indelible Fuzziness
3.1.3 Information Theory and Improvisation
3.2 Artwork as Idea in Fixed Written Form. Sharpening of Blurs Through the Notation
3.2.1 Enlarged and Restricted Frames of Determinations in the Notation
3.2.2 Starting with Mere Indications of Pitches and Durations to Excessively Precise Notation of Technical and Expressive Execution
3.2.3 ‘Transcription’ of Sounding Music as Re-Translation
3.2.4 Notation and Finalization of Uncompleted Works
3.3 „Tolerances” in the Real Music. Work as Acoustically Realized Idea: Sound Form
3.3.1 “Miserable Violin” (Beethoven). the Composable and the Composed, the Feasible—and then the Audible
3.3.2 Compositional Guiding Principles Complexity Versus Comprehensibility
3.3.3 Fuzzy Edges. Framework Institution, Tradition, Historical Changes of Interpretation
3.3.4 Desafinado. Tuning Systems and Standard Concert Pitch and Historical Change
3.3.5 The Work as Unspecific Stimulus. Postmodern “Constructivist” and “Deconstructive” Nihilism
3.4 ‘Uncertainty’. Work as Sensually Received and Mentally Reflected Idea: Perception Form
3.4.1 Unconscious Amending of Hearing, Playing, and Singing
3.4.2 Perception in the Trinity of Text, Sound, and Context
3.4.3 Reception as Processual Sensory-Mental Perception Between Anticipation and Recollection
3.4.4 Conditions, Situations, Distractions
3.4.5 Preconditions Activated and Updated: Expectation
3.4.6 Pre-preconditions. ‘Halo’ and ‘Devil’ Effect and Other Blurs—Prejudices as Pre-formations and Deformations of Perception
3.4.7 Soft Computational Modeling. Computerized Entanglement of Perception and Production
3.4.8 New and Negentropy—The Unexpected
3.5 Remembering and Forgetting. Work as Sensual Idea Preserved in Memory: Recollection Form
3.5.1 Ultra-Short-Term Memory, Short-Term Memory and Long-Term Memory. Cognitive Frames
3.5.2 The Lady Vanishes. Fading, Sharpening, Forgetting
3.5.3 „O, Du Lieber Augustin, Alles Ist Hin“ (O My Dear Augustin, All Is Gone) by Arnold Schönberg. Fading Away, Composed
3.5.4 Refreshing and Reinforcing
3.5.5 Reconstructing from Memory as Special Case of Reinforcement and Sharpening
3.5.6 Recalled Memories—Quotation, Leitmotif. Composed Memory as Reinforcement
3.5.7 Uncalled Memories as Hallucination Form
3.6 Blurring in the Technical Reproduction of Music. Work as Technically Recorded Sound: Phonography Form (I)
3.6.1 Media Mediated Power and Deception of Memory—‘False Memory’
3.6.2 A New Type of Sound Form from Technical (Re-)Production. Blurs and Permutations in the Transformation to Another Medium
3.6.3 “Noise” vs. „High Fidelity“. Technical-Medial Limits of Accuracy
3.6.4 The Audiovisual Form as a Variant of the Phonographic Form
3.6.5 Phonographic Form as Primary Form of Existence
3.6.6 Guiding Principle Immersive Reception as Overwhelming—Focus on Effect Instead of Work
3.7 Work and Effects. the Multiplication of Fuzziness Possibilities
3.7.1 Difference Between End and Aim of the Music Process
3.7.2 Considerations and Suggestions for Fuzzy Logic Experiments for Objectify Subjective Experiences
References
4 The Principle of Similarity: The Resultant of Identity and Difference
4.1 Such as and Different from: Approximations, Convergencies—Difference Instead of Identity
4.1.1 Different from and Such as: Expression Versus Imprint, Misleading Identification of Signifier and Signified
4.1.2 Comparing—Production and Determination of Similarities: Concrete and Abstract Analogy, Typology, and Classification
4.1.3 From Known to Unknown—Heuristic, Mirror-Neurons, and Empathy
4.2 Art-Specific Iconicity and Materiality of Reflection, Mimesis, Poiesis, Aisthesis, and Catharsis—Representation, Production, Perception, and Achievement
4.2.1 Art ǂ Science. The Artistic Reflection: Mimesis
4.2.2 Four Dimensions of Similarity in Music Process: Relations with Reality, Relations Between Components of a Work, Between Its Forms of Existence, and to Components of Other Works
4.2.3 Analogies, Synaesthesias, Subjects, Sources and Material of Musical Mimesis in Nature and Society
4.3 Nature and Arts, Mimesis and Poiesis. Real Tones as Readymade and Handmade, Musical Onomatopoeia and Painting
4.3.1 Things as Signs
4.3.2 Real Tones as Readymade and Thing Signs
4.3.3 Real Tones as Handmade—Mimesis by Means of Poiesis
4.3.4 Real Tones and Existing Pieces of Music as Readymade Material of a Work
4.3.5 Real Tone Transformed into Onomatopoeia
4.3.6 Painting as Mimesis and Poiesis. Hypernaturalism, Trompe D‘Oeil/“Optical Illusion“, „Organized Sound“ (Edgard Varèse)
4.3.7 Mimesis of Matter
4.3.8 Music as Painting
4.4 Art with Numbers. Musical Mimesis with Proportions as Paradoxical Abstract Iconic
4.4.1 Mimesis with Visual Abstractions and Geometric Proportions—Alvin Lucier and Alban Berg
4.4.2 Lengths of Structural Parts and Numerical Proportions as an Expression of Gender-Relations in Case of Artur Schnabel and Johannes Brahms
4.5 Art and Art—Intertextuality: Reflections and Interactions of Music with Texts, Pictures and Other Arts
4.5.1 Medium Change and Total Art Work (“Gesamtkunstwerk”)
4.5.2 Word Art and Musical Art, Setting to Music and Textualization (Tropatura)
4.5.3 Palimsest, „Transtextuality“, „Hypertextuality“
4.5.4 ‘Music Form‘ of Texts: Program-Music I
4.5.5 ‘Music Form’ of Pictures: Program-Music II
4.5.6 Real and Imagined Pictures as Objects—Respighi‘s Vetrate di Chiesa (1926)
4.6 Similarities, Affiliations, Structural and Processional Relations: Fuzzy Logic and Music-Analysis
4.6.1 The Range of Possibility Between Identity, Equality and Blurred Sophistication
4.6.2 One-, Two-, Three-Tone-Motifs and Four-Tone-Motif B-A-C-H – Modifications, Transformations, Permutations
4.6.3 BA, BAC, BACH—Variations and “Constancy of Shape” („Gestaltkonstanz“)
4.6.4 BACH: Counterpoint as Procedure of Variation and Transformation
4.6.5 Cross Motif and Chromatics—Wagner‘s Ring, Strauss‘ Arabella
4.7 Neuronal Iconic and Fuzzy Logic
References
5 The Principle of Sharpening (I): Filtering. Cosmos Out of Chaos—Aspects and Elements of the Musical Materials
5.1 The Development of Musical Materials Under the Aspect of Sharpening. Segmentation: Discrete Parts Instead of Continuum
5.1.1 Sharpening. Filtering of Components, Crystallization of Shapes
5.1.2 Selection. Filtering in Arts and Nature
5.1.3 Filtering of Elements: Musical Tone, Pitches- and Rhythm Systems, Tuning Systems
5.1.4 Tones from Noises and Sounds: Organizing and Structuring of Rhythmical-Temporal Acoustic and Non-Acoustic Processes—Culture Versus Nature. Historical and Logical-Systematic Dimensions
5.1.5 Development of Chords as Structured Vertical from Heterophonic Lines
5.1.6 Tuning Systems—Sharpening, Blurring and Fuzziness
5.1.7 Filtering: Technical Production of Tones and Sounds from Noises in Electro-Acoustic Music
5.1.8 Solmization as Soggetto Cavato (Carved Out Theme): Filtered Syllables as Pitch Names. System Building Within an Already Established Historical System of the Musical Material
5.2 Filtering as a Search for Similarities Using Fuzzy Logic
5.2.1 Detection, Storage and Retrieval of Patterns or Shapes
5.2.2 Melodic and Other Similarities—Computer-Based Analysis
5.2.3 Call Wolfgang via Voice Over IP (Johannes Kreidler). Automatic Phone-Tapping, Internet Censorship and Fabrication of “Terrorists”
5.2.4 BACH-Searching as a Test on the Internet. Sequence, Cross, Fate: Expected and Unexpected Results—Flexibility and Productivity of Fuzzy Logic
5.3 Sharpening Without Proper Filtering and Transitions Towards Crystallization
5.3.1 Precisioning of the Recollection Form Through Objectivation, Exteriorization and Repeatability—Phonography Form (II)
5.3.2 Audio- and Data-Compression as Ambivalent Filtering
5.3.3 Compositional Use of the Filtered Nature for Crystallization: Shapes and Motifs from the Partial-Tone-Spectrum—Wagner’s Prelude to Rheingold, „Spectralism“ Since the 1970s
References
6 The Principle of Sharpening (II): Crystallization. Development and Advancement of Musical Shapes
6.1 From Filtering to Crystallization: Extraction, Concentration, Core, Contour
6.1.1 ‘Soggetto Cavato’
6.1.2 Pre- and Para-Compositional Form of Hallucination: Arnold Schönberg’s War-Clouds Diary—Anthropomorphic Projections of Socially Significant Shapes into Natural Phenomena
6.2 ‚Motif‘ as Nucleus for Formation of Structures in Improvisation and Composition
6.2.1 Crystallization in the Historical Process. BACH as an Emblem Before, In, and After J. S. Bach—The Cross as Generating Deep Structure Since Guillaume Dufay
6.2.2 Crystallization Within the Work. Motif, Theme, Movement, Work
6.3 Work as Inspiration and Idea. Conceptual Form
6.3.1 Questions of Documentation and Translation. Verbal, Notational, and Pictorial Partial Concretization of the Idea
6.3.2 Emulation of Processes of Creation and Crystallization in the Work Itself
6.3.3 Conceptual Art as Discontinued Conceptual Form
6.4 Work as an Outlined Written Conception. Sketch Form
6.4.1 Exteriorizations of the Conceptual Form
6.4.2 Sketches and Music Process
6.4.3 “Writing” as Mere Dictation of Thought and Spontaneous Transcription
6.4.4 Accelerations on the Way to the Score. Partimento and Particell
6.5 Work as an Idea Completed in the Composers’ Mind. Thought Form
6.5.1 „Always Having an Eye for the Whole“ (Beethoven). „Gradual Generation“ of Thought and Anticipatory Completion of the Work
6.5.2 Disappointment. The Reduction of the Infinite Possibilities to the Only One Realized Possibility
6.6 Preliminary and Final Stage of the Work as a Notationally Completely Realized Idea. Anticipation Form and Score Form
6.6.1 The ‘Abstract Composition’
6.6.2 Stage I. The Naked, but Integral Body. From Thread to Fabric—Evolving the Polyphonic Composition
6.6.3 Stage II: The Clothed Body. Compositional Anticipation and Intentional Determination of Performance and Execution
6.6.4 Changing Cubicle. Sharpening with Turnaround—Transcription as Transformation of the Sound Form into a Notation Form
6.6.5 Changing Clothes. The ‘Postproduction’ of ‘Versions’
6.7 The Work as a Notationally Completely Realized Idea. Score Form
6.7.1 New Sounds, New Signs. M. Kagel’s Pas de cinq
6.7.2 Sharpening in a Round-About Way. ‚Graphical Notation‘
6.7.3 New Freedom from Order to Chaos. Sylvano Bussotti’s Siciliano
6.7.4 Graphic Notation on the Way to Fuzziness
6.7.5 Sharpening Notation of Non-notes: Ervin Schulhoff’s in Futurum (1919)
6.8 Bypassing Blurs: Direct Composition of the Sound Form Without Notation and Human Interpreters
6.8.1 Automatophones. Barrel Organ and Player Piano, ‘Abstract Composition’ and Secondary Subjectivity of the ‘Pianolist’
6.8.2 Electrification. Reproducing Piano as Production Instrument: Conlon Nancarrow
6.8.3 Film as Sound Carrier—The Optical Sound Track
6.8.4 Composition as Realization. „Musique Concrète“ and „Electronic Music”
6.8.5 Without Notes, Text and Graphic. Controlling the Sound Form via Brain Waves
6.8.6 Soundless. Music for Reading
6.9 Sharpening of Perception. Anticipative Preparation in the Production and Supporting Activities in the Reception
6.9.1 „From the Heart—May It Go to the Heart” (Beethoven). Rhetorics and Intensity
6.9.2 ‚Hookline‘. Catchiness, Repetition, Obtrusiveness
6.9.3 ‚Earworm‘. Undesirable Remembrance
6.9.4 Sharpening Through Motion and Reproductive Participation: Dancing and Singing Along
6.10 Sharpening Through Blurring. Fuzzy Logic as a Partial Logic of Compositional History
6.10.1 The Development of European Melodic Polyphony. Counter Movements Instead of Parallel Movement of the Parts
6.10.2 Poly-Textuality. Sharpening of Sound Perception, Blurring of Sense Perception in Motet and Quodlibet
References
7 The Principle of Blurring. Conscious, Artistically Produced Blurrings
7.1 “Dying” and Concealment
7.1.1 The “Morendo” Ending in the Prelude of Alban Berg’s Three Pieces for Orchestra
7.1.2 The Tarnhelm Motif in Wagner’s Ring
7.1.3 The Hidden Theme in Elgar’s Enigma Variations
7.2 Point of Departure. Idea and Conceptual Form. Blurred and Blurrings in the Service of Crystallization—Noises as New Material
7.2.1 ‚Cluster‘. Clumped Chords—Pitches in Transition to Noise
7.2.2 “Intonarumori”. Sirens, Airplane Propellers. Pre-electric Noise Production
7.2.3 Technical Re/Produced Noise as Musical Material
7.2.4 “Noise” as Blurry Real Residue and as Ideology
7.3 Point of Departure: Score Form. ‘Musical Graphics’
7.3.1 The Pictorial Instead of Notes and Writing as a Blurred or Vague Concept for the Realization
7.3.2 „Soundpainting“. Realtime Composing Alias Improvisation
7.3.3 “Visible Music”, Air Guitar and Air Drums
7.3.4 Text Form Instead of a Notation Form: Concept Art as Mere Verbalization of Ideas Without Realization
7.4 Point of Departure: Anticipation Form. Instrumentation, Ornamentation, Indeterminations
7.4.1 Notation as Blurring: The Main Theme of the IVth Movement in Tchaikovky’s 5th Symphony
7.4.2 Pitch. Embellishment as Blurring
7.4.3 Tone Color. Instrumentation as Blurring—Color Instead of Drawing, Brush Stroke Instead of Line
7.4.4 Musical Chiaroscuro, Sfumato, Clocks and Clouds. from the Transparent Polyphonic Structure to the Opaque “Texture”
7.4.5 Resulting Patterns as Pre-calculated Blurs—Between Bach/Gounod’s Ave Maria and Central/East African Xylophone Music
7.4.6 Musical ‘hatching’—Blurring as Structural Condensation. Iteration of Patterns in Minimal Music and Steve Reich’s Drumming
7.4.7 Indeterminacy Instead of “Fully Completed Unity”
7.4.8 Reworking and Arrangement as Blurring
7.5 Point of Departure: Sound Form. Subjective Vivifications of Tone and Tempo
7.5.1 Vibrato. Blurring in the Dimension of Pitches as Vivification
7.5.2 Modifications of Tempo, Tempi and Beat
7.5.3 Rubato. Blurrings in Relative Tempi as Vivification
7.5.4 Off-Beat. Generalized Rubato
7.6 Point of Departure: Phonography Form. Electroacoustic Simulation of Liveliness
7.6.1 “Humanizers”. Simulated Vibrato and Other Expression and Animation Effects
7.6.2 Composition, Indeterminacy and Improvisation: ‘Live Electronics’
7.6.3 People as Interface. Towards the Elimination of Professional Composers
7.7 Point of Departure: Perception Form. Mishearing and Misunderstanding Between Fuzziness and Blurring
7.7.1 Unintentional Parodies: “Lady Mondegreen” = “Laid Him on the Green”
7.7.2 Intentional Parodies, Deliberate Misunderstanding, Rewrites. Walther’s and Beckmesser’s “Preislied” in Die Meistersinger von Nürnberg
References
8 The Principle of Variation: Similarities, Differences, Development
8.1 Width and Diversity of the Principle of Variation
8.1.1 Permutation (I)—‚Change Ringing‘
8.1.2 Permutation (II)—Twelve Tone Technique
8.1.3 Difference and Identity: Repetition, Contrast, Alteration
8.1.4 Variance Without Constancy
8.1.5 Musical Variation Cycles
8.1.6 Universal Design Principles of Varying Music Making?
8.2 Variation Through Reconfiguration: Quotation Form
8.2.1 Metamorphoses
8.2.2 Large Quotation—The Work as a Completely Resurrected Whole
8.2.3 Embedding: Smaller Work as Complete Quotation Within a Larger Work
8.2.4 Palimpsest—Parts of the Work as a Changed, but Maintained Combination of Sound and Idea
8.2.5 Collage—Fragments of Works as Semantic and Syntactic Building Blocks
8.3 Variations Through Media Transformations (I): Word Form
8.3.1 Recrystallization and Reconfiguration in a Detour Through Fuzziness and Transformation into a Different Art
8.3.2 Word Form—Afterwards and Afore: Music Criticism, Music Analysis, Introduction to Works
8.3.3 Ekphrasis: Word Form Versus Program Music as ‘Music Form’ of Texts and ‘Music Form’ of Pictures
8.3.4 Program as Ekphrasis: Charles Ives’ Remarks on His Orchestral Pieces Three Places in New England
8.3.5 Facilitating the Imagination Through Verbal References to Pictures and Known Works
8.3.6 Fictional Musical Works in Word Form: Descriptions of Fictional Works with Reference to Real Ones in Thomas Mann’s Novel Doktor Faustus and Elsewhere
8.4 Variation Through Media Transformation (II): Picture Form
8.4.1 Demarcations: Pictures with Music, Pictures Based on and About Music, Picture Form of Works, Music Form of Pictures
8.4.2 Individual Works in Picture Form
8.4.3 Title Pages of Sheet Music Editions, Sound Carrier Covers and Advertisements as Picture Form of Works
8.4.4 Moving Picture Form of Works I: Dance/Ballet
8.4.5 Moving Picture Form of Works II: Translation of Musical Works in Sign Language
8.4.6 Moving Picture Form of Works III: Film
8.5 Variations Through Receptive Realization: Imagination Form
8.5.1 Mental Reconstruction of the Realized Work from Fragmentary and Vague Information—Optimum Fuzziness
8.5.2 Mental Construction of a Non-real Work—Imaginations of “Conceptual Art”
8.5.3 Imagination Form as the Translation of Conceptual Art Concepts into Subjective Realizations
References
9 Perspectives and Prospects
9.1 Productivity I. Historical Development and Progress of Music Through Fuzziness/Blurring and Sharpening—Fuzzy Logic as Logic in the History of Music
9.1.1 Pendulum Swings in Musical History Between Blurring and Renewed Sharpening: Expression Becomes Material—Material Becomes Expression
9.1.2 Analogies Between Music and Life with Movements in Space: Purposefully With or Without Parallels—Sharpening and Blurring
9.1.3 Quadrature of the Circle and Rules of the Game—Keeping Them, Consciously Breaking and Changing Them
9.2 ‚Musical Turn‘ in Natural Sciences, Liberal Arts, and Social Sciences. Generalizations and ‚Philosophy of Fuzzy Logic‘
9.2.1 Pragmatics and Practice: Acoustical and Musical as Technical and Psychosocial Instrument
9.2.2 Musical “Biofeedback”, “Mindball” and “Experimental Music”. Music as Science?
9.2.3 Chimera. Musical Parallels to Scientific-Technical Procedures
9.2.4 The Creation, Becoming Instead of Being in and as Music, and the Arrow of Time—A Mimesis of Nature. Music as an Active Component of World View
9.2.5 Seismograph. Music as a Historical-Social Document
9.2.6 “West-Eastern Divan Orchestra” and “Mozart Effect”—Chaos and Anomy, Cosmos and Harmony. Music as a Model for Dialectics
9.3 Productivity II. Interdisciplinary Cooperation Transgressing Disciplinary Boundaries and ‘Inner Interdisciplinarity’. Fuzzy Logic, Music and Musicology
9.3.1 Interdisciplinarity as sum and synthesis. Musical contribution to “The Philosophy of Fuzzy Logic”
9.3.2 ‘Fuzzy Logical Turn’?
9.3.3 ‘Inner Interdisciplinarity’. Answered, Processed, Open and New Questions
References
Bibliography