1. Guerino Mazzola U & ETH Zürich Internet Institute for Music Science guerino@mazzola.ch www.encyclospace.org/talks architecture du livre „The Topos of Music“ architecture du livre „The Topos of Music“

2. The Topos of Music Geometric Logic of Concepts, Theory, and Performance 1996 - 2002 www.encyclospace.org/... avec la collaboration de Moreno Andreatta, Gérard Assayag, Jan Beran, Chantal Buteau, Roberto Ferretti, Anja Fleischer, Harald Fripertinger, Jörg Garbers, Stefan Göller, Werner Hemmert, Mariana Montiel, Andreas Nestke, Thomas Noll, Joachim Stange-Elbe, Oliver Zahorka

3. Appendix:MathematicalBasicsGlossary Introduction and Orientation Local Theory Global Theory Harmony Counterpoint Operationalization of Poiesis presto ® String Quartet Theory Geometrie der Töne 1990

4. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: MathematicalBasics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM The Topos of Music 2002 The Topos of Music 2002

5. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 1. What is Music About? 2. Topography 3. Musical Ontology 4. Models and Experiments in Musicology

6. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 5. Navigation 6. Denotators 6.1 Universal Concept Formats 6.2 Forms 6.3 Coordinates and Pointers 6.4 Anchoring Forms in Modules 6.5 Regular and Circular Forms 6.6 Regular Denotators 6.7 Circular Denotators 6.8 Ordering on Denotators 6.9 Concept Surgery and Denotator Semantics

7. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 7. Local Compositions 8. Symmetries and Morphisms 9. Yoneda Perspectives 10. Paradigmatic Classification 11. Orbits 12. Topological Specialization

8. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 13. Global Compositions 14. Global Perspectives 15. Global Classification 16. Classifying Interpretations 17. Aesthetics and Classification 18. Predicates 19. Topoi of Music 20. Visualization Principles

9. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 21. Metrics and Rhythmics 22. Motif Gestalts

10. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 23. Critical Preliminaries 24. Harmonic Topology 25. Harmonic Semantics 26. Cadence 27. Modulation 28. Applications

11. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 29. Melodic Variation by Arrows 30. Interval Dichotomies as an Expression of Contrast 31. Modeling Counterpoint by Local Symmetries

12. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 32. Local and Global Performance Transformations 33. Performance Fields 34. Initial Sets and Initial Performances 35. Hierarchies and Performance Scores

13. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 36. Taxonomy of Expressive Performance 37. Performance Grammars 38. Stemma Theory 39. Operator Theory

14. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 40. Architecture 41. The RUBETTE ® Family 42. Performance Experiments

15. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 43. Analysis of Analysis

16. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 44. Principles of Music Critique 45. Critical Fibers 46. Grammatical Varieties

17. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 47. Unfolding Geometry and Logic in Time 48. Local and Global Strategies in Composition 49. The Paradigmatic Discourse on presto ® 50. Case Study I: „SYNTHESIS“ by Guerino Mazzola 51. The Syntagmatic Discourse on Open Music 52. Case Study II: „ Composition“ by Compositeur XY

18. I. Introduction and Orientation II. Navigation on Concept Spaces III. Local Theory IV. Global Theory V. Topologies for Rhythm and Motives VI. Harmony VII. Counterpoint VIII. Structure Theory of Performance IX. Expressive Semantics X. RUBATO ® XI. Statistics of Analysis and Performance XII. Inverse Performance Theory XIII.Operationalization of Poiesis XIV. String Quartet Theory XV. Appendix: Sound XVI. Appendix: Mathematical Basics XVII. Appendix: Tables XVIII. Appendix: References XIX. Symbols and Notations XX. Glossary XXI. Index CD-ROM 53. Historic and Theoretical Prerequisites 54. Estimation of Resolution Parameters

19. I. Introduction and Orientation 1. What is Music About? 2. Topography 3. Musical Ontology 4. Models and Experiments in Musicology

20. 6. Denotators 6.1 Universal Concept Formats 6.2 Forms 6.3 Coordinates and Pointers 6.4 Anchoring Forms in Modules 6.5 Regular and Circular Forms 6.6 Regular Denotators 6.7 Circular Denotators 6.8 Ordering on Denotators 6.9 Concept Surgery and Denotator Semantics

21. 7. LocalCompositions 8. Symmetries and Morphisms 9. Yoneda Perspectives 10. Paradigmatic Classification 11. Orbits 12. Topological Specialization III. Local Theory

22. IV. Global Theory 13. Global Compositions 14. Global Perspectives 15. Global Classification 16. Classifying Interpretations 17. Aesthetics and Classification 18. Predicates 19. Topoi of Music 20. Visualization Principles

23. V. Topologies for Rhythm and Motives 21. Metrics and Rhythmics 22. Motif Gestalts

24. VI. Harmony 23. Critical Preliminaries 24. Harmonic Topology 25. Harmonic Semantics 26. Cadence 27. Modulation 28. Applications

25. VII. Counterpoint 29. Melodic Variation by Arrows 30. Interval Dichotomies as an Expression of Contrast 31. Modeling Counterpoint by Local Symmetries

26. VIII. Structure Theory of Performance 32. Local and Global Performance Transformations 33. Performance Fields 34. Initial Sets and Initial Performances 35. Hierarchies and Performance Scores

27. IX. Expressive Semantics 36. Taxonomy of Expressive Performance 37. Performance Grammars 38. Stemma Theory 39. Operator Theory

28. X. RUBATO ® 40. Architecture 41. The RUBETTE ® Family 42. Performance Experiments

29. 43. Analysis of Analysis XI. Statistics of Analysis and Performance

30. XII. Inverse Performance Theory 44. Principles of Music Critique 45. Critical Fibers 46. Grammatical Varieties

31. 47. Unfolding Geometry and Logic in Time 48. Local and Global Strategies in Composition 49. The Paradigmatic Discourse on presto ® 50. Case Study I: „SYNTHESIS“ by Guerino Mazzola 51. The Syntagmatic Discourse on Open Music 52. Case Study II: „ Composition“ by Compositeur XY XIII.Operationalization of Poiesis

32. XIV. String Quartet Theory 53. Historic and Theoretical Prerequisites 54. Estimation of Resolution Parameters