Guerino Mazzola

1
Les mathématiques de linterprétation
musicale Champs vectoriels dinterprétation

• Guerino Mazzola
• U ETH Zürich
• Internet Institute for Music Science
• guerino_at_mazzola.ch
• www.encyclospace.org

2
The Topos of Music Geometric Logic of Concepts,
Theory, and Performance
in collaboration with Carlos Agon, Moreno
Andreatta, Gérard Assayag, Jan Beran, Chantal
Buteau, Roberto Ferretti, Anja Fleischer, Harald
Fripertinger, Jörg Garbers, Stefan Göller,
Werner Hemmert, Michael Leyton, Mariana Montiel,
Stefan Müller, Thomas Noll, Joachim Stange-Elbe,
Oliver Zahorka
www.encyclospace.org
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Fields
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x v(X)
X
Fields
T(E) (dvE/dE)-1 q /sec
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Product fields Tempo-Intonation field
P-Cells
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Parallel fields Articulation field
P-Cells
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• Work with
• Basis parameters E, H, L,
• and corresponding fields T(E), S(H), I(L)
• Pianola parameters D, G, C
• A cell hierarchy is a Diagram D in Cell such
  that
• there is exactly one root cell
• the diagram cell parameter sets are
  closed under union and non-empty intersection

P-Cells
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l
Typology
Stemma
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Big Problem Describe typology of shaping
operators!
????
??!!
Emotions, Gestures, Analyses
Typology
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RUBATO software Calculations via
Runge-Kutta-Fehlberg methods for numerical ODE
solutions
Calculations
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Tempo Operators
Typology
Deformation of the articulation field hierarchy
Zw Qw(E,D).Z
Qw J(vw)-1 w-tempo
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RUBATO Scalar operator
Typology
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Restriction
Inverse Theory
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Stefan Müller EspressoRubette
Inverse Theory
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Inverse Theory
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Inverse Theory
Roberto Ferretti
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Inverse Theory