(timings are tentative)
Introduction - about proportions, about time
What is music Formalization ? Music and logic/mathematics: a brief history
of formalized music.
Integral Serialism and sound parameters. Stockhausen's ...how time
passes... Complex waves; an "object-oriented" outlook.
Aesthetics: Pythagoras, Boetius; Schopenhauer's views on music.
Permanence and style; world views.
September 4, 9, and 11
Sets, Venn diagrams; operations with sets as basic thought processes.
Musical applications: sets of values at various parameters;
modal theory, modulation, and formal analysis.
Xenakis - Herma
Musical applications: serial music, counterpoint, heterophony, leit
motives, quotations, and parody.
September 16, 18, and 23
Relations, congruence relations modulo m, Peano's axiomatic, and their
relevance to music.
Sieves. Scales, modes with limited transpositions, rhythmic and amplitude
sieves; weighted sieves.
Operations. Isomorphisms, permutations, transpositions, and their possible
September 25 and 30
Higher structures: groups and rings. The vector space as a framework
for describing music - advantages and criticism of a point of view. Absolute
values and interval vectors.
Examples concerning various sound parameters.
The 3 "algebras" of Xenakis. Metabole: group transformations
as a substitute for modulations.
Nomos alpha an analysis.
A Little Physics
October 7, and 9
Minkowski's metric and the Lorenz transformations; relativity and the
concept of simultaneity. Bergson on time and duration.
Example: The observer's point in Maiden Voyages.
Quantum Theory, Feynman diagrams, the uncertainty principle,
Schrodinger's cat, and the "Many Worlds Interpretation".
Musical applications: Many Worlds.
Time asymmetry; negative time vectors ? Entropy and the arrow of time.
Prigogine's Being and Becoming
October 21, 23
Basis of probability. Probability axioms, conditional probability,
Bayes' Theorem. Random variables, standard deviation, probability
Example: stochastic music - sound mass: Pithoprakta.
October 28, 30
Analysis of a simple Mozart theme. Granular theory
Information Theory and Other Approaches
Music as a communication process. Information, redundancy, originality;
Musical applications: Translation as an example.
Fractals, brownian motion and tree structures in more recent Xenakis
Strategic games and improvisation.
Example: Linaia Agon.
November 13, 18
Morphogenetic music: Catastrophe Theory and the Thermodynamic
approach. Complex dynamic systems (Chaos theory). Generative
grammars - is music (only) a language ? Cellular automata and
genetic algorithms. Artificial Intelligence (AI).
A Unifying Approach - Aesthetics and Philosophy
November 20, and December 2
Manifold compositions. Open works and classes of compositions.
Example: A.N.L.-folds, Daria, decaf
Time scales and granularity; "windows" and object-oriented composition.
December 4 and 9
An all-encompassing theory of music. The Holly Grail: composition and
sound synthesis as a unified process.
Aesthetics. World view: determinism and chance. The relationship
between music, mathematics, and sciences (physics). What can music offer ?
Schopenhauer and Bergson revisited.
Music/art as a "parallel" reality. Computer-assisted composition,
thought experiments, and computational science.
Composer's new role.
Wednesday, December 12, 1:30 - 4:30 am
Final Project presentations
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