COURSE OUTLINE

FORMALIZED MUSIC

(timings are tentative)

Fall 2007

Introduction - about proportions, about time

August 23

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.

Algebra

September 4, 6, and 11

Sets, Venn diagrams; operations with sets as basic thought processes. Cartesian product.
Musical applications: sets of values at various parameters; modal theory, modulation, and formal analysis.
Xenakis - Herma
Mappings.
Musical applications: serial music, counterpoint, heterophony, leit motives, quotations, and parody.

September 13, 18, and 20

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.

Quiz

Operations. Isomorphisms, permutations, transpositions, and their possible musical meaning

September 25 and 27

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.

October 2

The 3 "algebras" of Xenakis. Metabole: group transformations as a substitute for modulations.
Nomos alpha an analysis.

Assignment

A Little Physics

October 4, 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.

October 11

Quantum Theory, Feynman diagrams, the uncertainty principle, Schrodinger's cat, and the "Many Worlds Interpretation".
Musical applications: Many Worlds.

October 16

Time asymmetry; negative time vectors ? Entropy and the arrow of time. Prigogine's Being and Becoming
Example: Cuniculi.

Controlled Indeterminacy

October 18, 23

Basis of probability. Probability axioms, conditional probability, Bayes' Theorem. Random variables, standard deviation, probability distributions.
Example: stochastic music - sound mass: Pithoprakta.

October 25, 30

Markov chains.
Analysis of a simple Mozart theme. Granular theory and micro-composition.

Quiz

Information Theory and Other Approaches

November 1

Music as a communication process. Information, redundancy, originality; Birkhoff's formula.
Musical applications: Translation as an example.

November 6

Fractals, brownian motion and tree structures in more recent Xenakis music.

November 8

Strategic games and improvisation.
Example: Linaia Agon.

November 13, 15

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).

Assignment

Thanksgiving Recess

A Unifying Approach - Aesthetics and Philosophy

November 27, and 29

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 6

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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