Get acquainted, organizational matters: how will the course be
run, grading, assignment, quizzes, final paper. Web access, etc.
Office hours. Other courses of interest:
- Music 448, Introduction to Computer Music
- Music 499 E, Advanced Computer Music
- Music 199T, Music, Science, and Technology (for your
What is Music Formalization ?
The term was introduced by Xenakis. His definition of music:
- to establish a procedure
- to put in a procedure
- to establish formal rules of thought
(& make sure they are correct... Logic: from known things we
derive new ones)
to make music means to express human intelligence by
His claim at transcending Geography and History.
What do we formalize ? What do we call music ?
- speculate; deliver a world view (a philosophy).
- (part of a) ritual
- systematic use of knowledge or skill
- use of skill & imagination in the production of things of
- Pythagoras (600 BC) and the music of spheres; numerical
- Anicius Manlius Severinus Boetius (480-524)(neo-Platonic/St. Augustine
& Aristotelian reconciliation)
- music is number made audible; the simple the ratio (number),
the more beautiful the sound. Music derives its beauty
from the pure world of numbers
- all things beautiful are subject to the power of number
- music:microcosmos can duplicate on a small scale the power
of numbers inherent in the otherwise almost incomprehensible
- 13th century Byzantium: a mirror of the higher worlds reflecting
- Medieval music and the contrast between
"human" and "divine" passing of time. The School of Notre-Dame metaphor.
- Rameau and his Treaty on Harmony (1728-30): his
explanations were based on acoustics.
- Schopenhauer: music expresses the Will - hence first among arts.
- the use of the golden mean: Bartok, Debussy; also Mozart and Beethoven.
- Joseph Schillinger (1941)
- Structuralism in the second half of the 20th century - logical,
- Xenakis, Hiller, Barbaud, and others.
Aesthetic trends and how are they reflected in the choice of musical tools
by composers. Baroque and classical periods.
Tonal system as a hierarchy.
Relationship between music, science, philosophical and social attitudes.
Monteverdi and Galileo as contemporaries;
Bach, Haendel, Newton, and the Enlightment;
John Cage, indeterminism and quantum mechanics
A parallel reality
(Physics, Acoustics) (Music)
[Reality] [parallel, artistic reality]
Xenakis: algebra = the queen of knowledge
Numbers: abstract realm, abstract thinking
Music: an application
Music could describe the world and our place in it (see Schopenhauer); it
has a specific language, different from science, and describes a "parallel"
Next question is: is there order in the universe ? People like
Feynman and Hawkins asnwer: yes.
Basis for and justification of formalization:
Another view (Zen):
- we, humans, discriminate => we recognize forms and patterns
- logic insures the operations we perform on these patterns are
- we look for and connect patterns (forms, structures, etc.) in an
organized way - as opposed to random, accidental ways.
- a formalism helps us get rid of unwanted conditionings of which we
are not aware most of the time.
Is it possible to use concepts and logic to transcent rational thinking
- form/discrimination belong to the human realm
- a higher understanding goes beyond discrimination, concepts, logic
Stochastics (chance, randomness) as a means to avoid conditionings.
Sound parameters. After WWII some composers attempted
to control in their compositions all sound parameters. The most obvious
sound qualities or parameters are:
Duration Time interval
Dynamics (loudness) Amplitude
The first column above includes terms used by musicians; the second,
their correspondent description in acoustics. Although widely
accepted, this chart is not without flaw since it represents a
rather crude description of the qualities of a sound as it was
proposed in late 19th century by Helmholtz.
It is interesting to observe that, in the Western musical culture,
pitch and rhythm were practically the only ingredients in the music
written before the 16-17th centuries. The Baroque period introduced
dynamics as an important element of music while only in the 19th
century composers started paying serious attention to timbre
(orchestration). A strong interest in composing the
way articulations are applied is very recent. Historically, the
list of parameters has increased from 2 to at least 5 in the
Structuralism. A general tendency in Western thinking
which flourished in the 40s, 50s, and 60s. More of a way of thinking
than anything else. Promotes a rational, logical and analytical
attitude in fields as various as: arts, medicine, anthropology,
mathematics, linguistics, psychology, etc. Ferinand de Saussure's
treatise on Linguistics, published in 1929 is sometimes
considered the trigger of this movement. According to Piaget who
performed ground breaking research in child psychology, a structure
has the following attributes:
Integral Serialist thinking is typical for this analytical, systematic
way of thinking. So is Xenakis's formalization.
- it is more than the sum of its parts
- when new elements are produced, they also belong to the structure
- a self-regulating, feedback type of mechanism prevents the
destruction of the structure.
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