Introduction

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 younger friends...)

What is Music Formalization ?

to establish a procedure
to put in a procedure
to establish formal rules of thought

The term was introduced by Xenakis. His definition of music:

to make music means to express human intelligence by sonic means

His claim at transcending Geography and History.

What do we formalize ? What do we call music ? Music can:

entertain.
experiment.
speculate; deliver a world view (a philosophy).
(part of a) ritual

"Art" music.

skill
systematic use of knowledge or skill
use of skill & imagination in the production of things of beauty

Examples:

Pythagoras (600 BC) and the music of spheres; numerical relationships.
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 through angels
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, analytical approach.
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.

A parallel reality

				   MATHEMATICS
 			       (algebra, numbers)
			        [abstract, order]



       WORLD						       APPLICATIONS
(Physics, Acoustics)					          (Music)
     [Reality]				 	       [parallel, artistic reality]

Xenakis: algebra = the queen of knowledge

Music could describe the world and our place in it (see Schopenhauer); it has a specific language, different from science, and describes a "parallel" reality.

is there order in the universe ?

Basis for and justification of formalization:

we, humans, discriminate => we recognize forms and patterns
logic insures the operations we perform on these patterns are consistent ("correct")
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.

Another view (Zen):

form/discrimination belong to the human realm
a higher understanding goes beyond discrimination, concepts, logic

Is it possible to use concepts and logic to transcent rational thinking itself ?
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
        Pitch                   Frequency
        Dynamics (loudness)     Amplitude
        Timbre                  Waveform
        Articulations           Envelope

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 last millenium.

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:

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.

Integral Serialist thinking is typical for this analytical, systematic way of thinking. So is Xenakis's formalization.