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What is Music Formalization ?

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:

"Art" music. Examples:

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

     			       (algebra, numbers)
    			        [abstract, order]
           WORLD						       APPLICATIONS
    (Physics, Acoustics)					          (Music)
         [Reality]				 	       [parallel, artistic reality]

    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.

    Basis for and justification of formalization:

    Another view (Zen): 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:

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

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