[Fis] What is music

Dear Colleagues,

I would like to present some general views on the musical topic. From the
informational point of view, music can be considered as some kind of a
knowledge. But this knowledge is not a �positivistic� kind of relation
between actual finite objects. It is a knowledge about the totality of the
word. Music can be viewed as a reflection from the infinity (potential
field) into the finite set of sounds. But in contrast to other arts, music
is prolonged and organised in time. And that is its advantage.

As a reflection of the total and universal of the world, music cannot be
one-dimensional. It is polysemantic, combining different structures
(languages) in one temporal continuum. These different structures are
present and organised in the musical composition, and this reflects complex
relation between the potential and the actual. The potential and the actual
may be in harmony or the harmony can be broken, but infinity of creative
process means that this breakage can be viewed as a higher level of harmony
with breaking of the simple rules. This resembles symmetry-breaking
phenomena and creation of Goedel numbers in arithmetical calculus. In
connection with this I would recommend to have a look at works of M.
Arcadyev. He develops ideas that music can be viewed as a structurised
silence, and that silent accents in music play even more important roles
than sounds. The concise presentation of these ideas (with concrete examples
of polylanguage structures) are at

http://www.philosophy.ru/library/arcad/time.html

The potential field is always a contradictory set of possible realisations.
It is silent. This set is realised as a process of appearance of sounds that
is organised in time. The most striking example of quasi-rationality of such
a process is a polyphonic music like fugue, such examples as the Art of
Fugue of I.S. Bach where the musical composition becomes closer to
mathematics. But this process cannot be counted, it is creative, being a
kind of construction of reflective loops as in creation of new structures of
calculus not present in the previous structures. Mathematics and music are
the similar arts in the Pythagorean school. Music can be more rational in
some pieces of baroque and more irrational as in romanticism. It may be
more rational in form, but as a reflection of infinity it cannot be
countable rationally. Great examples of this are the final (and actually all
movements) of Beethoven�s Op. 106 and his Grosse Fuge. Mathematics deals
with processes that are limits of iteration of infinite processes. But
because of the paradoxical properties of time (described e.g. in the
Achilles and tortoise), these limits can be realised in finite durations of
time. Without these paradoxes music may not exist.

Some words about the limits of iteration in music and universal
combinatorial principles. V. Lefebvre suggested that the golden section is
important in the European musical tradition. The golden ratio can be
considered as a limit of iteration in reflective measurements (see my paper
in FIS2002). I Ching book and the genetic code have in common that they are
combinations of reflective triads. Realisations of these combinations are
universal and they really contain different languages at the same time. Some
thoughts on this topic are in my paper at

http://home.cc.umanitoba.ca/~igamberd/files/semiosis.html

The styles in music can be viewed as different projections from the infinite
fields. Finally, I would remind the words of Gustav Mahler: to compose a
symphony is to construct a world by means of existing musical technique.
Constructing a world is to realise by finite means a Ding an sich or total
reality. Music is a powerful mean to do this.

Best regards,
Andrei Igamberdiev

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Received on Wed May 21 17:45:16 2003