[Fis] What is Music

Dear FIS colleagues,

Pedro in his recent letter asks
"What is Music". In my paper titled
"Musical Works are Maximal Memory Stores",
I give the answer developed in that title.
I argue that the organization of music
is determined by the need to make musical
works, maximal memory stores.

Below I give an abstract of the paper,
that explains this:

best,
Michael

Musical Works are Maximal Memory Stores

 Michael Leyton,

Center for Discrete Mathematics

& Theoretical Computer Science (DIMACS)

Rutgers University, USA.

The book A Generative Theory of Shape (Michael Leyton, Springer-Verlag,
2001) develops new foundations to geometry in which shape is equivalent to
memory storage. With respect to this, the argument is given that art-works
are maximal memory stores. The present paper reviews some of the basic
principles concerning our claim that, in particular, musical works are
maximal memory stores. The argument is that maximizing memory storage
explains the structure of musical works. We first review the basic
geometric theory of the book: A generative theory of shape is developed
that has two properties regarded as fundamental to intelligence -
maximization of transfer and maximization of recoverability. Aesthetic
structuration is taken to be equivalent to intelligence. Thus aesthetics is
brought into the very foundations of the new theory of geometry. A
mathematical theory of transfer and recoverability is developed, using a
structure we define, called symmetry-breaking wreath products. From this,
it becomes possible to develop a theory of musical composition, as follows:
Musical works are complex shapes. A theory of complex-shape generation is
presented, in which any structure is described as unfolded from a maximally
collapsed version of that structure, called an alignment kernel. This
process is formalized by proposing a new class of groups called unfolding
groups. The alignment kernel is a subgroup of that structure, consisting of
symmetry ground-states which are themselves formalized by a new class of
groups called iso-regular groups. In music, the iso-regular groups
represent the anticipation hierarchies, for example the regular meters of
the work. The process of musical composition is then described by an
unfolding group, which "unfolds" the work, by successively breaking the
iso-regular groups of the alignment kernel.

Full paper:

http://fis.iguw.tuwien.ac.at/resources/papers/Leyton_Music_Paper.pdf

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Received on Wed May 21 16:17:21 2003