matju at artengine.ca
Fri Nov 23 06:15:48 CET 2007
On Sat, 17 Nov 2007, Uur Güney wrote:
> But the musical data of composition (in the mind of the composer), or
> the sound producing mechanisms are not one dimensional. The composer
> builds its ideas not on one dimensional space but she has structures
> which may have certain hiyerarchies or orderings. For example, if there
> is harmony, there are more than one voice. Two voice works are two
> dimensional vector functions of one variable (time) (if we are at the
> abstraction layer of notes)
> An example of sound producing mechanism is
> plucked and vibrating string (or vibrating membrane) It is a continuum
> and so has infinite dimensions.
It's not because it's a continuum, that it has infinite dimensions. Real
numbers form a continuum, but have only 1 dimension.
The set of all possible continuous functions over a given finite interval,
forms a continuum that has infinitely (countably) many dimensions. This
continuum also happens to include some simple (Fourier-compatible)
discontinuities as well. (Including all possible discontinuities is
another story.) Physical sounds can be understood to have no
discontinuities, as several factors tend to "low-pass" the sound enough to
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