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 remove discontinuities.
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