[PD] tabread4~~

[Mathieu Bouchard]

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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| Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada