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.
_ _ __ ___ _____ ________ _____________ _____________________ ...
| Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada
_______________________________________________
[email protected] mailing list
UNSUBSCRIBE and account-management ->
http://lists.puredata.info/listinfo/pd-list
