On Nov 17, 2007 3:16 AM, Charles Henry <<a href="mailto:czhenry@gmail.com">czhenry@gmail.com</a>> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
We structure events in<br>music as a function of time.<br>f: R (time) -> (set of possible sound events)<br>The topology in this case is clear. It's a line, and music is a<br>function mapping 1-D into the space of all possible sounds.
<br><br>we can only have the paths as functions of<br>time. So, no matter how complicated the song structure gets, you can<br>flatten it into a single function. Any thoughts?</blockquote><div><br># Here is my conceptualization of sound as a 1-D function.
<br># Musical data is one-dimensional if it is recorded on a medium or is transmitted through some fluids. It is an array of number in digital media, changing voltage through cables and changing excess pressure of air when transmitting through air. All of these are simple functions of time.
<br># 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.
<br># What we hear is the projection of all these data (different instruments, song structure etc.) onto 1 dimension. (This parts can be called "bases of the space of all possible sounds" as mathematical metaphor in linear algebra.) This projection is done by mixing different tracks or listening to an ensemble, so by simply taking the superposition of different audio signals. And our perception system has full of analysers which guess/try to understand/estimate/visualize etc. the original data from this reduced 1 dimensional data, namely sound.
<br># If find it very interesing that we receive a one dimensional sound signal and perceive which instruments are there, who is talking, where the foot steps coming from, water in the pod is boiling etc... We extract the projected/compressed information as much as we can.
<br>-uğur güney-<br></div></div>