[PD] tabread4~~

[Charles Henry]

On Nov 19, 2007 11:06 PM, Mathieu Bouchard <matju at artengine.ca> wrote:
> On Fri, 16 Nov 2007, Charles Henry wrote:
> I don't mean frequencies of sine waves, I mean frequency of any kind of
> periodicity that is found.

Yes, I was sure you knew what you were talking about.  I just had to
jump on it, and add some parts that I felt you could have included.
Also, you got some good info here:

> Notes of many instruments have a percussive/click sound in the attack,
> which tend to have a wider spectrum than the main part of the note, so
> there could be a 4 Hz component anyway, but this is not what I mean
> anyway. What I mean could include the fact that the comb effect is at 4
> Hz, but it's more abstract than that: playing any melody, you can simply
> count the time between attacks or between changes of note, and see it as a
> set of periodic patterns. It could get as far as taking any interval and
> turning it into the corresponding frequency, even though there may be a
> complete absence of actual periodicity.

> On FidoNet in the mid-nineties, I was getting acquainted with the theory
> that rational intervals between notes (e.g. 5/4, 3/2) could correspond
> to rhythmic patterns as far as they could be expressed with a similar
> notation: thus you can see a major chord as being similar to a pattern
> involving a superposition of 4/4, 4/5 and 4/6 beats. Needless to say that
> in "normal" music, "normal" chords don't match the ratios of "normal"
> beats, except in extremely simple cases such as "power chords".

Yes, but there is evidence for the fundamental bass that occurs
between pairs of notes, with a strength dependent on those ratios.
Complex harmonies could have multiple fundamentals.  It's a mystery to
me how harmony/rhythm work at a fundamental level.  I'm planning to
apply for grad school at FAU this month.  My plans are not sure now,
but I will eventually work on this.

> I don't have the impression that we need topology in order to access all
> that we need to do what we have to do. So far, I think that the interest
> of using topology in music is just so that we have topology and music
> together... just an alternate way of expressing the already expressible.
> (Please convince me that some things in music are easier to think about
> using topology...)

The topology bullshit was plainly bullshit.  But I was trying to
stretch what I know, and try to see a way for song-structure and
rhythm to take on more than one dimension.  I have started working on
a patch lately to simulate the trajectory of a particle as it flies
across the surface of a torus (it's remarkable simple, so far--a
couple of phasors and boom, there it is).  Next thing is to add
functions that will map the particle's trajectory onto sounds (the
tough part).

> > Some current rhythm perception research focuses on dynamical systems,
> > which can have those long-range correlation properties.  (again the
> > action of perception is still a function of 1-D time)  The dynamical
> > system can have a non-integer dimension (a fractal), so you might be on
> > to something to speculate additional dimensions in sound.
>
> The Hausdorff dimension of a set that is a subset of some space can't be
> bigger than that of that space. If anything, you get above the 1-D of the
> time dimension, but never above the number of dimensions of the space that
> the trajectory lives in. Even then, you are approximating a phenomenon
> using a fractal, which does not mean that the phenomenon is fractal any
> more than real numbers are real and that infinity is infinite: there's a
> lot of theoretical gimmickry there. Many phenomena look fractal only
> within a precise range of orders of magnitude.

That's just the thing I was getting at.  We have music as a function
from 1-D into the space of all possible sounds.  Assuming the space of
sounds is band-limited and compact in time, it is actually a finite
dimension (a gigantically huge finite dimension).  But then, there's
the psychological space, which has drastically fewer dimensions, and
they're not linear.

I conjecture that timbre perception may be better explained through
topology.  A common figure in analyzing instrumental timbre is a
multi-dimensional scaling technique.  Similarity between timbres is
visualized in a linear space with a metric, corresponding to the
straight-line distance.  If it were possible for timbre space to be a
non-linear manifold, similarities would correspond to distances along
a path in the presumably curved space.  I feel absolutely certain that
I can convince you that timbre is *not* a vector space, using only the
defining properties of a vector space.
However, getting from A to B, and showing this is true would take an
exquisitely designed experiment, a real work of art :P

Chuck