On Nov 19, 2007 11:06 PM, Mathieu Bouchard <[EMAIL PROTECTED]> 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 _______________________________________________ PD-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list