On Tue, 13 Nov 2007, IOhannes m zmoelnig wrote:

no problem at all. [line~~] and [vline~~] will all come when the time is ripe. and probably they will move from zexy into iem~~ :-)

[line~~] will come when the time becomes two-dimensional.

Even in a Many-Worlds Interpretation of (meta)physics, you can't find a plane embedded in the structure of time: time is shaped like a tree.

_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada

On Wed, 14 Nov 2007, Charles Henry wrote:

Zen master Dogen tells us that we say time is passing because we live in time. In fact, we are passing in time, and time stays exactly where it is.

time seen as the 4th space dimension is also a result of Einstein-Minkowski theory. It wasn't the only step in that direction, not the first step, but it was a major shift. There's a version of Pythagoras' theorem for that space-time, in which the only difference between space and time is that they have a different sign. Thus time is a kind of space with a scale factor equal to square root of -1. (You may also get to this scale factor by fiddling with the wave equation.)

Whether time "moves" or "stays exactly where it is" is a metaphysical question: you can't make an experiment that distinguishes the two possibilities. Thus it's just a matter of how we explain things to ourselves.

Maybe we can find 2-D time through transcendance. hmmm an external for that?

I think that there is hope in reversing the roles of time and space in equations, such that you have 1-D space and 3-D time. I don't think that we'd be able to get to exactly 2-D time. Thus I believe that there is more hope in [line~~~] than in [line~~].

_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada

~~

What does appending a tilde mean? From the first post i thought is was just slang for 'this is really
a tilde object that does it's thing right' as in underlining. After
that the thread took a direction into discussion about time and space/ dimensions.

Btw. Late (as in not younger) Wittgenstein says: "Forget about this,
Patrick, and do some patching".

On Thu, 15 Nov 2007, Steffen Juul wrote:

...

~~

What does appending a tilde mean? From the first post i thought is was just slang for 'this is really a tilde object that does it's thing right' as in underlining. After that the thread took a direction into discussion about time and space/ dimensions.

The space-time thread was a joke of mine because of the way float-objects and signal-objects relate to each other. It was a thought experiment on what would be the most legitimate use of a second tilde in a way that is most like adding the first tilde in the first place. I tried to be as theoretically right as I could while knowing that in practice it's nonsense. I am not being a pure mathematician here, because pure mathematicians don't see the problem with having multiple time dimensions. (they wouldn't even mind working with infinitely many time dimensions and making a theory about it)

Anyway: I don't quite approve of the use of a double-tilde, which was my reason for the joke in the first place.

_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada

Hello again,

here's the -help file, as i promised.

(My apologies to Miller Puckette for stealing the -help files style.. :-))

#N canvas 354 145 966 694 12; #X obj 12 615 output~; #X obj 12 432 phasor~ 1; #X obj 12 357 vradio 30 1 0 2 tabread4~~test tabread4~~test empty 0 -8 0 10 -262144 -1 -1 0; #X text 51 362 <-- tabread4~; #X text 51 392 <-- tabread4~~; #X obj 12 13 tabread4~~; #X text 30 60 The tabread4~~ object takes two audio signals to specify the read position in an array \ which makes it way more precise in longer arrays than the simple tabread4~.; #X text 30 117 BEWARE!!!; #N canvas 466 186 745 640 crossfader 0; #X obj 12 424 +~; #X obj 154 403 *~; #X obj 12 398 *~; #X obj 297 382 line~; #X obj 57 377 line~; #X obj 57 324 == 0; #X obj 12 477 outlet~; #X obj 12 21 inlet~; #X obj 154 21 inlet~; #X obj 297 281 r tabread4~~test; #X msg 57 351 $1 50; #X msg 297 356 $1 50; #X obj 257 99 metro 500; #X obj 257 155 tabwrite~ tabread4~_tab; #X obj 258 190 tabwrite~ tabread4~~_tab; #X obj 257 41 loadbang; #X obj 257 71 1; #X connect 0 0 6 0; #X connect 1 0 0 1; #X connect 2 0 0 0; #X connect 3 0 1 1; #X connect 4 0 2 1; #X connect 5 0 10 0; #X connect 7 0 2 0; #X connect 7 0 13 0; #X connect 8 0 1 0; #X connect 8 0 14 0; #X connect 9 0 5 0; #X connect 9 0 11 0; #X connect 10 0 4 0; #X connect 11 0 3 0; #X connect 12 0 13 0; #X connect 12 0 14 0; #X connect 15 0 16 0; #X connect 16 0 12 0; #X restore 12 581 pd crossfader; #X obj 12 456 *~ 44100; #X obj 12 500 +~; #X obj 12 524 +~ 1; #X obj 273 479 sig~; #X obj 273 454 * 44100; #X floatatom 273 432 4 0 1799 0 - - -; #X text 114 13 high precision array lookup; #X obj 161 548 tabread4~~ testone; #X obj 12 548 tabread4~ testone; #N canvas 0 0 450 300 (subpatch) 0; #X array tabread4~_tab 512 float 0; #X coords 0 1 511 -1 400 280 1; #X restore 540 78 graph; #N canvas 0 0 450 300 (subpatch) 0; #X array tabread4~~_tab 512 float 0; #X coords 0 1 511 -1 400 280 1; #X restore 540 390 graph; #X msg 273 406 0; #X msg 273 366 381; #X msg 273 386 1522; #X text 30 131 You can't use this help file as it is unless there is at least 350-400 MB of RAM available to your system.; #X text 29 169 To initialize do the following:; #X text 30 191 1) Create a sine audio file (80-100 Hz , 32bit mono , 1800 sec) somewhere on your HDD (needs about 300 MB).; #X obj 401 228 bng 20 250 50 0 empty empty empty 17 7 0 10 -262144 -1 -1; #X text 30 226 2) Click here to locate and load the file -->; #X text 74 288 Now play with the following...; #N canvas 579 489 386 207 load 0; #X obj -66 121 soundfiler; #X floatatom -66 159 0 0 0 0 - - -; #X obj 149 16 table testone; #X obj -66 19 inlet; #X obj -66 67 openpanel; #X msg -66 94 read -resize -maxsize 8e+007 $1 testone; #X connect 0 0 1 0; #X connect 3 0 4 0; #X connect 4 0 5 0; #X connect 5 0 0 0; #X restore 401 253 pd load; #X text 270 338 jump to different positions..; #X text 11 333 listen to..; #X obj 273 524 +~ 1; #X text 321 431 <-- current position (sec); #X connect 1 0 9 0; #X connect 8 0 0 0; #X connect 8 0 0 1; #X connect 9 0 10 0; #X connect 9 0 16 0; #X connect 10 0 11 0; #X connect 11 0 17 0; #X connect 12 0 10 1; #X connect 12 0 32 0; #X connect 13 0 12 0; #X connect 14 0 13 0; #X connect 16 0 8 1; #X connect 17 0 8 0; #X connect 20 0 14 0; #X connect 21 0 14 0; #X connect 22 0 14 0; #X connect 26 0 29 0; #X connect 32 0 16 1;

p.s. 1: [tabread4~~] lies in the latest zexy lib.

p.s. 2: I tried to find a way to create a 30min sine array "on the fly" but I ran into the same "32bit resolution" problem (array index specification)... Sorry....

p.s. 3: Music is for me the way to control time and matter, even if it's only in my imagination. But isn't imagination (or the observers location and speed..) the only thing that matters?

On Thu, 15 Nov 2007, Ypatios Grigoriadis wrote:

If i may now borrow the theory and terminus Arrow of time by Arthur Eddington, according to which time is the fourth dimension in space,

Afaik, Arthur Eddington made the first English translation of Einstein. This is probably what got him in that 4th dimension thing, or perhaps it was the other way around (that he had thought of a 4th dimension concept and sought in Einstein's work a confirmation of it). I don't really know.

Anyway: in some way, the past is equally hard to "postdict" as the future is hard to predict, but it depends on what one looks for. We are used to think of the past using what remains from it, but almost every event of the past is virtually unreachable due to having been blurred beyond repair. For any set of things you observe, everything else is left unobserved. The attention span of observers is tiny compared to what could become relevant to the observers later.

(One could wonder: Exactly how straight is this axis? Could it bend and go back? Of course! In music this is called a "reprise".)

"reprise", "beat" and such, are just larger scale splittings of the time dimension in the same way that frequency separates from time. Reprises and beats and rhythms are full of periodic patterns, just like the sound waves themselves, but at a different scale, which doesn't make the physical ear resonate anymore, but appeal to the brain's taste for sequencing. Thus a beat may have frequencies like 4 Hz and 2 Hz and 0.333 Hz in it (whatever is roughly in that range), whereas larger-scale song structures may have frequencies like 0.1 and 0.01 Hz. You could call rhythm and song structure a third dimension of music.

_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada

Patrice Colet a écrit :

Mathieu Bouchard a écrit :

...

On Thu, 15 Nov 2007, Ypatios Grigoriadis wrote:

...

If i may now borrow the theory and terminus Arrow of time by Arthur Eddington, according to which time is the fourth dimension in space,

Afaik, Arthur Eddington made the first English translation of Einstein. This is probably what got him in that 4th dimension thing, or perhaps it was the other way around (that he had thought of a 4th dimension concept and sought in Einstein's work a confirmation of it). I don't really know.

Anyway: in some way, the past is equally hard to "postdict" as the future is hard to predict, but it depends on what one looks for. We are used to think of the past using what remains from it, but almost every event of the past is virtually unreachable due to having been blurred beyond repair. For any set of things you observe, everything else is left unobserved. The attention span of observers is tiny compared to what could become relevant to the observers later.

I'm very happy to read anything else than space-time gibbering, thanks.

gibbering = drivel, sorry for bad translation.

On Nov 17, 2007 3:16 AM, Charles Henry czhenry@gmail.com wrote:

We structure events in music as a function of time. f: R (time) -> (set of possible sound events) The topology in this case is clear. It's a line, and music is a function mapping 1-D into the space of all possible sounds.

we can only have the paths as functions of time. So, no matter how complicated the song structure gets, you can flatten it into a single function. Any thoughts?

# Here is my conceptualization of sound as a 1-D function. # 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. # 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. # 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. # 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. -uğur güney-

On Nov 23, 2007 7:15 AM, Mathieu Bouchard matju@artengine.ca wrote:

On Sat, 17 Nov 2007, Uur Güney wrote:

...

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.

# Ok. I got it. Thanks for clarification. # Once I asked to my Non-linear Dynamics teacher. "Isn't the shape of a string a 1D function of its length? Why we are calling it as continuum?" And she said that: "A simple harmonic oscillator makes a 1D motion (in time). It goes back and forth. You can approximate a string as N connected harmonic oscillator lying along a line. if N goes to infinity we'll have a SHO at every point in space, which makes a 1D motion in time. And this is a field, and hence it is a continuum." # This is in accordance with your definition, an ideal string can have any shape, so its possible shapes form "the set of all possible continous functions over its length".

On Fri, 16 Nov 2007, Charles Henry wrote:

You won't be able to find those low frequencies like 4 Hz, unless one of your instruments contains them, like drums for example.

I don't mean frequencies of sine waves, I mean frequency of any kind of periodicity that is found.

Percussion instruments can have those low frequencies. And the result of adding up the fourier contributions from periodic sequences has an effect like a comb filter on the spectrum of the orignal instrument, which makes the peaks. If you have an instrument in a higher frequency range, you probably won't find those low e.g. 4 Hz frequencies, but you could find them in the envelope following signal of the original.

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.

but that's just nitpicking..haha I find it interesting to consider how a song structure could have more than one dimension...

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".

But a loop is a path. So, we start from point A, we go to point B and come back. So, if we have a measure of 8/8, we can represent it as the path in the plane which follows e^(2*pi*i*t/8) or many other paths. Still we have a clearly defined topology (btw, I'm just learning topology, so I'm feeling my way through this).

A function maps points in time onto the loop. Again we have just one dimension. We can extend our loop into a sphere. or a torus or any other surface in more than two dimensions with holes in it.

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...)

but still it breaks down... we can only have the paths as functions of time. So, no matter how complicated the song structure gets, you can flatten it into a single function. Any thoughts?

And yet, to express this function, you'll probably want to break it down into several functions, for modularity. The advantage of putting everything in one big function is somewhat overrated. Already, any abstraction mechanism in math is a way to modularise and outsource meaning so that it doesn't have to be specified in the main function(s) themselves.

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.

_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada

On Tue, 20 Nov 2007, Charles Henry wrote:

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.

Well, so far, most of the time you see "fundamental", there's only one at a time, for each block of music you want to figure out the fundamental of. But different fundamentals can be extracted for any given interval, and those intervals can be a window sliding through time, looking at any "dinote" (pair of notes), and there can be multiple windows of different sizes that account for different levels of human memory and of musical understanding... (?) I think that we could analyse music using whole networks of fundamentals...

and also, a theory of musical understanding should be resistant to "detuning", because many forms of detuning are used in music and yet humans can automatically figure out what the fundamental is _intended_ to be (rather than what it is physically).

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.

There are many discrete or semi-discrete phenomena in construction of music, so using the Reals, an uncountable noncompact continuum, is pretty counterproductive. Instead of trying to use cartesian powers of the Reals in some form, try cartesian products of different algebraic structures that you will not use as (math) vectors.

I have started working on a patch lately to simulate the trajectory of a particle as it flies across the surface of a torus

Are you doing it in terms of a particular embedding with a particular curvature of the space, or do you use a modulo-Euclidean space in the style of PacMan ?

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).

Not necessarily... if you fit all sounds in one master period, yes, but if you are using a continuum of frequencies, you have a continuum of possible dimensions. The finite dimensions of the FFT (and of other discrete interval transforms) are because there is a master fundamental frequency (that is not zero).

But then, there's the psychological space, which has drastically fewer dimensions, and they're not linear.

Did you get into algebraic psychology yet?

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.

Ok, let's do that. How do you prove it?

However, getting from A to B, and showing this is true would take an exquisitely designed experiment, a real work of art :P

That's a detail :-P

Especially as I believe that timbre is a vector space. This is as long as we agree that timbre is a reduced form of the spectrum of a periodic sound, and not the more complicated things that happen with attacks, nor the whole range of an instrument.

_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada

On Nov 23, 2007 10:16 AM, Charles Henry czhenry@gmail.com wrote:

...

...

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.

Ok, let's do that. How do you prove it?

With another little thought experiment. If I can't convince you, I'll eat my words (yum)

When I look at that previous post, I realize that the notation/concepts were confusing at the least, and abusive at the worst. It's not an easy topic to work with. A more concrete example: we could take a trumpt and violin, two instruments with distinct timbres. We cannot mix them together as signals to produce a new, unified timbre. You would perceive them as a combination of two timbres, that cannot be condensed into a single instrument, because they are so distant from one another in timbre. However, we could deform one instrument to another. Suppose we had a good phase unwrap function, unwrap(G(f)) Example: z(t,a)=ifft(unwrap(X(f))^a*unwrap(Y(f))^(1-a)) Then, we have a way to deform one spectrum into the other. Anyhow, see what you think...

Chuck

On Fri, 23 Nov 2007, Charles Henry wrote:

First off, we need a loose definition of timbre--timbre is the quality by which two sounds may be distinguished, where pitch, loudness, and onset time are the same. (in terms of signals, we have just described a non-linear space in the first place { s(t) such that |s(t)|^2 = E }... but we're not just talking about signals, we mean the sound experience itself)

I think that you are right that it can't be all done within a linear framework: there needs some slight mangling of a linear space to do the work.

Oh, well, you could do most of the work using a linear space, and then at the last possible moment, divide the space by products by a positive real, so that there is one element per possible direction (or by any real, so that there is one element per possible axis). This could be called R[x]/R+ or R[x]/R respectively. Also, this could be called "spherical space" and "projective spherical space", respectively.

You could also suppose that the fundamental's amplitude is always 1, which is another way to give you exactly one element for all possible loudnesses of a sound that is otherwise the same. This is also better because then it ensures that it's a unique timbre, as you can't set all odd harmonics to 0 in such a situation (this would have allowed you to pretend a 440 Hz sound is also a 220 Hz sound and such). Also, sometimes affine spaces are easier to work with than quotient spaces even if you use those quotient spaces as little as possible.

A neato aspect of R[x]/R+ is that even though vector addition doesn't work on it, vector multiplication by matrix works quite well, and for example R^42/R+ can be acted upon by SO(42,R) and most any other matrix group... although SO(42,R) is the most tightly fitting matrix group in this case: SO matrices preserve the L2-norm of vectors, so what nicer thing can there be for a set of pseudo-vectors in which L2-norm has been made irrelevant?

As such, it cannot be silence. And if silence is not a timbre in our space, what is the additive identity? The additive identity of x(t) most closely resembles x(t) itself, since loudness is irrelevant.

If you are using the affine space, you can't simply add and you can't simply multiply by a scalar: instead, the fundamental operation is the convex sum of "vectors": as a single operation, you add together any number of vectors, weighted, where the total weight has to be 1, so that the amplitude of the fundamental sticks to 1.

OK, so how about linearity? If we take two timbres x(t) and y(t), then we can construct a timbre z(t,a)=ax(t)+(1-a)y(t) (0<=a<=1) which interpolates between x and y.

This is a special case of the "convexity" requirement.

And let's take a particularly bad example. We'll take x(t) to be a harmonic series. Then, we'll let y(t) be the same harmonic series, with a single mis-tuned partial, while keeping pitch constant. Then z(t) becomes dissonant moving between x(t) and y(t), even though dissonance was not significant in x(t) or y(t).

I don't quite understand how this works. Can you make a version of this example with actual figures?

Can we move the central moment of spectral density all the way to infinity while keeping pitch constant?

What do you mean "to infinity" ?

Anyway, it depends on how "perceptual" you are trying to be, supposing that we don't argue on the meaning of "to infinity".

If the space of timbres is bounded, then it cannot be a vector space (because it fails to be closed under scalar multiplication).

You mean bounded how? bounded in amplitude or in frequency? if it's bounded in frequencies, it's still linear. but you sound like you mean it'd be bounded in amplitude, which wouldn't be as much linear, but the spherical space above would make this issue moot anyway.

_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada

The problem with my examples, which I thought were bad was that sometimes, I was using x(t) and y(t) as if they were signals, which can be added and subtracted, and sometimes as vectors as functions of time in an abstract timbre space. Some of the presumed dimensions of timbre are things like consonance/dissonance, formant location, which seem to be consistent with the loose definition of timbre. I have to be more careful, so I don't bullshit myself out of existence or make some other bad argument :)

I think that you are right that it can't be all done within a linear framework: there needs some slight mangling of a linear space to do the work.

On the signals level, we could have a non-linear manifold in a Hilbert space. Sets of functions with constant total energy and identical pitch, for example. Then, psychoacoustics represents the map of this space into timbre space (a psychological space).

If we start with the assumtion that timbre space is a linear vector space, the psychoacoustical mapping function has to be pretty wild. On the other hand, we can map a sphere onto a plane with fixed boundaries (not a vector space), without any trouble.

Oh, well, you could do most of the work using a linear space, and then at the last possible moment, divide the space by products by a positive real, so that there is one element per possible direction (or by any real, so that there is one element per possible axis). This could be called R[x]/R+ or R[x]/R respectively. Also, this could be called "spherical space" and "projective spherical space", respectively.

You could also suppose that the fundamental's amplitude is always 1, which is another way to give you exactly one element for all possible loudnesses of a sound that is otherwise the same. This is also better because then it ensures that it's a unique timbre, as you can't set all odd harmonics to 0 in such a situation (this would have allowed you to pretend a 440 Hz sound is also a 220 Hz sound and such). Also, sometimes affine spaces are easier to work with than quotient spaces even if you use those quotient spaces as little as possible.

A neato aspect of R[x]/R+ is that even though vector addition doesn't work on it, vector multiplication by matrix works quite well, and for example R^42/R+ can be acted upon by SO(42,R) and most any other matrix group... although SO(42,R) is the most tightly fitting matrix group in this case: SO matrices preserve the L2-norm of vectors, so what nicer thing can there be for a set of pseudo-vectors in which L2-norm has been made irrelevant?

If you are using the affine space, you can't simply add and you can't simply multiply by a scalar: instead, the fundamental operation is the convex sum of "vectors": as a single operation, you add together any number of vectors, weighted, where the total weight has to be 1, so that the amplitude of the fundamental sticks to 1.

This makes good sense to me. The operators on this space are still a little fuzzy, though.

...

OK, so how about linearity? If we take two timbres x(t) and y(t), then we can construct a timbre z(t,a)=ax(t)+(1-a)y(t) (0<=a<=1) which interpolates between x and y.

This is a special case of the "convexity" requirement.

...

And let's take a particularly bad example. We'll take x(t) to be a harmonic series. Then, we'll let y(t) be the same harmonic series, with a single mis-tuned partial, while keeping pitch constant. Then z(t) becomes dissonant moving between x(t) and y(t), even though dissonance was not significant in x(t) or y(t).

I don't quite understand how this works. Can you make a version of this example with actual figures?

suppose f(t) is a complex tone with frequencies of 100, 200, 300, 400, 500 and g(t) has frequencies of 100, 200, 330, 400, 500

Then, when we mix the two tones together there is dissonance between the frequencies of 300 and 330, which wasn't present in either of the two tones.

...

Can we move the central moment of spectral density all the way to infinity while keeping pitch constant?

What do you mean "to infinity" ?

Anyway, it depends on how "perceptual" you are trying to be, supposing that we don't argue on the meaning of "to infinity".

One kind of dimension of timbre is the sharpness/dullness of a tone, based on the distribution of spectral energy among the components. By infinity, I mean, can we take a harmonic complex tone and change the amplitudes of the partials, to achieve any given sharpness/dullness of the tone? Essentially being able to increase the central moment of spectral denisty without bound.

...

If the space of timbres is bounded, then it cannot be a vector space (because it fails to be closed under scalar multiplication).

You mean bounded how? bounded in amplitude or in frequency? if it's bounded in frequencies, it's still linear. but you sound like you mean it'd be bounded in amplitude, which wouldn't be as much linear, but the spherical space above would make this issue moot anyway.

Bounded in terms of the dimensions of timbre. For example, dissonance. Can we have a tone which is maximally dissonant? Are there boundaries on the other dimensions of timbre?

I don't think I did a very good job of laying out my ideas. But this was a good discussion (for me) to examine them in detail and try to be specific enough.

Chuck

On Sun, 23 Dec 2007 13:50:04 -0500 (EST) Mathieu Bouchard matju@artengine.ca wrote:

Functions with constant total energy are a convex space. This is like a linear space except it changes one rule: in a vector space, if a,b are scalars and x,y are vectors, then ax+by is a vector. In a convex space, there's the additional restrictions that a+b=1 and a>=0 and b>=0,

Any easy pointers on different spaces for us old Euclidians Matju Cheers,

Andy

On Sun, Dec 23, 2007 at 10:54:51PM +0000, Andy Farnell wrote:

On Sun, 23 Dec 2007 13:50:04 -0500 (EST) Mathieu Bouchard matju@artengine.ca wrote:

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Functions with constant total energy are a convex space. This is like a linear space except it changes one rule: in a vector space, if a,b are scalars and x,y are vectors, then ax+by is a vector. In a convex space, there's the additional restrictions that a+b=1 and a>=0 and b>=0,

Any easy pointers on different spaces for us old Euclidians Matju

I am definately no expert in this area, but this guy and his ideas always fascinated me as an alternative to Euclidean geometry:

http://en.wikipedia.org/wiki/Riemann http://en.wikipedia.org/wiki/Riemannian_manifold http://en.wikipedia.org/wiki/Riemannian_geometry

Best,

Chris.

http://mccormick.cx

On Dec 23, 2007 12:50 PM, Mathieu Bouchard matju@artengine.ca wrote:

Functions with constant total energy are a convex space. This is like a linear space except it changes one rule: in a vector space, if a,b are scalars and x,y are vectors, then ax+by is a vector. In a convex space, there's the additional restrictions that a+b=1 and a>=0 and b>=0, so that you can only blend vectors together by various ponderations, without adding any gain. In 2-dimensional space, any base of a convex space generates a convex polygon (polyhedron if 3-dimensional space instead).

To split hairs, we want to constrain the total energy in mixing signals, which means we have to expand the inner product. This ensures that we have a solid homotopy, where we're not interpolating outside of our space (I stated this wrongly in the first place!). It also shows that any two signals in the space are connected by a continuous function, with no additional definitions.

so, |x|^2=|y|^2=1 and |a*x+b*y|^2=a^2*|x|^2+b^2*|y|^2+a*b*<x,y>=1 a^2*|x|^2+a*b*<x,y>+(b^2*|y|^2-1)=0 (quadratic formula to split things up)

a=-b*<x,y>/(2*|x|^2) +/- sqrt( (b*<x,y>)^2-4*|x|^2*(b^2*|y|^2-1))/(2*|x|^2) simplifies to a=-b*<x,y>/2 +/- sqrt( (b*<x,y>)^2-4*(b^2-1) )/2 and we want good numbers out of this, so we'll take an additional step to show that we have a smooth curve (no complex numbers in our mixing function) and we want a and b >=0

(is it the triangle inequality?--side note: why doesn't the triangle inequality get attributed to someone? ahhh here it is. The Triangle inequality is named for British mathematician Arthur Triangle (bullshit :P) 0 <= <x,y>^2 <= |x|*|y| :=1

we let b be in [0,1] and a(b) will be a function of b 0<=b<=b^2<=1 b^2*<x,y>^2-4*(b^2-1)=b^2*(2*<x,y>^2-4)+4 then, -4 <= 2*<x,y>^2-4 -4 <= -4*b^2 <= (2*<x,y>^2-4)*b^2 0 <= (2*<x,y>^2-4)*b^2 + 4 No complex numbers! Next, we require that a > 0, so we will throw away one solution from our quadratic equation, and see if the result is positive!

a(b)=-b*<x,y>/2 + sqrt( (b*<x,y>)^2-4*(b^2-1) )/2 and we have to make an inequality 0<=-b*<x,y>/2 + sqrt( (b*<x,y>)^2-4*(b^2-1) )/2 b*<x,y>/2 <= sqrt( (b*<x,y>)^2-4*(b^2-1) )/2

b^2*<x,y>^2/4 <= ((b*<x,y>)^2-4*(b^2-1))/4 (which we want to prove to show that a is positive) turns out to be easy b^2*<x,y>^2 <= (b*<x,y>)^2-4*(b^2-1) b^2*<x,y>^2 <= (b*<x,y>)^2-4*b^2 + 4 0 <= -4*b^2 + 4 4*b^2 <= 4 True!

so, the correct thing to do is take b on [0,1] and a(b)=-b*<x,y>/2 + sqrt( (b*<x,y>)^2-4*(b^2-1) )/2 easy to check that a(0)=1 and a(1)=0 , no matter what <x,y> is

(another side note: suppose y = -x and <x,y> = -1 Then, for b on [0,1] a=b/2+sqrt( -3*b^2+4) )/2 b=0 -> a=1 and b=1 -> a=0 b=0.25 -> a=1.1 ??? I'm still doing something wrong apparently! but I'm not erasing it! It's too late!!! What did I do?

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If you are using the affine space, you can't simply add and you can't simply multiply by a scalar: instead, the fundamental operation is the convex sum of "vectors": as a single operation, you add together any number of vectors, weighted, where the total weight has to be 1, so that the amplitude of the fundamental sticks to 1.

This makes good sense to me. The operators on this space are still a little fuzzy, though.

I've always been fascinated (obsessed maybe? meh) with convolution operators. I have often said some wrong things about these, but later worked out proofs of general properties that are essential. L1 norms and L2 norms are the most important. Convolution preserves L1 norms (proof on request) in the following way (here | . | represents the L1 norm, |f| = integral( -inf, inf, |f|dt) and * is convolution

|x*y| = |x| |y|

and in the L2 norm shown here with same notation |f| = sqrt( integral( -inf, inf, f^2dt) )

|x*y| <= sqrt( |x| |y| )

To me, convolution makes a good operator for consideration in this type of space. Maybe there's a modification to the definition we can make to be sure that |x*y|^2=1 ?

Actually, note the difference with convex space: in an affine space, you are not restricted to a>=0 and b>=0. I can only call the latter a convex sum because energy is nonnegative. (Btw, are the values in the vector supposed to be energy values or amplitude values?)

The values in the vector should be amplitudes of orthogonal components, right?

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suppose f(t) is a complex tone with frequencies of 100, 200, 300, 400, 500 and g(t) has frequencies of 100, 200, 330, 400, 500 Then, when we mix the two tones together there is dissonance between the frequencies of 300 and 330, which wasn't present in either of the two tones.

Dissonance is a somewhat complicated operation, imho. How you compute it? It's definitely non-linear. It could be a quadratic form, perhaps. Think of it as a matrix sandwiched between twice the same vector so that the result is a scalar. e.g. diss(x) = x'*A*x, where apostrophe means transpose. What would be a good A ?

Dissonance arises from narrow-band tones close together. Chuckk Hubbard posted the dissonance function a while back, on the list in a pd patch. I expanded on Chuckk's function to make the typical dissonance curves you see (like Partch's one-footed bride) by using the exact approach you've just mentioned, but I didn't do it so elegantly. X has a set of frequencies f1, f2, etc... with amplitudes a1,a2, etc...

Then, dissonance arises between pairs of frequencies by a nonlinear function N(X) which takes the dissonance between each pair and creates a vector of all possibilities. diss(X)=N(X)*A*N(x)/2 where A= [0 a1*a2 a1*a3 a1*a4 .... [a1*a2 0 a2*a3 a2*a4 ..... [a1*a3 a2*a3 0 a3*a4 ..... . . . where you see a1*a2, etc... I mean for it to be sqrt(a1*a2)

The elements are on the diagonal are zero because a single frequency makes no dissonance with itself.

However, I have not seen a single study that actually will say *how* dissonances add together! AFAIK there is no data on it!

Forget the matrix syntax, because this vector space is R^R... but matrix ideas can be mapped to functions. What's the dissonance function A(i,j) for two frequencies i,j? Or maybe A(i,j,w) where w is the window size that the dissonance is relative to. I guess that there are many valid and useful dissonance functions, depending on taste.

diss(x) = integral of integral of A(i,j)*x(i)*x(j) di dj

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By infinity, I mean, can we take a harmonic complex tone and change the amplitudes of the partials, to achieve any given sharpness/dullness of the tone? Essentially being able to increase the central moment of spectral denisty without bound.

This looks like a job for equalisers... but it requires a signal that has infinitely many partials.

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Bounded in terms of the dimensions of timbre. For example, dissonance. Can we have a tone which is maximally dissonant? Are there boundaries on the other dimensions of timbre?

Apart from A(i,j)=A(j,i) and A(i,i)=0, I don't have much knowledge of what would make a good dissonance function. I can't tell what's maximally dissonant without having a dissonance function first.

Plus, there's the added complication of non-linear critical band rate. So, the dissonance function is different for different registers (like the difference between a major third harmony in bass as opposed to treble). It is complicated. Attached is my resurrected/re-designed dissonance curves patch. The last thing I was doing with it was to look at dissonace relations with odd-harmonic series. Yes, it's very crudely coded--see for yourself--if anyone wants to collaborate, I'm up for a fundamental overhaul.

Chuck

On Nov 22, 2007 11:55 PM, Mathieu Bouchard matju@artengine.ca wrote:

On Tue, 20 Nov 2007, Charles Henry wrote:

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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.

Well, so far, most of the time you see "fundamental", there's only one at a time, for each block of music you want to figure out the fundamental of. But different fundamentals can be extracted for any given interval, and those intervals can be a window sliding through time, looking at any "dinote" (pair of notes), and there can be multiple windows of different sizes that account for different levels of human memory and of musical understanding... (?) I think that we could analyse music using whole networks of fundamentals...

Actually what I'm referring to is the dynamical systems perspective on pitch perception that I keep harping on about (work by Julyan Cartwright and colleagues, and articles from Chialvo). It's the only analysis I've seen that gives some kind of outside support for the perception of a fundamental bass. For example, Schenker analysis is a well-developed music analysis technique, but I haven't personally read any support for it, outside of music theory.

and also, a theory of musical understanding should be resistant to "detuning", because many forms of detuning are used in music and yet humans can automatically figure out what the fundamental is _intended_ to be (rather than what it is physically).

The theory (dynamical systems/pitch) is actually good for this too. There is a slight pitch shift when the frequency ratios become slightly detuned, but the overall fundamental produced is reliable under detuning.

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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.

There are many discrete or semi-discrete phenomena in construction of music, so using the Reals, an uncountable noncompact continuum, is pretty counterproductive. Instead of trying to use cartesian powers of the Reals in some form, try cartesian products of different algebraic structures that you will not use as (math) vectors.

Like using the mod 12 arithmetic, or other groups? Or making loops (using finite groups)? I think I can see how it would be useful. The whole idea was confusing to me in the first place... it still is.

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I have started working on a patch lately to simulate the trajectory of a particle as it flies across the surface of a torus

Are you doing it in terms of a particular embedding with a particular curvature of the space, or do you use a modulo-Euclidean space in the style of PacMan ?

PacMan :) I would take two variables to parameterize the surface a1 on [0,1) and a2 on [0,1) and use x=cos(2*pi*a1)*(2+cos(2*pi*a2), y=sin(2*pi*a1)*(2+cos(2*pi*a2), z=sin(2*pi*a2) or using cylindrical coordinates theta=2*pi*a1, r=2+cos(2*pi*a2), z=sin(2*pi*a2)

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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).

Not necessarily... if you fit all sounds in one master period, yes, but if you are using a continuum of frequencies, you have a continuum of possible dimensions. The finite dimensions of the FFT (and of other discrete interval transforms) are because there is a master fundamental frequency (that is not zero).

My reasoning was that we can create 1-1 functions on a subset of the continuous functions to R^N. If we have a function on a finite interval which is also band-limited, we can map this space onto the coefficients of a finite fourier series. All of the non-integer frequencies on the continuum still exist, but the spectrum can be sampled. When we have a real-valued continuous function on the interval [0,T), we can sample the spectrum on 1/T without losing any information. Just like when we have a complex function (a spectrum) on the interval [-fs/2,fs/2) or any other half-open inteval, we can sample in the time domain on 1/fs seconds, without losing information, as long as we know the interval of the spectrum.

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But then, there's the psychological space, which has drastically fewer dimensions, and they're not linear.

Did you get into algebraic psychology yet?

That's the first time I've ever read those words put together. That sounds interesting. I can see that "A Functional Theory of Cognition" by Norman H. Anderson deals with this topic..

Chuck

On Nov 27, 2007 1:06 AM, Mathieu Bouchard matju@artengine.ca wrote:

On Fri, 23 Nov 2007, Charles Henry wrote:

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The theory (dynamical systems/pitch) is actually good for this too. There is a slight pitch shift when the frequency ratios become slightly detuned, but the overall fundamental produced is reliable under detuning.

In a nutshell, how does it work? E.g. I have a tone at 200 Hz and another at 301 Hz and we want it to believe that it's a fifth, that the fundamental is 100.16 Hz or so, and perhaps also that the fifth interval is good within 0.33% and that the fundamental is good within 0.16%.

I have looked up that one. We can calculate the pitch according to the Farey sum. The fundamental is 100.2 Hz = (200+301)/(2+3), which is actually a negative pitch shift from a fundamental of 101 Hz. The theory agrees well with existing experimental data on the pitch shift effect (again it's just those papers by Cartwright).

Have you ever noticed beats between mistuned pure tone ratios? I have tried before to make simple experiments in Pd to count/match rates with a given tremolo comparison. It's hard to hear and make judgements, but it's there. For example, the phase of a 200 Hz and a 301 Hz tone sync up on every 1 second, but the beats do not match this frequency. It's something else entirely.

Ultimately, the notion of dynamical systems in pitch perception should be judged according to whether it jives with other psychoacoustical phenomena and generalizes well.

Overall, I want to say that what's important is to imitate the hearing of sounds, not to imitate what individual neurons do nor what we think they do. Let's say the brain might work only with sigmoid-clipped matrix products with approximate real numbers (they don't, but computer neural networks do). Then it's possible that you are better off using a structure that does more directly what you want (relative to what you know and how you think), rather than whatever contorsion of the same thing a billion years of random mutations has come up with.

"random mutations" heh heh... sounds like something a creationist might say. It's natural selection, dammit. It's not random :P

It is tempting to try to find sounds that match up with the theory, and see if it works. For example, when I started using pd, I tried to make some complex tones, where I could shift the partials around while keeping pitch constant. It didn't work. But I messed with it enough to make electronic sicadas (attached)

The auditory system is just too danged complex for something as simple as that to work.

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PacMan :) I would take two variables to parameterize the surface a1 on [0,1) and a2 on [0,1) and use x=cos(2*pi*a1)*(2+cos(2*pi*a2), y=sin(2*pi*a1)*(2+cos(2*pi*a2), z=sin(2*pi*a2)

You don't have to embed it in a non-modulo space, especially if computing things in terms of x,y,z is more complicated than in terms of a1,a2. If you already plan to compute directly in the a1,a2 square, then I don't know what x,y,z are for.

Yeah, I know. X, y, and z are just for show. Superfluous 3rd dimension.

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My reasoning was that we can create 1-1 functions on a subset of the continuous functions to R^N.

So, if your subset of continuous functions is isomorphic to R^N, what's the basis of your subset?

I have been giving plenty of thought into how to show this, without defining the answer. I'm still not sure whether or not I have done it.

Suppose we start with a function:

g(t)=sum( k= -N/2,N/2 , e^(2*pi*i*k*t)

The result has frequencies from -N/2 to +N/2, where we use N/2 as a kind of Nyquist frequency, defining a bandlimited function.

If we take g(t) as a periodic function, then we get a series of kronecker deltas in the fourier transform. On the other hand, if g(t) is non-zero on (-1/2, 1/2) and 0 everywhere else, the continuous fourier transform of g(t) is G(f)=sum(k= -N/2,N/2, sinc(f+k)

This spectrum falls off pretty quickly, but slower than e^-x. So the function is not strictly bandlimited, when we use the continuous fourier transform as opposed to fourier series. The spectrum is a rectangular function with ringing (screenshot of an example, also attached).

I would consider this function and its translations to be a convenient basis for the set of continuous band-limited compact functions. It is mainly useful because it allows this sampling property. If we sample the function on frequency N, we can re-create the original continuous function, by convolution of g(t) with a series of kronecker-delta functions with coefficients of the samples.

And more importantly, when you say band-limited, what kind of spectral analysis is it relative to? Does "compact in time" mean that your function is zero everywhere outside of an interval, or that it is periodic? If it's periodic, then you end up with a finite number of frequencies, but else, you still have an infinite number of possibilities in a compact set of frequencies, because the frequencies in-between the supposed harmonics are not aliased to a specific weighting of harmonics: e.g. with a function that is sin(1.5*x) over [-pi;+pi) and 0 elsewhere, the spectrum has a dirac at frequency 1.5/2pi and is 0 elsewhere, right?

The function you mention is not band-limited. It has a discontinuity at x=pi, which means that it has infinite frequency content.

So, my idea here is that the set of continuous band-limited compact functions (S) can be written as the image of a function. h: (compact continuous functions) -> S where h( f(t) ) = g(t) convolved by f(t) f(t) acts like a distribution. Then if a signal in S is sampled (mapping it onto R^N for some N), the result is unique for each function in S. Then, a set of continuous functions on [a,b] defined this way is finite dimensional.

Sorry it took so long for the reply...

Hello, I'd like to add some 0.5 cents experiment...

Mathieu Bouchard a écrit :

On Tue, 20 Nov 2007, Charles Henry wrote:

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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.

Well, so far, most of the time you see "fundamental", there's only one at a time, for each block of music you want to figure out the fundamental of.

Symmetric chords has as much tones as it has notes, diminished chords, has four fundamentals, also a minor seven chord might be relative with three major scales, and we have the choice between different chords with the same bunch of notes. eg: A C E G is both Am7, and C6 (C E G A), or FM7 (F A C E G) or G13 (G B D F A C E)... This is what you are explaining later:

But different fundamentals can be extracted for any given interval, and those intervals can be a window sliding through time, looking at any "dinote" (pair of notes), and there can be multiple windows of different sizes that account for different levels of human memory and of musical understanding... (?) I think that we could analyse music using whole networks of fundamentals...

Hardness of understanding increases when window size diminishes, like a blues we could play with only one scale with a little understanding, or all scales with applying knowledge of harmony all along the twelve bars structure.

and also, a theory of musical understanding should be resistant to "detuning", because many forms of detuning are used in music and yet humans can automatically figure out what the fundamental is _intended_ to be (rather than what it is physically).

Dominant chords can contain all the notes that aren't into the fundamental chord, so we know by experience that the moment after this dissonant ambiance, the next sound will be different but nearly the one we've heard before,. From fundamental the dominant chord contains the nearest intervals, the fifth and the fourth are mathematicaly the simpliest non-integer intervals, the seventh is the preceding frequency of the fundamental in tempered major scale (when 9b is used it goes more complicated...).

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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.

The fundamental appear in harmony once we know an amount of informations determinded by edges expressed with rythm. Following the dominant ==> fundamental motion explained just before, odd beats would contain fundamentals and even beats would contain dominants.

Mathieu Bouchard a écrit :

No, we were thinking specifically about close detunings, all those intervals that are confused with a much simpler interval, and usually, which *should* be confused. It's the basis of logarithmic temperaments: 2^(7/12) is over 0.1% off from 3/2, and that's one of the best-matching intervals relative to just temperaments. So, my question is, how do we deal with that? When is a major third played like 2^(1/3) considered to be an approximation of 5/4, and when is it considered to be an approximation of 81/64 or some other?

Here we see how rythm and harmony behaves differently for our perception. If all intervals in a chord has the same ratio contained in their harmonics, the chords looses energy by consonnance, and even worst, we couldn't hear a distinction between notes, while in rythms if sounds aren't played accurately together, it would become harder for the listener to make a distinction of the structure.

On Tue, Nov 20, 2007 at 10:47:06AM -0600, Kyle Klipowicz wrote:

Uhm, just the fact that the majority of musicians don't even know what topology is, yet their music still sounds great, is enough for me to believe your conjecture. All this maths talk reminds me about why I've started playing a lot more guitar and focusing on content/lyrics/melody in music.

So you're saying that if someone makes good art and they are ignorant, then we should take their lead and try to be more ignorant? For me it doesn't follow that if most musicians don't understand mathematics and their music is still good, then we should all aspire to not understand mathematics.

You can get lost in the mathematics and never be able to communicate with an audience of anyone but geeks (self included).

Yes, I think that's true.

Music is communication, so as musicians we have a responsibility to communicate in a language that is understood by our audiences.

Sometimes in understanding something more fully and on multiple levels, we can deliver an artistic experience that is understood by our audiences, or makes them dance, or moves them, even more easily and fully than if we had less understanding.

I'm guilty of sometimes writing esoteric algorithmic maths music, but I like to think that on those often horrible sounding explorations I gain a greater understanding into what it takes to really make a booty shake. :)

Of course, if you want to be bitter and elitist and feel that the audience needs to take a complex analysis class to 'get' your music...

Just because you are not interested in the conversation, or don't understand it, doesn't mean that other people aren't interested, or that those speaking are trying to be 'elitist'. I really think you are imposing your own feelings onto a discussion between two other people. I think that what Matju and Chuck were discussing was very much on topic, and was quite interesting.

Best,

Chris.

http://mccormick.cx

On Tue, 20 Nov 2007, Kyle Klipowicz wrote:

I suppose my comment was leakage of some of my thoughts about my own musical production and how ultimately burned-out I've become from over-intellectualized sound design. My main concern is that when people get so far into "mathematizing" music there is an emotional connection that is severed and everything sounds like it was made by Vulcans.

It's not about getting far, it's about getting lost.

You can get as far as you want, as long as you keep a string that connects you back outside of the maze, just like Ariadne.

I haven't heard Vulcan music before so I can't comment on that. Are you suggesting that Vulcans don't have emotions?

Nothing against brainy music, but it just seems that there's sometimes too much head and not enough heart in the computer music scene.

Perhaps it's just not enough right ventricle. In that case, it can be because of failure of the tricuspid valve to close properly, which causes an abnormal and inefficient blood flow.

Seriously now, I believe that it's not about head vs heart competing for resources, it's more of a matter of effective collaboration between the head and the heart.

_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada

On 21 Nov 2007, at 3:47 AM, Kyle Klipowicz wrote:

You can get lost in the mathematics and never be able to communicate with an audience of anyone but geeks (self included). Music is communication, so as musicians we have a responsibility to communicate in a language that is understood by our audiences.

Of course, if you want to be bitter and elitist and feel that the audience needs to take a complex analysis class to 'get' your music...but the ladies still dance more to a hard hitting beat or a good ol' melody.

The structures that that underlie a good piece of work don't need to
be understood on a direct analytical level by an audience member,
formal structures - mathematical or otherwise - can often help create
a work that is more whole and reads better regardless of whether that
structure is read directly (if an individual audience member also
understands the structure this can add another kind of interest to
the work for them).

On the other hand it is very important for the artist using formal
structures in their work to understand what they are doing. It
certainly isn't the only way to make art, but if you are going to go
that way then understanding the structures you could use is crucial.

And work that is more purely formal, intended only for an audience
with a knowledge of and interest in the structures being used, isn't
only for the 'bitter and elitist' artist - it is also part of the way
artists can share and build techniques, a way to 'talk about'
structure and form in a more practical way, perhaps in parallel with
formal analysis, perhaps not.

This feeds into work for a broader audience and helps the artist and
others understand what is going on in their practice.

simon