Although I love computers in music, I think the most important and least talked-about aspects of music are Gestalt perception (especially Pragnanz): http://homepages.ius.edu/rallman/gestalt.html and tuning mathematics: http://www.chrysalis-foundation.org/Manuscript.htm Western thinkers have become preoccupied with thinking of intervals as steps to be added and subtracted rather than as ratios to be multiplied and divided. But the effect they have on the brain of the listener derives from ratios, not sums.

The Gestalt principles are often forgotten by computer music researchers (as well as all kinds of musicians). I think it would be quite possible to teach a computer program to account for these grouping tendencies, and to create tension between them.

-Chuckk

On 8/1/06, Gerda Strobl gerda.strobl@student.tugraz.at wrote:

Hi Steffen,

I just got a book from the library that is quite new: "Mathematics and Music" A Diderot Mathematical Forum, G. Assayag, H. Feichtinger, J. Rodrigues (Editors), 2002, Springer Verlag Heidelberg).

It gives a very good overview about several topics that are music, maths and computer music related. Perhaps you can find it in your university library--might give you some nice ideas ;-).

Gerda

Steffen wrote:

...

Hey Pd-List,

Fist of all: Im sorry if this is too off-topic, i know it's on the edge.

I'm soon gonna write the final paper/thesis, before jumping to the "master" studies of mathematics. I'm not too familiar with the all educational systems in the english speaking world, but it's the part of my studies, that, when finished, gives me what's equal to a master degree in mathematics.

To the point: I'm hoping to find a topic that combines "computer music" with mathematics, or maybe more correctly; a mathematical topic on a fitting level, that has (some) relations to computer music (in a broad sense).

I'm kind of blank and lack computer music knowledge, hence i ask you lot: got any ideas?

Hope you can help. And thanks a grand.

Oh, my minor is philosophy if that matters.

Best, Steffen

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I see mathematics in "music" as occupying three distinct branches that are loosely coupled. I call these the three Ms, the model, the method, and the music (for want of a better term beginning with M :)

The model posits declarative knowledge firmly grounded in physical reality. It's about real physical vibrating structures and signals that are "real" in the common usage of the word. It's largely a branch of fluid dynamics, or just general dynamics if you consider electronics as a production mechanism. This is good old school engineering math with a huge dollop of classical physics. Here we concern ourselves with such things as propagation, waves, superposition, turbulence, boundary conditions and reflection, diffraction and refraction...

The method is the imperative branch. As C Henry indicates, operator theory, or the mappings/transformations of spaces onto other spaces is the highest view of this. We concern ourselves with parametric equivalences, identities and so on. For the mostpart it's very theoretical and personally, quite beyond my mind. We deal with matrices a lot. But it's very important from a computational perspective, it's the "how to" part. For example, we know what a vibrating string is and what it does, but one may choose a number of methods to implement the model, scanned synthesis, FM, Karplus-Strong, modal/tensor and so on. Each method picks a salient feature of the model and helps us to realise it in an computationally expedient way.

The music is a whole different branch that links the two together. It says what those salient features are, at least to human beings made of wetware neural networks educated by learning, examples, and context. It is the psychoacoustic/cognitive aspect of signal mathematics. It basically says why a certain method fits a given model for *PRACTICAL* uses. To do so we leverage a lot of statistics and empirical studies. Those practical uses (for the production of sound) might depart a lot from the practical parts of another discipline (say building bridges that don't collapse).

Making music/sound involves all of these branches. As C Hubbard indicates, here is the gestalt. We design instruments/synthesisers using methods which in turn implement models which in turn correspond to internalised music (sound).

From a creative viewpoint a good understanding of each, explicit or implicitly

empowers the artist because the quicker one can move from an imagined (target) sound to its realisation as a signal in the real world.

This is of course all "philosophy", which may engage your interest. In my own work I try to avoid maths for it's own sake, at least in the studio it all happens at a subconscious level until something doesn't work and I have to fall back to the textbooks to figure out why. In the "conscious" process I "see" the signals

• geometry plays a big part. Most "practical" maths in the studio

is basic mental arithmetic, everything else is abstracted into black boxes with well known behaviour, it's the only way to manage complexity while working.

I hope that gives you some ideas for where to sail your boat.

Andy

ps I was flicking through "Mathematics and Music" - Assayag &c just this morning in Borders, it looked very good from a composers POV.

On Tue, 1 Aug 2006 14:23:12 -0500 "Charles Henry" czhenry@gmail.com wrote:

...

To the point: I'm hoping to find a topic that combines "computer music" with mathematics, or maybe more correctly; a mathematical topic on a fitting level, that has (some) relations to computer music (in a broad sense).

If you're interested in synthesis/DSP, I recommend to study operator theory and numerical analysis. All of your transforms come from analyzing differential/integral operators, their eigenfunctions/values, and inverses.

Music theory itself is pretty mathematical, but it's practically a pointless endeavor to try to apply mathematics to "explain" music. You just wind up finding structures (like the lattices with minor and major thirds along the axes) with practically no relevance to the real experience of music. However, I believe that studying dynamic systems (non-linear operator theory) has some promise for physiologically based theories of music. I've been thinking about doing a math masters as well....and those are the two topics that I consider most significant.

Chuck

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Hi all,

My approach is much arithmetic with notes. List form scales and/or chords. I am thinking od using a cloud of probablities for note events. Neural network are an "easy" way to let the computer make his connections by "learning". Otherwise, adjacency matrices, with probabilities of such and such event (chord, melodic note) after the current serie of event...

Cheers,

aalex