Fractal music

[mikkeljs]

In my research on fractals, I found out, that my music history teacher Lars Bisgård have written a fractal analysis on pieces by Chopin, Beethoven, Sibelius and Nørgård. I found a very interresting model that could be drawn on any piece, and the infinity seria (Nørgård) appeared:

Exposition, reexposition, polarisation and regeneration...

The exposition (not to compare with a sonata form exposition) means the introduction of the Gestalt (motif or thema, indivisible).

Reexposition is the return with a slightly variation.

Polarisation is the first real contrasting situation, something new happens.

Regeneration is supposed to regenerate the start, the exposition.

Now if you describe the first periode of a traditional sonata, you can find theise 4 phases in each the 4 phases and etc. In that way, everything is prepared. The reexposition prepares the polarisation of the gestalt and the polarisation makes the point of the regeneration. The interferrance of theise phases makes it possible the combine every musical action besides the gestalt (the indivisible).

Just wanted to share the informations.   

[bwv 1080]

I do not know what that means.  Fractals are geometric shapes that exhibit self-similarity at different scales and have a non-integer dimension, usually greater than their topological dimension.  There is no direct correlation to music other than the broad concept of self-similarity at different scale lengths.  A traditional sonata form does exhibit some, although it is perhaps trivial, where the harmonic progression at the top level of the form (Tonic exposition - cadence in dominant - development - recap in tonic) has some parallels to what happens at the phrase and period level.

[karlhenning]

What musical motif which is not a single note, is at all possibly "indivisible"?

[bwv 1080]

What musical motif which is not a single note, is at all possibly "indivisible"?

Even single notes are divisable

[karlhenning]

And there is that.

[bwv 1080]

You could even divide them like this

[greg]

bwv & Karl,

http://www.pernoergaard.dk/eng/strukturer/uendelig/ufraktal.html

is what Mikkel is talking about.
(haven't been to that site in a while!)

[greg]

music for the sense of sight:

[mikkeljs]

What musical motif which is not a single note, is at all possibly "indivisible"?

I was also thinking a lot about that. If the basic motif were indivisible, the selfsimilarity into smaller phrases would not be infinite. 

[millionrainbows]

Even back in 2008, I was aware that fractal composition was a possibility. It seem Charles Wuorinen has done some work in this area.

It also seems obvious that a simple arithmetical system like fractals could be applied to music. I find this fascinating. I'm sure that by now there are books.

After seeing some of the nit-picking queries on this thread, it would be nice if someone could actually discuss the subject. I think it's a very interesting area.

[71 dB]

Even back in 2008, I was aware that fractal composition was a possibility.

I think I heard the term "fractal music" around 1990. I think I even heard some computer fractal music. I'd say fractals should stay visual. 

[Contemporaryclassical]

I found this interesting:


https://youtu.be/mq0z-sxjNlo

[Uhor]

There is Stockhausen's formula compositions.

[millionrainbows]

It seems to me that fractal music would sound different depending on who is doing it, and how. I don't see "fractal music" as a term which could be used to characterize the results, or as a desire to see it not used.
This is the same old objection to mathematics and music.