Fractal Tune Smithy

[Robert Walker-7]

Hi there,

Thanks for the link. I was particularly interested to read it, as my fractal tune smithy program uses exactly the technique that Harlan Brothers describes as "motivic scaling"

Many of the pieces are strict mensuration canons, and also fractals according to his definition. All the pieces in the Sloth Canons folder are strict fractal canons according to his definition. It has been available for download since the late 1990s, and I first thought of the idea in the 1980s. It is a natural idea for a mathematician interested in fractal music to think of, and as he doesn't mention Tune Smithy on his web site, I assume he came up with his desription independently - perhaps FTS didn't turn up in his web searches. For some reason it has a low Google ranking in the search for "fractal music" though high ranking for "fractal tune".

http://www.robertinventor.com/software/tunesmithy/tune_smithying.htm

If you want to be pedantic I think one could argue that though these definitely have a "fractal quality" - a scaling similarity - they aren't really fractals in exactly the same way as the visual fractals. He skates over that point by making his definition a fractal if it has enough detail for the fractal description to be the most concise way to describe it. But a visual fractal like the mandelbrot set has endless detail as you zoom in and in.

A fractal construction that stops after say ten steps wouldn't stricly count as a fractal. So I think one that you can only zoom in say ten steps or whatever is something slightly different from a strict visual fractal in that sense, though decidedly fractally inspired and fractal in structure. But I think it is reasonable enough, just as one can say that trees are fractal - everyone knows that they only divide a finite number of times unlike a true fractal, but it is reasonable to call a fractal.

A musical fractal would have to do that in the time dimension, as you zoom in the only way to do that would be to have arbitrarily short notes and arbitrarily small time pitches. You can do that too with Tune Smithy, and I have a an example on the web site based on a Cantor set here:

http://robertinventor.com/software/tunesmithy/tune_smithy_seeds.htm#fractalpitches
That really is a strict musical fractal.

Most of the tunes in FTS are so transformed by the various options and transformations that the original fractal structure is entirely obscured. But I feel somehow it is still the thing that somehow gives the music a unity and structure, and makes it more than just random notes, even if you can't hear the similarities at all in the result or even pick it out mathematically if you don't know how the tune was constructed.

It's like - musical fractals are more easily hidden from the listener by transformations. In a fractal landscape, the visual fractals are more obviously fractal in a visual sense. But in the domain of sound, the fractals are much more easily obscured, mainly because you have to do just a finite number of steps I expect.

So - I too would vote for "fractal music" to include all music that is inspired by fractals and uses them in any way at all, including e.g. ones that use the mandelbrot set to generate music which isn't itself fractal in structure in a way obvious to the listener who doesn't know how it was constructed.

Most of the tunes in FTS are so transformed by the various options and transformations that the original fractal structure is entirely obscured. But I feel somehow it is still the thing that somehow gives the music a unity and structure, and makes it more than just random notes, even if you can't hear the similarities at all in the result or even pick it out mathematically if you don't know how the tune was constructed.

If we need a special word for this motivic scaling type music, and want to make sure that the reader understands that this is the type of fractal music refered to, why not just call it "motivic scaling music"?

You could call it "strictly fractal music" - except that it isn't really unless it goes to arbitrarily small steps in the time and pitch domain. Well that's my two cents worth.

 I see the difficulty for mathematicians (as a mathematician by background myself). It's awkward to have a word fractal meaning something rather tighter in the visual domain than it does in the musical domain. But the word is kind of quite flexibly used even visually - and I think perhaps it can bear this stretching of the word. I think the reason it is used more flexibly in music is partly because of the natural limits to the divisions of music in the pitch domain and often in the time domain too, and because the hidden fractal structure is much more easily obscured in music than visually.

Robert

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