Re: AW: fractal loops (was: keeping loops interesting)

["Krispen Hartung" <khartung@cableone.net>]

----- Original Message ----- 
From: "Brian Good" <bsgood@adelphia.net>

> You could make things even "fractaler" by applying the same method to 
> pitch, if you don't mind jettisoning the twelve-note-per-octave 
>chromatic 
> scale. Play a chord.  Pick one note as the root.  Note the ratios of the 
> frequencies of all the other notes to that of the root. Scale the ratios 
> by a number much less than one, generating a new "chord" whose pitches 
>are 
> likely much closer together than a half step. Replace each note in the 
> original chord with a copy of the "chord," pitch-shifted to the original 
> root. Repeat until traumatized.

I like this. Now this is starting to seem like the fractal examples I am 
accustomed to reading about or seeing.

By the way, having a background in philosophy, I discovered that some of 
Leibniz' thoughts influenced fractal theory, which makes a lot of sense to 
me in the above example. He built a metaphysical system of thought, his 
depiction of the universe, which consisted of an infinite number of 
"monads"...sort of like self-contained "windowless" metaphysical atoms. 
According to his system each monad is a world unto itself, in that it 
reflects the whole like a mirror. It's a bizarre theory, very spooky.  In 
short, each part reflects some nature of the whole, as in the example 
above 
with those chords, as in the phenomenon of holographic images (though only 
in similarity, not exactness, to appease Rainer and Andy)....the whole is 
the big monad, or "Modad" as I like to call it. :)

By the way, Leibniz looked like a modern rock star: 
http://en.wikipedia.org/wiki/Leibniz

"Mandelbrot's well-known fractal geometry drew on Leibniz's notions of 
self-similarity and the principle of continuity: natura non facit saltus. 
We 
also see that when Leibniz wrote, in a metaphysical vein, that "the 
straight 
line is a curve, any part of which is similar to the whole..." he was 
anticipating topology by more than two centuries."

Here is another really interesting article on Leibniz' monads and their 
fractal properties...fascinating. Now I want to go back and read his 
Monadology again.

Another analogy to fractal theory, which actuallyl came before fractal 
theory is the Rationalist theory of knowledge (Leibniz was a Rationalist 
by 
the way, so this makes sense), such as from Decartes and Spinoza.  One 
might 
describe Descartes system of knowledge by the "pocket paradox" analogy, 
wherebye putting my hand in my own pocket, I can tell what is in the 
contents of someone else's pocket, direct knowledge with no empirical 
data. 
Likewise, according to Rationalists, you can actually reveal the secrets 
of 
the universe (truths) via the mind alone...again, that concept of the 
whole 
being contained in each part in some fashion. The cosmos inside the mind, 
such that we can metaphorically "view" its structure and deduce truths.

Kris