


Fractal Music Gallery


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Music Gallery
Contents |
About Fractals | Music
Software |
Music Gallery

Fractal Music Overview
Fractal Window I by Forrest Fang
Omar's Fractal (Bifurcation fractal) Example
Sonification of Mandelbrot Set Examples
Examples from Logistic Equation
Chua's Oscillator Examples
Anti-Odysseus, the Irreversibility
of Time by Insook Choi
Examples created using Iterated Function
Systems

Fractal Music

While fractals are 'sets of points' having particular properties they are
usually created by simple feedback processes.  The term 'Fractal Music'
typically refers to music composed wholly or in-part using the same types of
mathematical feedback processes that are used to create fractal images.  For
fractal music composition the numerical outputs of the feedback process are
mapped to musical parameters such as pitch, duration, volume, etc to produce
melodies, harmonies, rhythms, and textures.


A Sampling of Fractal Music on the Web

Fractal Music by
Bob Devore


Fractal Window I by Forrest
Fang
One of my favorites, this composition, copyright  1996 by Forrest
Fang, is background music at
Sprott's Fractal Gallery


Omar's Fractal MIDI
Example
 This fractal music example was composed with Omar's Fractalby
Charles Neville, the programs author.  This program produces MIDI output by
iterating the Bifurcation Fractal equation x' = x * (1-x) * a (where 'x'
is a number less than 1 and greater than 0 and 'a' is a number between 3 and 4)
and mapping the 'x' values to particular note numbers . 
 The output of iteration is a series of numbers, 'x' values, that might be
an ordered repeating pattern, a chaotic non-repeating pattern, or a mix of both
depending on the value of 'a'.
Find out about
Fractal Jazz by visiting Omar's Basement .


MandelBrot
single voice example (325 KB)
MandelBrot
multiple voice example (704KB)
These examples were produced by assigning numeric values to the image pixels
for a portion of the Mandelbrot set and then mapping the values of linearly
sequential pixels to pitches.
 For
more info on Hearing the Mandelbrot set


Example
by Martin Guertner
This example was created by iterating the the logistic equation  x' =
x*b*(1-x) and mapping the output values 'x' to different musical parameters
such as pitch, duration, etc.  More information and additional examples can be
found at the Fractal
Music Project.

Chua's
Oscillator Musical Example
Chua's Oscillator is one of a few physical systems for which the presence of
Chaos has been observed experimentally, verified by computer simulation, and
proven mathematically.  It has been used to generate both musical signals and
compositions.
You
can find a full description of Chua's Oscillator here.
Visit
this site for additional musical examples.

Anti-Odysseus, the Irreversibility of
Time (Insook Choi, 1993) presented at the 1993 Asian Contemporary Music Festival
used the Chua Circuit.
Excerpt
Additional
information and excerpts can be found here.


 My particular interest is mappings which produce 'familiar' styles of music
from fractal processes.
This interest in mappings for fractal-based algorithmic composition goes
back to an early article by Charles Dodge and Curtis Bahn in Byte called
Musical Fractals, (June 1986, pp185-196). Three comments from
that article have stuck with me:

Self-similarity was a characteristic of all the fractals that they found to
be musically interesting.
Heinrich Schenker's classical music analytical techniques reflect the parts
of a musical form as self-similar structures.
Certain compositional procedures that make new musical material by
systematically transforming previous materials, i.e. canon, fugue, and motivic
development, can result in clearly self-similar musical structures. 
'Music Theory 101' teaches that unity and coherence in music is often
achieved by repetition and development of a smaller number of musical motifs or
themes.  The hierarchical structure of  'self-similar' fractals appears to
inherently have some of these same qualities.  This article suggested to me that
with appropriate mappings a wide range of musical styles could be composed from
fractals.
My composition algorithms are currently all based on Iterated Function
Systems.  These systems are interesting because both the image (attractor)
formed by plotting the successive iterates and the pattern formed by the number
of times different points on the attractor are 'hit' (the measure) are
fractals...and they are almost always self-similar fractals.
More about Iterated Function Systems (IFS) can be found at: 

IFS Playground
Sprott's Fractal
Gallery
Here are some of the ways that I use Iterated Function Systems for
composition:

Use the IFS measure in a fashion similar to that described in the
article Iterated Functions System Music by Michael Gogins: Computer
Music Journal 15(1): p40-48, 1991 MIT Press.
Example 1..
Assign starting pitches to particular x,y coordinates on the attractor. 
Then follow the orbit of successive iterations along the attractor and map
either the absolute values of the coordinates or the change in coordinate to a
given pitch range.  The sequence currently playing is an example of this
technique. Example 2.
Create a 'pattern-template' via the above techniques and apply different
chord progressions.
Create a 'background layer' by one of the above techniques and produce
additional harmonic layers as described in the Musical Fractals
article.
Two short anthologies of original fractal music compositions utilizing some
of the techniques mentioned above.  Both anthologies contain several MIDI Format
1 files orchestrated for General MIDI; I used the SB AWE 32 sound card.  You
will need an unzipping program.

Download Anthology
I (FRACTAL1.ZIP - 12K)
Download Anthology
II (FRACTAL2.ZIP - 17K)


If you have some fractal music or fractal music composition software
that you would like to link to this site, composition ideas, or any comments
please drop me a line.
Update: 1/18/97 
Copyright  1996 DTStrohbeen 

