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Chaos and Fractals in
Music
By Jarrod Best
Theodore Love
Andrew Myers
Advisor: Mr. Robert Quackenbush
Introduction
To study the fractal properties of music,
we set out to create our own rules of
iteration and translation for our own
compositions. We then analyzed the
final structure of each composition and
its fractal properties.
Musical Properties Used
To begin our composition, it was
necessary to identify what properties of
music we thought fractals could apply
to. Those we found are:
Rhythm
Intervals
Dynamics
Pitch
Rhythm
Rhythm is the structure of the placement
of notes in musical time. To create our
rhythmic fractals, we used different
types of rhythmic patterns and different
note lengths
Intervals
Intervals are the distances between notes
in the musical scale. These are easily
measured in half-steps, which makes it
very simple to create a simple fractal.
Dynamics
Dynamics are the changes in volume
during a musical piece. There are
approximately 8-10 general dynamic
levels which can have fractal properties.
Though we did not use dynamic
properties in our own fractals, they are
another important aspect of the fractal
properties of music
Pitch
Pitch is the sound frequency of any given
note. This is an important part of
creating fractals as it allows a musical
phrase to be raised or lowered in its
pitch in order to further an interval or
rhythmic fractal
Jarrod’s Piece, Part 1
This is the initial pattern of intervals I used and the
longest rhythmic pattern. This phrase is repeated as
harmony for each successive phrase and also ends the
piece.
Jarrod’s Piece, Part 2
This is the beginning of my iteration. The original phrase
is repeated as a harmony while the melody becomes half
the time of the original rhythm. In order to keep the
musicality, I did change the pitches of the second phrase
by beginning the same interval pattern on the 4th note of
the first 6-note phrase. Also, the melody is moved up an
octave in order to maintain the harmonic undertones.
Jarrod’s Piece, Part 3
This is the peak of the rhythmic fractal. After this phrase, the
previous two phrases are repeated in reverse order to descend
from this peak. Notice I maintained the rule I used for splitting
the melodic phrases in part 2. Once again, this was to maintain
musicality while preserving fractal properties
Jarrod’s Piece – Wrap-up
My piece is primarily based upon fractals
in rhythm, as well as slight iteration in
pitches. The rhythm is focused around
one 6-note phrase which speeds up and
slows down. The pitches slightly jump
around due to the necessity of not
creating constant repetition.
Theo’s Piece
A graph of the tones of my piece
My Piece
Andrew’s Piece
The original goal of our project was to
find fractal patterns in classical music.
This proved to be to difficult, because
there are a variety of aspects that must
be analyzed at once, and because of
the complexity of the music we chose.
Andrew’s Piece
Instead, we decided to create our own
music using a fractal rule, and then see
what conclusions we can draw about
fractal patterns in music.
Andrew’s Piece
This is my song. It is a C Major
Arpeggio iterated three times.
Compare that to Chopin’s Etude in C
Major. Hear the similarities?
Andrew’s Piece
Consider for a moment what we did
here. Using a seed and iteration, we
created a song that is very similar to a
piece from the classical repertoire. This
is one of our strongest arguments for
fractal properties in music.
Conclusions
From our creation of music with fractal
properties, we found that music can
have fractals in many different aspects
of its structure. It also can have many
different rules of iteration for each of
these aspects. We also analyzed the
musicality of our pieces and found that,
indeed, fractals can create music.