fractalmusic

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Information about fractalmusic
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Published on January 15, 2008

Author: Dolorada

Source: authorstream.com

Chaos and Fractals in Music:  Chaos and Fractals in Music By Jarrod Best Theodore Love Andrew Myers Advisor: Mr. Robert Quackenbush Introduction:  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:  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 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 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 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 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:  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:  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:  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:  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:  Theo’s Piece A graph of the tones of my piece My Piece:  My Piece Andrew’s 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:  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:  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:  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:  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.

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