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Generative Music, Fractal Music, 1/f music

Like generative art, electronic coin flips and dice tosses can generate music as well.  I first stumbled across the concept in the late Martin Gardner's book Fractal Music, Hypercards and More: Mathematical Recreations from Scientific American. My dad was a big fan of Gardner's and kept his books around the house while I was growing up. 

In his chapter "White, Brown and Fractal Music," Gardner described several types of noise in terms of the musical scale. White noise is just a picking a note at random with no sound correlated to the next one. Brown noise is simply a walk up and down the musical scale; no large jumps from note to note. However, Gardner describes Fractal Music as pink noise, or 1/f noise. It is defined as a power law decay. In other words, notes aren't picked randomly, but using probabilities, depend upon what note came previously. In the back, he describes an algorithm to generate such music.

For me, I didn't really see an application of his chapter on fractal music until I got my first Mac with GarageBand. GarageBand allowed me to input a sequence of notes via a keyboard, to input the sequence of notes generated with Gardner's algorithm. As mentioned previously, as a math teacher at the time, I was trying to find applications for the concepts to engage my students. I never really developed a lesson on this, but I created a lot of music!

I should note that the sequences generated with Gardner's algorithm were only a starting point. In some cases, I constrained the possible notes it could pick to only one key consisting of 8 possible notes. In others, I allowed it to pick from a modal scale, a scale consisting of 12 possible notes. From this initial sequence, I used some basic musical compositional tricks to enhance the tunes. Sometimes the sequences sounded better as a bass line. Others sounded better as a melody. I experimented with playing two sequences simultaneously in the same key, one acting as the melody, the other as the harmony. I also played around with the instrumentation and the music genre. In some cases, I added my own guitar work. 

Check out my first album over on Bandcamp. I guess it's pop? The first track Beethoven's Monster Attacks contains a melody based on a modal scale. Most of the rest are based on scales from various keys. There is a marked difference. Here's a link. it can also be accessed off the main page at the bottom if this link doesn't work.


I've got two albums more coming. One is jazzy and the other is more rock oriented. As for the name of my "group", that was a result of me playing around with Google translate, and it kind of fit the idea of this primate having an idea.

I'm thinking about how to apply Gardner's algorithm to creating some abstract art. I'll post some of that work here or on Instagram.

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