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Algorithmically Generated Chord Progressions

The PDF below is a discussion that I had presented to Dr. Roman Yampolskiy‘s CyberSecurity Lab at the University of Louisville.  Though this topic has little to nothing to do with cyber-security, it raised a lot of interesting questions and provided insightful suggestions from the audience.  Two questions that were raised during the presentation but was unable to answer at the time will be answered in this blog entry.  The second question goes into brief detail on how the Markov Decision Process (MDP) works.

What additions to Computer Science and Computational Music does you work bring to the fields?

Yes, much of my work is not new to this field.  I am a Masters student and my thesis does not need to provide conclusively new work to the field.  However, despite this, a portion of my work is new to both Computer Science and Music Theory in general.  My work on the chord progression algorithm using Markov Decision Processes would help to solidify Dr. Dmitri Tymoczko’s recent development of Geometric Music theory (more on his website:  http://www.music.princeton.edu/~dmitri/).

It does this by showing that the decision making process that composers go through can be replicated through complex decision making algorithms such as the Markov Decision Process discussed in this presentation.  I have also seen very little research in the use of MDPs in algorithmic music generation.

Why did you decide to use Markov Chains for your thesis?  This has been tried and was moved away from because it wasn’t robust enough to capture chord progressions.

I think you are confusing the Markov Decision Processes.  The Markov Decision Process has very little to do with Markov Chains.  A Markov Decision Process is a mathematical framework for decision making in situations which are partially stochastic (random) and partially under the control of a decision maker.

If you are familiar with Chord Progressions, you know that there is an ultimate goal in mind but in most music the way that you reach that goal is not explicitly defined; there are exceptions in Blues and Rock where the I-iv-V and I-ii-V progressions prevail.  Since Dr. Tymoczko’s geometric model for chord progressions captures the implicit definition of movement of chords in the progression, we can weight certain chords as a goal that we want to reach and use MDPs to decide on the best path that would maximize utility in the model.  By doing this, we leave a bit of the randomness in the chord progressions, keep the implicit definition of chords through Dr. Tymoczko’s model, and allow the decision maker (the computer) the ability to decide where to go given its current location.

This is different from Markov Chains, where we would define a limited set of actions and make probabilistic movements to one or the other leaving most of the model as stochastic.  This would be similar to Xenakis’ work in stochastic music, which is respectable in its own right.  However, I am attempting something far different than stochastic music.  My hope is that I will be able to define tonality in chord progressions as both a complex decision process and through Dr. Tymoczko’s work in Geometric Music Theory.