Three Node Markov Chain

The graph above shows a three node musical Markov chain. And the source code/audio below is this Markov chain realized in Csound.

Download: 3_node_markov_chain.csd
Listen at SoundCloud

What is a Markov chain? According to wikipedia, “A Markov chain is a discrete random process with the property that the next state depends only on the current state.”

This Markov melody starts with state_0, playing an E-flat for an 8th note duration. A new state is then chosen for the next course of action. There is an equal chance (1 in 3) that state_0, state_1 or state_2 will be chosen. Assuming state_2 is selected, G below middle C is played for a 16th note duration. From state_2, there is a 1 in 10 chance state_0 will be chosen at random, 2 in 10 chance for state_1, and a 7 in 10 chance for state_2. I’m guessing you can figure out state_1. This chain plays until time runs out.

Though there are various ways of creating Markov chains in Csound, I landed on this design, which utilizes Csound instruments as Markov nodes. My first draft used a lot of gotos and jumps, which has its place, but I really wanted to encapsulate each state in it’s own block of code. Instruments do the trick, though I believe user-defined opcodes would work as well. Node connections, along with their weighted probabilities, are defined as f-tables in a centralized block of code in the global space of the orchestra; This allows a user to quickly change the probabilities, and to quickly create/modify new Markov networks.

In order to allow multiple instances of the Markov melody to play simultaneously, I’ve equipped each running Markov thread with a string identifier. You can hear two chains playing in the last 4 bars, with the second chain offset by a 32nd note.

As an alternative Markov chain design, Andrés Cabrera has a Csound example in his Csound Journal article Using Python Inside Csound. Python is actually better suited to the task than pure Csound, so definitely take a look.

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