Thursday, October 18, 2012

Markov chain music

I played to you some Markov music, taken from the web site: Mathematics, Poetry, and Music by Carlos Pasquali. The tune is very monotonous and simple sounding because the distribution of $n$th note depends only on the $(n−1)$th note. More interesting music could be obtained by letting the state be the last $k$ notes, $k>1$. You might enjoy reading the Wikipedia article on Markov chains. It has a nice section about various applications of Markov chains to: physics, chemistry, testing, Information sciences, queueing theory, the Internet, statistics, economics and finance, social sciences, mathematical biology, games, music, baseball and text generation.

There are lots of other crazy things that people have done with Markov chains. For example, at the Garkov web site the author attempts to use a Markov chain to re-create Garfield comic strips.

A much more practical use of Markov chains is in the important area of speech recognition. So-called hidden Markov models are used to help accurately turn speech into text, essentially by comparing the sound that is heard at time $t$ with the possibilities that are most likely, given the sound heard at time $t−1$ and the modelling assumption that some underlying Markov chain is creating the sounds.