Independent Parallel Tracks and Hidden Markov Models

OK, so now we have code that analyzes each track of a multi-track midi file, and creates transition tables. These transition tables are used to generate new music that has some influence from the analyzed track. 

However, each new track is used independently. While the behavior of each new track is based completely on the statistics of the analyzed track, they will not sound like they are "composed together” when they are recombined. 

Organ Donor Frank Brickle says, "To keep them together you actually need to model the interaction in some way. Looking ahead a bit, you can probably see why a hidden Markov model of all the activity is one of the best ways of coordinating the subordinate parts."

Ok so what does this mean? 

A hidden markov model is where the observation and the state are separated. The simplest example is a coin. Usually you see the coin, and can read whether it came up heads or tails. A hidden markov model has the coin hidden, like behind a screen, and the observations (heads or tails) are read out to an audience (or user, or participant, or contestant). 

One of the jobs of the contestant is to figure out how many states are required to best explain the observations. For example, for five minutes the coin flipping produced about half heads and half tails. Then it suddenly changed, and the observations were mostly tails for four minutes. Then mostly heads for three minutes. Then it went back to a fair distribution for the rest of the session.

One way to explain this is with three coins. A fair coin, a heads-heavy coin, and a tail-heavy coin. The person behind the screen switched from one coin type to another and read off the resulting observations. The number of states in this hidden markov model would be three. Each coin is a state. Each state has an alphabet of two possible values. Each state’s alphabet has a different distribution of likelihoods. The probability distribution for each state (each coin) is different.

I believe our job is to figure out how to keep the tracks working together when new music is created. Analyzing each track separately stays in the toolbox, but analyzing the entire piece, and using that analysis to coordinate the production of new tracks must be done as well.