Harmonic Track List Generator

Harmonic track list maker based on the Camelot key system.

The Problem

To understand the objective of this program, and why we do it, we need to understand what the Camelot Key System is and why we care about it.

Camelot Key System

This system is just a transformation from classic musical keys to a simpler format; with the sole purpose of facilitating harmonic track mixing. The following diagram shows how each of the classic keys is assigned to a Camelot key:

The idea behind this system is that any track with a given key will be harmonic with any other track that either shares it's key or has a neighbour key. For example, if we had Track A with key 1A, then Track B would be harmonic with it if it had keys 1B, 12A or 2A.

Interpreting the system as a graph

Having explained the idea behind the system we can now translate it to a non directed graph, were each edge means that we could mix tracks from nodes A to B harmonically. Said graph would be (sorry for the color inconsistency and A->B order replacement):

Track list graph example

Now, if we wanted to do the same as before but connecting those tracks that could be mixed harmonically, then we would have something like this:

Having seen this, our objective should be to create a track list that included all of our tracks (once) with harmonic transitions. Basically, we need to find a path in our graph that includes every node and has no loops. Something like this:

Of course, this is one of the many possible results, as our example had a very well connected graph.

Few track graph example

In this other (suspiciously similar) example:

We can see there are a lot less nodes, and therefore less edges; which inevitably brings less options in the creation of our track list. Particularly, we can see that it is not possible to create a list with ALL of our tracks without loops; the best we could do is leave one out, resulting in this:

Of course, if we wanted to add the song we left out really badly, we could just eliminate it's other two light green cousins and add it. Two for one swap.

The solution

As explained before, the idea is to create a non directed graph with the tracks we have and find all the possible paths that include as many tracks as possible without any loops. As a result, we would have many track lists with all harmonic transitions.