Animating a melody as a mathematical object

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This is an exploratory project beginning with the thought that given music can be digitised, there must be a way to translate it to a dataframe in R, and then wrangle to something that can be transformed to a graph, plotted using ggraph, and finally animated with gganimate.

The melody

As is only right and proper, I used the subject of Contrapunctus I from J.S. Bach’s The Art of Fugue, a towering study of melody by the composer who defined the rules of melody.

(Image source: wikipedia)

Happily, wikipedia provides the midi along with the image of melody.

The math

It’s impossible to talk about graphs without beginning with Euler’s solution to The Seven Bridges of Konigsberg problem, where the puzzle was to find a walking path through the city that crosses each of its seven bridges exactly once. Euler invented graph theory to show it could not be done.

A graph comprises a set of nodes, and a set of edges, where each edge is a set of two nodes. The brilliance of Euler’s solution was to realise the size and shape of the landmasses were irrelevant, only the the bridges (edges) between them.

(Image source: wikipedia)

The code

To animate a midi as a graph, I took these steps:

1. Convert midi to R object using pyramidi.

2. Create melody dataframe.

3. Use gt to make a table of notes.

4. tidygraph graph of notes.

5. ggraph plot.

6. gganimate graph plot.

7. Add audio.

In the next sections, I describe each step in more detail.