Knowledge graphs and music
A chord progression is a walk on the tonnetz, the toroidal lattice where every triangle is a triad and every edge is a voice-leading move. Counterpoint rules aren’t stylistic preferences; they’re path constraints on a weighted graph. The parallel fifths prohibition? It’s an excluded subgraph. The resolution of a tritone? A shortest-path problem in harmonic space.
The link between molecules and graphs was figured out decades ago. Graph-native reasoning (subgraph isomorphism, centrality, motif detection) transformed how we understand chemical structure and reactivity. Drug repurposing followed.
Nobody has seriously done this for music (as far as I can see). The patterns are there though. The circle of fifths is a Cayley graph of Z12 (the ring of integers modulo 12.). Modulations are graph homomorphisms between tonal regions. Bach’s voice leading follows rules that look exactly like flow constraints in a network. The question isn’t whether the graph structure exists, it does. The question is whether graph-native reasoning can surface compositional patterns that centuries of human analysis missed.
I don’t think I will get any time soon a customer asking me to help out but I love the idea and what it could reveal. I think the right tool isn’t a music theory thing, rather a knowledge graph that encodes harmonic objects as nodes, voice-leading moves as edges, and lets you query across a corpus the way chemists query molecular databases.
There is an interesting angle related to category theory but I’ll leave that for another post.