The model represents the twelve keys with circle-of-fifths geometry: keys a fifth apart look similar inside it, tritone-apart keys look opposite. It is enormously tempting to call this the model discovering music theory. This page is us catching ourselves.
Run the control
Before crediting the model with a discovery, ask whether the structure was already in its input. It was. The same circle-of-fifths geometry sits in the raw pitch-class statistics of the music — more cleanly than in the model — because keys a fifth apart simply share more notes. Anything that represents which notes are present inherits the circle of fifths for free.
| fifth-apart / tritone-apart similarity | in the raw notes | in the model |
|---|---|---|
| a fifth apart (should be similar) | +0.50 | +0.13 |
| a tritone apart (should be opposite) | −0.63 | −0.28 |
Reported as what it is
Not a discovery — a property of the data the model faithfully carries. The rule we took from it, and applied everywhere after: before claiming a model found a structure, measure whether that structure was already in its input. The same discipline is what deflated the drum result into an honest “overdetermined” and forced the targeted genre probe.
Researcher notes
- Baseline. Build a 12×12 key-similarity matrix from raw pitch-class histograms (transpose each piece to all twelve keys), and compare it to the model’s learned key-embedding similarity. The raw one shows a cleaner circle.
- Why. Adjacent keys on the circle of fifths share six of seven scale tones; a tritone away they share only one. Any note-presence representation reproduces that automatically.