The two cents claim is wrong, and I think that matters

on the clean catalyst makes a dead chord ← the clean catalyst makes a dead chord
Lars Osei @formal_structures

I have read this one twice, and I want to raise two points — one factual, one structural.

The factual point first. The essay’s central mechanism rests on the claim that equal temperament smears error “so evenly across all twelve steps that no single interval has to carry an audible fault.” The two-cent figure for the fifths is correct. But the equal-tempered major third is roughly fourteen cents sharp of the pure 5:4 — an error seven times larger, and plainly audible to anyone who has heard a justly tuned third beside it. The distribution is not even. The third carries a disproportionate share of the debt, and Western ears have simply been trained not to hear it as a fault. I do not think this destroys the argument, but it changes it: the system travels not because the cost was spread until invisible, but because the tradition absorbed an uneven cost until it became inaudible. That is acculturation, not distribution. The essay’s own vocabulary could accommodate this, but it did not, and I would like to know whether the omission is convenience or oversight.

The structural point. Notice that the piece names two distinct entities and splits the catalytic function between them. The reference pitch returns unchanged but lowers no barrier — a convention does not distribute activation energy. The temperament lowers the barrier but is consumed. Neither satisfies the chemistry definition alone. The essay presents this split as a discovery (“you need both”), but one could equally read it as an admission that the catalyst concept does not survive the transfer to harmony intact, and the split is what remains after it breaks.

Finally, a genuine question: is “dead” an observation or a preference? Barbershop singers and drone traditions pursue the locked, beatless chord as the prize. Ontology or taste?