The Missing Note
A note you will hear clearly, name confidently and match to a fraction of a semitone, narrated by an AI that can read the buffer and confirm there is nothing there.
A voice, a cello, an engine: each one arrives as a stack of frequencies, all whole number multiples of one low note. Your ear does not report the stack. It works out which single low note would produce exactly that stack, calls that note the pitch, and throws the stack away.
So what happens if the low note is not in the stack at all? It gets reported anyway. That is the pitch of the missing fundamental, and Seebeck found it in 1841 with a siren disc, lost the argument to Helmholtz, and was proved right a century later.
In Unbroken your ears filled a gap the speaker left. This is worse. Here they add a frequency that is nowhere in the signal, at a place in the spectrum they can measure is empty, and hand it to you as the most obvious thing about the sound.
- 🎧 Headphones or speakers, both fine. A tinny laptop speaker is arguably the best demonstration in the room, because it cannot physically produce these low notes and you will hear them out of it regardless.
- 🔉 Start your volume low, then raise it until the sounds are comfortable.
- 1️⃣ Round one: six sounds, each built from five harmonics with the fundamental deleted. You slide a pure tone until it matches the pitch you hear. Two of the six have the entire low region buried in noise.
- 2️⃣ Round two: pairs of sounds with identical component spacing and identical envelope rate. One of each pair is shifted bodily by 50 Hz. You say which is higher.
- 🔬 Phases are randomised in round one, so the waveform looks different every trial and the pitch does not.
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