As you know, we have an innate sense of musicality and we can sense when certain tones are off key and wrong. Im curious to what degree can we sense it? Is there a limit of deviation from the correct pitch where we can’t recognize that the note is off pitch anymore and it starts sounding normal?
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It varies *enormously*
My housemate can’t hear the difference between notes closer than about a tone, and I have another friend who hilariously couldn’t even tell when she was over-blowing a note when she was forced into trying to learn euphonium as a child (she wasn’t sure even when the notes were an octave apart!)
I, in contrast, regularly find my cheapo guitar tuner not quite sensitive enough to do the job without going back and tweaking it by ear after the fact, and that’s a [cent]( https://en.wikipedia.org/wiki/Cent_(music) ) or two at most (a cent being a hundredth of a semitone) and I’m sure there are plenty of professional musicians who out-do me by a fair margin – I’m just a dabbler in the musical arts who happens to have a fairly good ear.
Of course, the timbre of a sound makes a fair difference. If the sound you’re listening to is a pure sine wave, then it’ll only have one frequency in it and that makes measuring that single frequency easier (by ear or with whatever other apparatus you might want). If it’s something with lots frequencies that are neatly on the harmonic series (i.e. the main frequency and simple multiples of it) then that’s even better^1. There’s a limit to this, though – a square wave is the limit of the sum of harmonic series pattern and ends up sounding a little “noisy” so there’s presumably a sweet spot somewhere between sine and square waves.
If the sound has lots of non-harmonic overtones (e.g. base frequency multiplied by some non-obvious ratio like 1.43x or whatever) then that can make it difficult to hear it as a single note at all, let alone identify the base frequency precisely. An example of sounds rich in this way include the “gravelly” voices of certain singers.
It’s worth noting that “being exactly on key” isn’t necessarily what we mostly train our hearing to, though. A lot of music uses deliberately not-quite-in-tune notes for stylistic reasons and we learn to perceive these notes as the note they’re nearest to, because that’s how that kind of music works.^2
Is there a fundamental limit to how good a human ear can get? Presumably, there’s a point at which the difference between two notes is smaller than the gap between two consecutive hairs in the cochlea. That might not be a hard limit, though, as there are subtle clues even to higher frequency resolutions than that. Consider what neural networks do to upscale video, for example – we’re probably doing similar things all the damn time in our auditory cortices (and elsewhere in our brains, of course). I can’t imagine that would extend your resolution by a *long* way, though.
I’d love to hear from somebody with a really *really* in-depth understanding of acoustics & ear physiology to get some actual *numbers* to this 😛
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^1 Our ears/brains are very good at responding to the harmonic series and we’ll even “hear” frequencies lower than our ears can actually directly detect by *inferring* them from higher harmonics. A sound with a rich set of overtones fitting the harmonic series will hit all these sweet spots, giving our brains a lot to work with to nail down the base frequency.
^2 Obvious examples include sliding into/out of a note, or using vibrato (wibbling around slightly either side of a note) which we perceive as the note at one end or other of the bend, or the one in the middle of the wibble, even if most people could easily tell the difference between the note as played and the note as written if we heard them side by side.
A particularly amusing example is the first note of “Yesterday” by the Beatles, which isn’t really one note or the other at all, causing much consternation among those trying to score the tune! I wanted to link an Adam Neely video that touched on this, but haven’t managed to find it, sadly…
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