[jacquesm]

It's even more complex than that. The low notes are hard to tune because the fundamentals are very close to each other and you need to have super good hearing to match the beats, fortunately they sound for a long time so that helps. Missing fundamentals are a funny thing too, you might not be 'hearing' what you think you hear at all! The high notes are hard to tune because they sound very briefly (definitely on a piano) and even the slightest movement of the pin will change the pitch considerably.

In the middle range (say, A2 through A6) neither of these issues apply, so it is - by far - the easiest to tune.

[fallingfrog]

Welll. On guitar you cant really use the "matching the beats" or the thing where you play the 4th on the string below and make them sound in unison, because if you do that all the way up the neck your guitar will be tuned to Just intonation instead of equal interval intonation and certain chords will sound very bad. A series of perfect 4ths and a perfect 3rd does not add up to an octave. Its better to reference everything to the low e string and just kind of know where the pitches are supposed to land.

That's a side note, the rest of what you wrote was very informative!

[TheOtherHobbes]

See also, psychoacoustics. The ear doesn't just do frequency decomposition. It's not clear if it even does frequency decomposition. What actually happens is lot of perceptual modelling and relative amplitude masking which makes it possible to do real-time source separation.

Which is why we can hear individual instruments in a mix.

And this ability to separate sources can be trained. Just as pitch perception can be trained, with varying results from increased acuity up to full perfect pitch.

A component near the bottom of all that is range-based perception of consonance and dissonance, based on the relationships between beat frequencies and fundamentals.

Instead of a vanilla Fourier transform, frequencies are divided into multiple critical bands (q.v.) with different properties and effects.

What's interesting is that the critical bands seem to be dynamic, so they can be tuned to some extent depending on what's being heard.

Most audio theory has a vanilla EE take on all of this, with concepts like SNR, dynamic range, and frequency resolution.

But the experience of audio is hugely more complex. The brain-ear system is an intelligent system which actively classifies, models, and predicts sounds, speech, and music as they're being heard, at various perceptual levels, all in real time.

[jacquesm]

Yes, indeed, to think about the ear as the thing that hears is already a huge error. The ear is - at best - a faulty transducer with its own unique way of turning air pressure variations into nerve impulses and what the brain does with those impulses is as much a part of hearing as the mechanics of the ear, just like a computer keyboard does not interpret your keystrokes, it just turns them into electrical signals.