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According to wiki, the human eye has an angular resolution of ~1 arcminute, which means you can distinguish things that are 30 centimetres apart at a distance of 1 kilometre.

But your ears have a much lower angular resolution than that. Any idea what it might be?

The thing that prompted this question was - when I looked at the balance control in an audio mixer, and it allows continuous control. I think if I change the balance by 10% I probably couldn't hear the difference. Does the balance pot really need such fine resolution?

After posting this, I realised that a balance fader changes the relative levels of a signal reaching each ear. But when you listen to a sound in a room your brain can locate the source of the sound because (amongst other things) the audio arrives at your ears at different times.

And so moving the balance fader from one extreme to the other produces an effect that is only superficially similar to that of a performer walking from one side of the stage to the other.

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    Human directional hearing is a bit more complicated than just different volume for each ear.
    – ojs
    Commented Apr 11, 2022 at 13:15
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    I’m voting to close this question because it is not really depending on music, but a addresses a general perceptional/physiological/psycho-acoustic question.
    – guidot
    Commented Apr 11, 2022 at 13:18
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    There's more than one question here (and not music but biologic). We easily "sense" continuous motion of a sound source, but whether we can assign a static position to high accuracy is a separate question.
    – Carl Witthoft
    Commented Apr 11, 2022 at 14:42
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    @guidot The question is about application of psycho-acoustic knowledge to music mixing. Maybe it would fit a bit better Sound Design SE, but I don't think it's really off-topic here, the division between MP&T and SD seems not to be very well defined so far.
    – user1079505
    Commented Apr 11, 2022 at 16:30
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    @user1079505 Although my feelings are generally broad about what we leave open, I see this as "a biological question with implications for music." One of the reasons for closing and reposting elsewhere is not just "humph, we don't wanna talk about that," but the fact that another site might have better expertise. This one beats the heck out of me. I wonder if it's actually better under medicine...
    – Andy Bonner
    Commented Apr 12, 2022 at 12:22

1 Answer 1

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The human brain has several different ways to localize sound depending on the pitch and the direction of the sound. These include not only volume difference between ears, but also timing difference for higher frequencies and the way earlobes filter the sounds coming from different directions. Simulating all of these on a stereo recording requires that listener wears headphones and the recording is done using artificial head or HRTF filtering that simulates the listener's head. In optimal conditions, using all these cues, for sound sources in front of the listener, the resolution is about 1 degree. The minimum audible volume difference between ears is 0.5dB.

Sources: https://en.wikipedia.org/wiki/Sound_localization, Thomas D. Rossing: The Science of Sound

For the "Does the balance pot really need such fine resolution?", continuous adjustment has the benefit that it is simple to implement. Adjustment from -90dB on one channel to -90dB on other at 0.5dB increments would require 360 discrete steps, which is not really simpler than continuous adjustment. Consider that high end consumer audio manufacturers can sometimes resort to really complicated solutions for very small or nonexisting sound quality improvements and even there discrete volume adjustment is uncommon.

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