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The frequency range of human hearing is fairly common knowledge, at around 20Hz-20kHz. The range of volumes we can hear is between about 0 and 130 decibels.

What is the resolution of human hearing between those limits, both in the frequency and amplitude domain? That is, what is the minimal change in frequency and amplitude that we can distinguish? Also, does this resolution change much along the range? For instance, do we have more difficulty determining the difference between a quarter tone at high frequencies than we do at low frequencies?

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    Note that we use 24 bit for recording, but that is mostly useful for adding headroom for effects processing and mixing, and I assume that the 'bit-depth' of human hearing is actually much lower than that.
    – naught101
    Commented Sep 24, 2013 at 1:45
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    You might try googleing using the phrase, "just noticeable difference" and "human hearing". You'll find a number of highly technical references that may be of interest to you.
    – JoshP
    Commented Sep 24, 2013 at 4:21
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    Thanks Josh. I don't think I would have found that terminology on my own. Would be interesting to work out what ["just noticeable difference"]en.wikipedia.org/wiki/Just-noticeable_difference) in hearing translates to as a bit-depth (for volume). Not sure if there'd be an equivalent for frequency...
    – naught101
    Commented Sep 24, 2013 at 5:50

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Amplitude

Taken from here:

The human ear can consciously discriminate amplitude differences of about 1dB, and experiments show subconscious awareness of amplitude differences under .2dB.

Although a complete answer would probably have to account to the equal loudness contours - we may be able to tell a 1dB difference with 1kHz, but not so for 100Hz.

Frequency

Taken from Wikipedia, which references to a masters research:

It is difficult to establish how many cents are perceptible to humans; this accuracy varies greatly from person to person. One author stated that humans can distinguish a difference in pitch of about 5-6 cents.

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I'm not saying this answers everything but the Fletcher Munson curves give an indication of how our hearing is sensitive to some frequencies and not others. Here is the graph taken from wiki that shows the FM curves and the ISO equal loudness curves for various sound pressure levels: -

enter image description here

A small side-note. As the sound intensity drops our ability to hear bass dramatically reduces and to some extent so does the treble - this is why on older stereo systems there was a "loudness" button - when the volume was low (whatever low means) you could press the button and it would boost the bass and treble a little bit.

It's also worth noting that between 2kHz and 4kHz our ears are very sensitive and capable of "hearing" sound pressure levels significantly below 0dB (20 micro pascals)

Personal experience leads me to believe that a human can detect a 1dB increase or decrease in SPL if they are concentrating.

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    It's also worth noting that these curves are 'population average'. Frequency range is highly individual and very age-dependent.
    – Jim Mack
    Commented Sep 24, 2013 at 11:23
  • Appreciate the answer, but it's not exactly what I'm asking. Basically, my question could be rephrased in terms of that graph though: what is the minimum resolution of that graph that would contain all the information for a representative person? That is, what is the minimum change in both the x and y axis of that graph that a person would be able to distinguish?
    – naught101
    Commented Sep 25, 2013 at 7:29
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The search term is JND, just noticeable difference. Yes, the resolution changes over the frequency range, and of course this is true if frequency is given in cents from a reference and even more obvious if given in Hz.

There's much more to read if you find a copy of Brian Moore's Hearing, or Psychoacoustics by Zwicker and Fastl. There is also data about spatial resolution and several other things.

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  • Hey oberdada, welcome to the site :) Usually, StackExchange sites encourage complete self-contained answers, so that the question and answer is useful to users who don't have access to external resources. If those books you mention address the question directly, could you add some information that speaks directly to the question, using them as a reference?
    – naught101
    Commented Sep 25, 2013 at 13:00
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5 cents for most timbres since that's where chorus detune starts to become pleasant (from non-scientific reading of guitar pedal forums). I imagine spectral content matters a lot since activating more cochlea can only increase the chances a particular harmonic is near a detection threshold. I also imagine blurrier signals would be harder to discern and most natural pitches resemble a gaussian distribution with a peak at some target frequency. Hz, db, spectrum, and std-dev are all probably parameters in a real answer.

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    Mmm. Not sure that's relevant. That's acoustic beating. You can hear acoustic beating by just playing two independent tones, and you can hear it down to a tiny fraction of a cent (it gets bigger the smaller the difference). That's not the same as hearing the difference between two consecutive tones. I just tried with a sine generator at 1khz and a 1hz square LFO, and can JUST hear a 10 cent difference. Definitely can't hear a 5 cent difference. At 100Hz it's worse - can hear a 40 cent difference, but not a 30 cent difference.
    – naught101
    Commented Jun 7, 2022 at 6:47
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the minimum distinguishable frequency that a human ear can hear is not an absolute value in hertz but a percentage of the the frequency in question. For example, to go from C to C# in the first octave C0 is ~ 1Hz, in C1 is ~ 2Hz,..., in C8 is 248.91Hz. The percentage difference from C to C# is 5.95% +-0.02%, and this is constant throughout. In tuning my guitar around C4 octave (261.63 - 493.88Hz) I can here ~3 subdivisions from C to C# (I am not that good at it:) so I would estimate that I can distinguish about 2% of the frequency being played.

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  • Hi Nikolas, thanks for your answer, but I'm not really following what you're trying to say here. It probably isn't helping that you're using non-standard notation. In standard A4=440Hz, C0 is 16.35Hz, not 1Hz. Also, the question doesn't ask for or assume an answer in Hz. And I would fully expect the resolution to vary along the frequency spectrum (probably somewhat correlated with the Fletcher-Munson curves posted above.
    – naught101
    Commented Nov 23, 2020 at 3:41

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