Having read through the discussion, I would add one small sub-point to the discussion below. Even those who understand the psychoacoustic arguments behind noise and dynamic range limits, i.e. noise integration in the cochlear filters, commonly refer to "hearing 10-15 dB below the noise floor” and to "limits of dynamic range at 19-20 bits” without specifying spectral dependency. This is because the limit is normally understood to refer to audibility at any spectral frequency, with an implicit understanding that the region around 3-4 kHz is most sensitive. In other words, for unshaped noise, saying that it is below audibility means at all frequencies. It’s likely that people in forums pick up on that usage, possibly without understanding it.
As far as measurements of how far “into the noise” we can hear, there aren’t a lot of good published numbers that I know of (having reviewed the subject a couple of years ago), but Bob Stuart and Peter Craven argue dynamic range and, to a certain extent, audibility below the noise floor in a couple of papers published in JAES in 2019. They are based on psychoacoustic arguments as well as listening test results, the latter as part of their studio and lab work on MQA. If interested, their (open access) papers are in the AES e-lib, “The Gentle Art of Dithering” and “A Hierarchical Approach for Audio Capture, Archive and Distribution”. > On Jan 9, 2022, at 2:26 PM, Nigel Redmon <[email protected]> wrote: > > OK, but you’re missing the fact we don’t listen to music at the top end of > that range. That is, you didn’t specify the noise floor level, so I can’t > give and exact max SPL from your “111 dB”, but suffice to say that no one is > listening anywhere near that top end of your range, not within tens of dB. > > I don’t consider this a primary concern, just worth discussing as practical > limits—the fact our floor starts well above 0 dB SPL, and we don’t (can’t, > practically speaking) listen at 120+ dB SPL is worth say, especially for > those who don’t believe there are limit to hearing (I guess they don’t > consider the mass has to be displaced). But physical limitations of > electronics and hearing are foremost. > >> The human hearing system can detect non-random signals well below the noise >> floor. I could not find any reference for how many dB below the noise floor >> we can hear, but even if I found some numbers they'd surely be frequency >> spectrum dependent. > > The idea of hearing below the noise floor is used way to loosely, from my > observations of various forums. I’m not saying that you are making a mistake, > just taking the opportunity to express caveats that a lot of people don’t > consider. > > First, people most often seem to make this claim with regards to dither, and > especially shaped dither—often something like “we can hear 20 dB below the > noise floor”. I agree with your comment about being spectrum dependent, but > I’ll just not that in context of shaped dither especially, the signals people > hear “20 dB below” are not 20 dB below at that part of the spectrum—the total > or average noise is considered. > > Also, I see people assume that means we can hear 20 dB below *any* noise > floor. This is obviously not true. If you can't hear a signal at -20 dB SPL, > adding a noise floor 20 dB higher doesn’t make the signal hearable.
