We've discussed the frequency range of the ear, but what about the dynamic range from the softest possible sound to the loudest possible sound?
One way to define absolute dynamic range would be to look again at the absolute threshold of hearing and threshold of pain curves. The distance between the highest point on the threshold of pain curve and the lowest point on the absolute threshold of hearing curve is about 140 decibels for a young, healthy listener. That wouldn't last long though; +130dB is loud enough to damage hearing permanently in seconds to minutes. For reference purposes, a jackhammer at one meter is only about 100-110dB.
The absolute threshold of hearing increases with age and hearing loss. Interestingly, the threshold of pain decreases with age rather than increasing. The hair cells of the cochlea themselves posses only a fraction of the ear's 140dB range; musculature in the ear continuously adjust the amount of sound reaching the cochlea by shifting the ossicles, much as the iris regulates the amount of light entering the eye [9]. This mechanism stiffens with age, limiting the ear's dynamic range and reducing the effectiveness of its protection mechanisms [10].
Environmental noise
Few people realize how quiet the absolute threshold of hearing really is.
The very quietest perceptible sound is about -8dbSPL [11]. Using an A-weighted scale, the hum from a 100 watt incandescent light bulb one meter away is about 10dBSPL, so about 18dB louder. The bulb will be much louder on a dimmer.
20dBSPL (or 28dB louder than the quietest audible sound) is often quoted for an empty broadcasting/recording studio or sound isolation room. This is the baseline for an exceptionally quiet environment, and one reason you've probably never noticed hearing a light bulb.
The dynamic range of 16 bits
16 bit linear PCM has a dynamic range of 96dB according to the most common definition, which calculates dynamic range as (6*bits)dB. Many believe that 16 bit audio cannot represent arbitrary sounds quieter than -96dB. This is incorrect.
I have linked to two 16 bit audio files here; one contains a 1kHz tone at 0 dB (where 0dB is the loudest possible tone) and the other a 1kHz tone at -105dB.
Above: Spectral analysis of a -105dB tone encoded as 16 bit / 48kHz PCM. 16 bit PCM is clearly deeper than 96dB, else a -105dB tone could not be represented, nor would it be audible.
How is it possible to encode this signal, encode it with no distortion, and encode it well above the noise floor, when its peak amplitude is one third of a bit?
Part of this puzzle is solved by proper dither, which renders quantization noise independent of the input signal. By implication, this means that dithered quantization introduces no distortion, just uncorrelated noise. That in turn implies that we can encode signals of arbitrary depth, even those with peak amplitudes much smaller than one bit [12]. However, dither doesn't change the fact that once a signal sinks below the noise floor, it should effectively disappear. How is the -105dB tone still clearly audible above a -96dB noise floor?
The answer: Our -96dB noise floor figure is effectively wrong; we're using an inappropriate definition of dynamic range. (6*bits)dB gives us the RMS noise of the entire broadband signal, but each hair cell in the ear is sensitive to only a narrow fraction of the total bandwidth. As each hair cell hears only a fraction of the total noise floor energy, the noise floor at that hair cell will be much lower than the broadband figure of -96dB.
Thus, 16 bit audio can go considerably deeper than 96dB. With use of shaped dither, which moves quantization noise energy into frequencies where it's harder to hear, the effective dynamic range of 16 bit audio reaches 120dB in practice [13], more than fifteen times deeper than the 96dB claim.
120dB is greater than the difference between a mosquito somewhere in the same room and a jackhammer a foot away.... or the difference between a deserted 'soundproof' room and a sound loud enough to cause hearing damage in seconds.
16 bits is enough to store all we can hear, and will be enough forever.
Signal-to-noise ratio
It's worth mentioning briefly that the ear's S/N ratio is smaller than its absolute dynamic range. Within a given critical band, typical S/N is estimated to only be about 30dB. Relative S/N does not reach the full dynamic range even when considering widely spaced bands. This assures that linear 16 bit PCM offers higher resolution than is actually required.
It is also worth mentioning that increasing the bit depth of the audio representation from 16 to 24 bits does not increase the perceptible resolution or 'fineness' of the audio. It only increases the dynamic range, the range between the softest possible and the loudest possible sound, by lowering the noise floor. However, a 16-bit noise floor is already below what we can hear.
When does 24 bit matter?
Professionals use 24 bit samples in recording and production [14] for headroom, noise floor, and convenience reasons.
16 bits is enough to span the real hearing range with room to spare. It does not span the entire possible signal range of audio equipment. The primary reason to use 24 bits when recording is to prevent mistakes; rather than being careful to center 16 bit recording-- risking clipping if you guess too high and adding noise if you guess too low-- 24 bits allows an operator to set an approximate level and not worry too much about it. Missing the optimal gain setting by a few bits has no consequences, and effects that dynamically compress the recorded range have a deep floor to work with.
An engineer also requires more than 16 bits during mixing and mastering. Modern work flows may involve literally thousands of effects and operations. The quantization noise and noise floor of a 16 bit sample may be undetectable during playback, but multiplying that noise by a few thousand times eventually becomes noticeable. 24 bits keeps the accumulated noise at a very low level. Once the music is ready to distribute, there's no reason to keep more than 16 bits.
https://people.xiph.org/~xiphmont/demo/neil-young.html
