Harmonic Structure of the Basilar Membrane

He was not able to reproduce the pattern initially, but did finally reproduce it exactly for a very important reason. He found that the pattern is not immediately revealed using 32-bit Adobe Audition but instead only an the earlier 16-bit version of Audition named Cooledit Pro, v1.2a, that Adobe had acquired in 2003. He also found that increasing the amplitude made the pattern more apparent, leading him to eventually reproduce it in 32-bit Audition by increasing the gain beyond 192.7dB (making it equivalent to a 25-bit resolution sampling). The conclusion is that a combination of "gain and grain" is what reveals the natural Gaussian distribution pattern of harmonics over an octave.

Continuing our correspondence, we then delved into why this would be the case and how this low-res quantization of sound might be related to human auditory perception.

It turns out that the basilar membrane in the cochlea of the inner ear happens to be quantized much like the low-res spectral analysis. The typical length of the basilar membrane is about 35 mm and actually performs a spectral analysis of a 10-octave range. Since there are about 15,000 stereocillia hairs on the membrane and one-tenth of the membrane represents an octave, the ear's resolution is about 1,500 hairs over a 3.5 mm octave section. This is a much coarser quantizing of the incoming wave form than what we see happening even with the 16-bit spectral analysis of Cooledit.

The implication is the human ear must recognize the spectral pattern over an octave much like a 16-bit program - but at an even lower resolution of about 2^10 = 1024 or between a 10-bit and 11-bit resolution. This would be a very coarse recognition somewhere between the attached image by Finch and the full 16-bit image in the comment. We might conclude that the ear evolved only enough auditory resolution to approximately recognize the essential harmonic proportions and aid survival and nothing more, a perfect model of efficiency.

But there's one more thing we might conclude. This low-res Basilar analysis could also account for the ear's tolerance for different tunings. With only an approximated low-res recognition of harmonic proportions, there is a built-in slack for the recognition and enjoyment of equal tempered intervals, just intervals and other 12-step temperaments. As I stated in my book, the critical thing for harmonic recognition is the division of the octave into twelve semitones - not the particular scale temperament. Different temperaments only create different flavors of an overarching Gaussian distribution of harmonics, each delicious in its own right.

* Image by David L. Finch using Cooledit Pro, 1.2.