Re: 11 Bark channels

So to finish up on the storm analogy - every incoming storm dissipates energy, to first order, in the same manner. Every storm has a linear dB-distance curve, with the same slope. The only variation is the absolute level of damage.

Hence if you know the level of damage at one place, then you can predict what damage occurred elsewhere - with a single knob adjustment for representing the degree of damage at, say, 4 kHz.



> On Nov 4, 2025, at 07:37, David McClain <[email protected]> wrote:
> 
> There is an interesting and very simple approximation that can be made. To overcome hearing impairment, you first of all must amplify the signal by enough to reach the elevated threshold at each frequency. 
> 
> Then on top of this amount of gain, there is a double-sided exponential decline - a skirt centered at the elevated threshold. The most additional gain from this skirt comes right at the elevated threshold level, being just enough to “double” the apparent sound level, e.g., boost by 9.8 Phon.
> 
> And for levels departing away from the elevated threshold, in either direction, there is less and less additional gain needed, in an exponentially declining manner. I don’t recall the half-width of this skirt, but I can go look it up in my notes.
> 
> If you know anything about Black-Scholes, then the compensation gain curve looks exactly like a Put option with some time value remaining.
> 
>> On Nov 4, 2025, at 07:27, David McClain <[email protected]> wrote:
>> 
>> Yes, It sounds like your reasoning is exactly parallel to my early reasoning. We both want to be sure that we properly capture the fact that our hearing is not actually channelized into discrete Bark bands at the commonly assumed frequencies. But rather, these Bark bands are self organizing around the loudest spectral peaks.
>> 
>> And for that purpose we think that oversampling in the Bark frequency domain will allow us to more faithfully represent these self-organized bands.
>> 
>> But after years of experiments, having started out with 100 bands and going all the way as low as 5 bands, there seems to be a happy medium around the standard audiology testing half-octave bands, which work out to pretty close to 2 zBark spacing and width.
>> 
>> One zBark is supposed to represent the width of a critical band. In fact I think they are somewhat narrower, and I include a correction factor to my ERB’s computed from the integrated squared filter shapes in Bark space.
>> 
>> // Widening of zBark ERB to ERBS narrower critical bands
>> static const Float64 erb_corr[11] = {
>>     1.7656471408430956,
>>     1.5228202413437684,
>>     1.377500488857015,
>>     1.2965004248294488,
>>     1.2511680396918075,
>>     1.2450925981903152,
>>     1.280018694958076,
>>     1.355985480009144,
>>     1.470871992963292,
>>     1.6195766260552696,
>>     1.7934642493495124 };
>> 
>> These factors are normalizers applied as divisors on the computed power coming through each Bark band filter. They have the effect of diminishing the measured power in each band. That in turn causes a bit more hearing compensation gain. 
>> 
>> As you can see from the (inverse of) the table, the more effective ERB measurement is around 80% of the one obtained from Bark frequency analysis.
>> 
>> Of course, none of this stuff is hard and firm. We are blind men in a room without lights, feeling our way around the perimeter…
>> 
>> I cannot really tell you that my analysis for hearing corrections will also work for spatialization. They might well be the same. But our localization sensations arise from activity in our spinal chord and brainstem. More like birds. It does not seem to be directly related to loudness perception.
>> 
>> Even the Haas Effect demonstrates this separation from loudness perception. You can have a fainter sound on one side, but with Haas Effect, you can make the sound appear to come from that fainter side. Think of our spatialization of loud bangs in a metropolitan area - gunshots or exhaust pops.
>> 
>> The key discoveries about loudness perception are just a few, but very important:
>> 
>> 1. All corrections must be computed in perceptual space (Phons & Sones), then mapped back to dBSPL which corresponds to the world of physical gains and amplitudes measured with microphones and oscilloscopes.
>> 
>> 2. We make the identification of Sones measure with the EarSpring vibration amplitude ratio measured against its value for 40 Phon. Because our hearing is a feedback control system with stiffening in response to growing loudness, the EarSpring vibration amplitude exhibits a cube-root compression compared to incoming power levels.
>> 
>> 3. For audiology corrections, the perception of sound is how many Sones above threshold the sound produces. The Sones / Power curve starts out very shallow at low sound levels, and then grows much more steep at higher power levels. Even though it is cube-root compression, it is still a positive exponent and so looks like a hugely steepening slope at higher input power levels. 
>> 
>> And so, to get the same perception of a loud sound as a person with normal hearing, you need to amplify the incoming sound by just enough to make the rise, in Sones, above the impaired threshold, produce the same Sones rise as heard by the person with normal hearing.
>> 
>> Since the curve is steepening at higher power levels, it takes much less amplification to produce the same delta in Sones.
>> 
>> This is quite different from our usual engineering and physics approach of looking at SNR’s to discern detectability. I can’t think of another arena where we look for changes above a threshold in the same manner.
>> 
>> But I attribute this profound difference to the difference between the physical world and our perceptual world. Our perceptions are not measurable with laboratory instruments.
>> 
>> —————————
>> 
>> Your ideas about trading gain expansion for gain compression with amplification might be interesting in your application. But for impaired hearing the worst thing you can do is to suppress the sound even more with gain expansion. At low sound power levels we are already below threshold and no amount of gain expansion is going to help raise the sound above our threshold.
>> 
>> ———————————
>> 
>> The single knob adjustment - imagine a hurricane storm offshore, heading for landfall. At the beach zone the most damage will be inflicted. But that damage drains away energy from the storm, so that as you move further inland the damage becomes less and less.
>> 
>> So too with hearing damage - the sounds enter the cochlea at the oval window and proceed downrange toward the apex of the cochlea. Treble frequencies are sensed by hair cells nearest the oval window. Bass sounds at the apical end of the cochlea. 
>> 
>> As damaging sound levels enter the cochlea, like a hurricane impinging on land, the damage wrought by the sound dissipates some of its energy as the storm moves deeper into the cochlea.
>> 
>> This is a simple system first mentioned by Isaac Newton, where the amount of damage is in direct proportion to the power of the storm, and hence energy dissipation is also in direct proportion. The solution of this differential equation is an Exponential decline. 
>> 
>> But if you measure sound in dB units, i.e. logarithms, then an Exponential decline is a straight line decline in dB power versus distance. But Bark frequency measure is a distance measure along the uncoiled cochlea. Hence hearing damage from loud sound exposure (Sensioneural) ought to exhibit a straight line decline in dB versus declining Bark frequency.
>> 
>> That straight line is best seen in dB-Bark space. If you try to show in dB-log Hz space, the overemphasis of the bass region in the log Hz axis cause an apparent cliff around 1 kHz, which masks the linear relation that you see in dB-Bark space.
>> 
>> So overall, there were just a handful of simple, but profoundly important, discoveries leading up to the Crescendo algorithm.
>> 
>> 
>> 
>>> On Nov 4, 2025, at 02:08, Yuri Davidovsky <[email protected]> wrote:
>>> 
>>> 
>>>> On 3 Nov 2025, at 23:40, David McClain <[email protected]> wrote:
>>>> 
>>>> For good musical listening, my current system in the lab here is using 11 bands, each 2-Bark wide. And it sounds amazingly good to me. The band centers are identical to the standard audiology testing frequencies.
>>> 
>>> I am not through the article yet, it will take me a few days to figure it out properly, but you also seem to mention there that 11 bands turned out to work quite well for the purpose, which is good news. I have been long brooding on a potential side project that does binaural processing (in short, it should take a multichannel record and upmix it into spacial audio for headphones (similar to what AirPods do when you are watching a movie with a DTS soundtrack)) and could not come up with a ballpark figure of the number of bands necessary without experiments, for which I simply do not have time at the moment looking into things that are supposed to make money.
>>> 
>>> I was planning to start as high as 96 Bark channels per ear and see how low it could go while still sounding convincing (96 was chosen as it is 4x of 24 bands number that I came up with for the optimal number of Bark channels, so 1/4 Bark channel resolution would be the result) but it appears according to your research that a relatively low number of bands can be usable. Now, binaural processing can be more finicky as your spatial resolution will worsen as the number of available bands decreases but it appears that even a relatively small number of channels might work, according to your findings.
>>> 
>>> A couple notes/questions in relation to the parts of the article I went through.
>>> 1. As I understand, essentially the algorithm is fairly straight forward: we have a sensitivity drop in each band below a certain dB threshold and so we attempt to make up for this drop by applying gain to the affected amplitude range?
>>> 
>>> 2. You call it [dynamic] compression in the text, however it also appears that it could also be called expansion, where instead of making loud parts quieter we make quiet parts louder (in other words, instead of applying gain adjustment to the signal above a threshold, we apply the adjustment below it)? One could be expressed in terms of the other, of course, but I think expansion is a little more descriptive since compression often assumes making things quieter by its very definition.
>>> 
>>> 3. I did not quite get the single knob correction philosophy (might be because I haven’t gotten deep enough into the article yet) as according to what has been said you need to apply the gain to each band individually. Does it mean there is a linear relationship among impairments across the bands? Meaning, say if in a band centered at 4kHz we detect some impairment, each subsequent band will have more and more of it with some simple scaling factor applied? (e.g. the threshold increases by 2dB in each subsequent band, or something similar).
>>> 
>>> There is a bit of maths to wade through too but for now I want to understand the core principle behind the correction, hence the questions. An interesting part is that it appears I came up with a lot of the same findings in relation to how Bark channels work as you show in your article (like the fact that they appear to dynamically anchor to a prominent frequency, a point of view that hasn’t made it mainstream yet, it seems), so it is reassuring to see confirmation in others’ work as it probably means that the chosen direction is correct.
>> 
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