This is the question:
Lets get basic. A Channel should mean a slice of the hearable audio spectrum which the aid can control the loudness AND compression and possibly other parameters.. A Band is a slice that you can only control how loud it is (gain) and narrows the noise gate.
Many experts think that the majority of loss types require only 4 to 6 channels.
There is a penalty to more channels....more means increased processing time which can lead to conflict with the sound coming through the vent which has zero processing time. And each additional channel increases the amount of inter-channel distortion and phase shift to the input signal.
So more is not always better.
It is a rare patient that benifits from more than 4 to 6 channels (notching out distorting hair cells.)
For most losses the only benifit to lots of channels is increased cost and more profit for the manufacturers and retailers. Ed
Just one caveat about the 'flat losses' as they appear on the audiogram: yes, that might look like you can just whack in one gain setting: in reality your canal resonance added to the insertion gain/loss of the device will produce a pretty squiggly line. Coupled with this, the output of the receiver is a damped sinusoid saw-tooth in it's natural state. Put all these things together and you have the potential to be massively askew at a particular frequency - in terms of the actual gain needed.
Now, as to the actual resolution: if you follow the articulation index measure that each octave contains roughly 20% of the speech cues (with a greater bias in the 2-4KHz area), you have a starting point. If you remove one of these octaves entirely to deal with a feedback issue, then you have eliminated the response from up to 20% of your potential speech area. I appreciate that there are other factors at play: including the roll-off between each channel and the efficacy of different feedback systems, but ultimately, if the aid is whistling, you have to turn down the gain a bit at that point - whether you do it obviously or not.
This leaves us with a trade off - how many channels is enough, how many is too much? - (NB Bernafon). Ultimately this is a design choice based on the parameters of the circuit, especially the clocking speed: going forward its going to be less of an issue due to Moore's Law. In a previous response on here I postulated that a 10-12 channels was probably enough, given that it adequately represents every conceivable audiogram, provides half octave accuracy for the feedback issue and allows frequency specific noise management to function properly with minimum disturbance of the adjoining channels. More than 12 channels is probably chewing more processor cycles than absolutely needed, but if you have the lateral capacity on your chip, why not, if there is a potential improvement in the end signal.
I'd like to address another point in relation to the alleged 'inter channel distortion' or 'compression artefacts'; you can bet your bottom dollar on the fact that whatever you think of the electronics engineers at a modern hearing aid factory/design house, they are doing their absolute utmost to prevent such issues. Likewise the delay within the circuit. Nobody benefits from more rubbish being thrown at their residual hearing.
Going forward, simultaneous binaural processing is pushing the aids to do more with the incoming signal on both sides, so the number of channels per aid will effectively double as the processing of the stereo signal can be done separately to improve performance in background noise with a combined decision on the output to each ear.
In conclusion a dozen channels is probably enough: that much used study illustrating the patient benefits of less than half a dozen channels doesn't actually have great credibility at all when you think about it, as the patient is unaware of what they are missing in all situations, therefore they can't tell relatively how effective an aid is being in those situations. It might sound prescriptive, but you can't ever appreciate the full effect of a view from inside, can you.
NB: Bernafon - Channel free or 10,000 channel technology has been around for a few years; having fitted quite a few in the past, some people really like the kind of performance, some don't. It's a shame that their not one of the 'main' manufacturers as this delivery mechanism will always be considered a bit 'second string' in the DeMant catalogue.