Neuro person here.

Yes, many neurons fire at discrete intervals set by their morphology. In fact, this DFT/FFT/Infinite-FT/whatever-FT is all the hell over neuroscience. Many neurons don't really 'communicate' in just a single action potential. They are mostly firing at each other all the time, and the rate of firing is what communicates information. So neuron A is always popping at neuron B, but that tone/rate of popping is what affects change/information.

Now, this is not nearly true of every single neuron-neuron interaction. Some do use a single action potential (your patella knee reflex), some communicate with hundreds of other neurons (pyramidal cells in your cerebellum), some inhibit the firing of other neurons (gap/dendrite junction/axon interactions), some transmit information in opposite ways. It's a giant mess and the exact sub system is what you have to specify to get a handle on things.

Also, you get whole brain wave activity during different periods of sleep and awake cycles. So all the neurons will sync up their firing rates in certain areas when you're dreaming or taking an SAT of something. And yes, you can influence mass cyclic firing with powerful magnets (TCMS).

For the cochlea here, these hair cells are mostly firing all the time and then when a sound/frequency that they are 'tuned' to is heard, then their firing pattern changes and that information is then transmitted toward the parietal lobes. To be clear too, there are a lot of other brain structures in the way before the info gets to a place where you can be conscious of it. Things like the medial nuclei, the trapezoidal bodies, the caleyx of Held, etc. Most of these areas are for discriminating sounds and the location of sounds in space. So like when your fan is on for a long while and you no longer hear it, that's because of the other structures.