The piezo goes through a very simple high-pass filter into the op amp w/ PGA set to 16x, then on to the ADC. 

(piezo is connected to the terminal on the right)

This should give me about 1.5Khz cutoff to filter out the DC and any bass. I don't yet know exactly what kind of frequencies I'm dealing with yet. What does a 'tap' look like? The connectors (J4, J9) let me probe and experiment with values if necessary. 

So with everything hooked up, lets see what we get:

Beautiful! But... WTH are icicles doing in the data? Also my circular buffer math is off, signal starts about 1/16th of the way in and wraps around.

It's on all channels at the same time! 

I double checked power supplies. Maybe something on the chip (USB perhaps?) was activating on some interval causing load spikes on the power supply? I thought I added enough decoupling caps by following the datasheet!

Maybe some kind of ADC spitback even though it's fed into the op amps? Did I create some kind of resonant circuit with the piezo?

I tried disabling everything else the chip was doing. I tried changing the PGA gain. 

Scoped everything (power, piezo inputs, pre op amp, post amp, ref voltages). I didn't find any causes, my poor scope (owon DS7102V) is either blind to the icicles or the probe suppresses them. 

Mystery Fix

I experimented a bit. Adding a 10k resistor in series with the piezo fixed the weird icicles, but I don't yet know why. 

Noise is now about 2-3 LSB and some of that might be background audio getting picked up, or stray EMI on the piezo leads. Will have to check that out at some point, but the above looks plenty fine for tap detection and correlation!

Maybe Related

The PGA has a fixed GND reference, so I can't just float 1/2 of 3.3v on the op amp. Instead I use the DAC to output a reference voltage that once multiplied by the PGA is about 1.65v. By changing the DAC and PGA at the same time, I can keep close to ideal range and still have programmable gain control.

So theoretically glitches on the DAC or extra buffer could be the cause, but scoping this didn't show noise.