Biasing cap and filter response

1uF

While looking for the reason why the filter output jumps frantically between +/- max when the cutoff is low or the input is close to zero when turning up distortion (spoiler: it's the biasing capacitor), I realised that I should have a closer look at what the output biasing/centering capacitor is actually doing to the filter's response. 

The cap is there to make sure the output is centered around 0, i.e. filter out any DC component (AC coupling the signal). The higher the capacitor, the longer the filter takes to change to 0V after an abrupt (DC) change. In the case of the jumping described above, I would like the change to settle as fast as possible, which means replacing the current 1uF cap with a smaller one, but what would that do to the output?

Looking online, it seems that the most common value of cap is 10uF. The Juno synths use 1uF. The cap in combination with a resistor/resistance creates a high pass filter with the cutoff frequency f=1/(2*PI*C*R). In my case, I have an 82k resistor immediately following the cap so I assume that this is R in the formula (the JP8 uses 100k and Juno 6 56k + a 20k trimmer).

The red line in the first plot here shows what our current 1uF cap does.

0.47uF

1uF 3dB

The 470uF cap clearly moves the cutoff frequency higher. Its -3dB point is at approximately 2.9Hz, compared to the 1.4Hz of the 1uFthe calculated values are 1.94Hz and 4.2Hz so 82k is at least close to the "real" resistance).

0.47uF at 20Hz

The human hearing is usually considered incapable of hearing frequencies of less than 20Hz. At this point the 0.47uF cap attenuates the signal by 90mdB. This in itself is not a lot, but it means that any sub-audible, ground shaking frequencies are filtered out. This may not be a problem as the equipment later in the chain may also have similar filtering, but it is something to think about.

10uF

In comparison, the 10uF cap gives a cutoff of less than 0.2Hz which is probably the reason why it's the more common choice.

0.047uF

I've seen some designs use a 47nF cap. This gives a -3dB cutoff at 370Hz which is a complete no-go combined with my 82k resistor.