How this tone stack works

This is the tone control that ships in the classic Big Muff, and it is nothing more than a potentiometer that sort of "pans" between a low pass filter and a high pass filter. The treble path runs from the input through C1 to the top of the pot, with R1 holding that node to ground: a simple RC highpass, corner at 1/(2π·R1·C1), about 1.54 kHz stock. The bass path runs through R3 to the bottom of the pot, with C2 shunting that node to ground: an RC lowpass, corner at 1/(2π·R3·C2), about 408 Hz stock. The pot track spans the two paths and the wiper is the output, blending between them.

The scoop comes from the gap between those corners. The lowpass gives up at 408 Hz, the highpass does not wake up until 1.54 kHz, and in the octave and a half between them neither path passes much of anything. With the stock parts at noon the response bottoms out at −12.7 dB around 934 Hz, while the band edges hold about −7.0 dB (bass) and −6.1 dB (treble). That puts the audible scoop roughly 6 dB below the shoulders, and it means the stack throws away more than half the signal even at its strongest point. That loss is a design choice: the Big Muff has huge gain ahead of this network and a recovery stage after it, so the stack can afford to be wasteful in exchange for its shape. However, this is part of the tradeoff with passive tone stacks.

At high frequencies C1 is effectively a short and C2 has already grounded the bass path, so the treble you keep is set directly by the wiper: the high-frequency level is exactly the knob fraction, −6 dB at 50%, 0 dB at full treble. At the bass end the caps drop out and the whole thing is a resistive divider, (R1 + (1−t)·pot) over (R1 + pot + R3). In between, turning the knob toward treble drags the dip down the band: about 2.0 kHz at 25%, 934 Hz at noon, 534 Hz at 75%. Near the ends of the travel the dip dissolves into a plain bass or treble tilt and the scoop cards blank. The pot value matters too, because the track loads both paths: a 1k pot at noon musters only a −10.0 dB dip way up at 4.3 kHz, the stock 100k gives −12.7 dB at 934 Hz, and a 500k barely improves on it at −13.4 dB. Past 100k the paths are essentially decoupled, which is exactly why the stock pedal uses that value.

The numbers above assume a buffered, low-impedance source in front and a high-impedance stage behind the wiper, which is how the real pedal runs it (a transistor stage on each side). Break the input assumption and the source impedance piles onto both paths at once: 10k of source resistance deepens the noon dip to −15.2 dB and drags the treble edge down about 5 dB. Break the output assumption and the load bends the blend: a 100k load on the wiper pulls the whole curve down 2 to 3 dB and sinks the dip to −15.0 dB. The dashed curve is the nearest-E12 build; the stock values are already E12, so it hides under the solid curve until you type in something odd.