An Arduino Nano? What a waste... Just use a PIC or an ATTiny. Spending even $1 for something so simple is unnecessary.

For personal projects, it's not often the case that you need to get BOM cost as low as possible and disregard other factors (like debuggability, or having enough DSP available to run the FFT for tuning calibration (though I suspect they'd be better off with autocorrelation...), or room for future expansion (adding multiple channels, adding a sequencer, adding control over the filter, implementing envelopes, running the Pi's audio output through the filter too...)

Plus, they might have had the Pi before, and still have it afterwards. That's the nice thing about general-purpose computers- you can put a whole bunch of different software on them, and then switching between uses just involves moving the board itself and plugging cables in.