If you know you have a single frequency close to an actual frequency of interest, you can use the fact you know you're in an aliased band to get a precise frequency estimate.
Presumably there is an antialiasing low pass filter somewhere before JS gets to the data. I have a similar sample rate and it certainly didn't work at all for me.
aka a stroboscopic measurement,
but I don't think it will work well for this case.
I guess thats sort of like a weird PLL thing? But I'd imagine you'd have to have prior knowledge of which string you're tuning otherwise the analysis is going to alias against every harmonic.