> I tried learning to play a recorder (flute) using some internet howtos as a guide, but got stuck at the first lesson, when the sound produced by the flute didn't match what the Fourier analyser in audacity measured.

> That is, I tried to play a C, but the Fourier transform resulted in a bimodal distribution, and none of the bumps was near the expected C frequency.

What a wonderful experiment! You've uncovered "harmonics": your recorder (or any instrument) sounds a complex mixture of frequencies, even when you play just a single note. The different mix of frequencies from one instrument to another is what gives each a unique sound, called the "timbre". The harmonics of wind instruments like your recorder are particularly complex! Try the same experiment with a stringed instrument, which will make something closer to a pure sine wave. Try it with anything that will make noise!

But I'd recommend not using Audacity to learn to play an instrument. You need your ears for this, so it may as much effort developing listening as developing playing technique. But in the end, don't worry too much about that, just have fun making music!