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I haven't done FFT yet, but what I have done is make a spectrogram from the Discrete Fourier Transform.

The audio being visualised is white noise that is being put through a band pass filter, with the passband being sweeped up and down the frequency range to "pitch" the noise.

The x-axis is logarithmic because otherwise note frequencies got scrunched up on the far left. It also has the nice effect of showing the sine clearly, though! https://mastodon.social/media/tKafhn8piHPKK2OjAjw