[munificent]

Not a DSP expect by any means, but I think you can do better pitch detection without using an FFT. Instead, you want something like auto-correlation:

https://en.wikipedia.org/wiki/Autocorrelation

[whiw]

I'm not sure it is better, unless you can do autocorrelation in hardware without using an fft. This option is unavailable on standard PCs.

If done in software then a simple implementation of autocorrelation is O(n^2). An efficient implemementation is O(n.log(n)) (it uses two ffts).