Quickest and easiest algorithm for comparing the frequency content of two sounds
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I want to take two sounds that contain a dominant frequency and say 'this one is higher than this one'. I could do FFT, find the frequency with the greatest amplitude of each and compare them. I'm wondering if, as I have a specific task, there may be a simpler algorithm.

The sounds are quite dirty with many frequencies, but contain a clear dominant pitch. They aren't perfectly produced sine waves.