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Sensitive dependence of ratios

For the comparison between the two musical extracts at the start, it might help a bit if you're listening through a good-quality audio device. The two extracts were created in Noteflight. The spectrograms were produced in Wavacity. The music is from the 2nd movement of Beethoven's Sonata No. 32, Op. 111, which you can hear professionally performed at    • Maria João Pires:  Beethoven Sonata n. 32 ...   (The part occurring in this video begins at 6:24, but it's nice to listen from at least about 10 seconds before that point.)