My mind is kind of blown that birdsong virtually does not include higher harmonics. I didn’t even think that was possible for a physical resonator. Great post
I think the mystery has a simple explanation: when a bird sings at 7 kHz and the mp3 file captures only first 20 kHz, there isn't much room for harmonics. Maybe birds do have interesting harmonics at 56 kHz, we just don't know.