[topspin]

It makes sense to me that bird song would have few harmonics. Although we may appreciate the beauty of bird song they don't sing for aesthetics. They are signaling. Concentrating energy into a narrow band delivers greater range for the same energy than harmonically rich signals. We do likewise with electromagnetic communication.

[crazygringo]

I think the explanation is even simpler.

For a loud, high-pitched sound produced from a tiny object like a bird, is it even physically possible to have the loud resonances needed for overtones and timbre? I think it's just physics.

Whales are "signaling" over huge distances too but have plenty of overtones, since that's what low frequencies in huge cavities produce.

I'm not sure the dichotomy between "aesthetics" and "signaling" you suggest actually exists. A peacock's plumage is certainly aesthetics but also certainly signaling. And what is a birdsong's melody if not aesthetics?

[periheli0n]

When a bird sings to attract a mating partner, competing against other birds, does it not sing for aesthetics?

Also, couldn’t harmonics be used to improve decoding in noisy environments? Spreading the signal over a wide band is not unheard of in man-made electromagnetic communication either.

[karmakaze]

When using spread-spectrum transmission it would be counterproductive to utilize harmonics. Non-sinusoidal noise at frequency F would pollute frequencies k*F. Also the transmission band is likely less than an octave.

[enchiridion]

I just had two thought considering this:

1. Do we appreciate bird songs because they indicate a resource rich/hospitable environment?

2. Do birds hear the entire range of the song, or just pick up specific bands?