[birdbrain]

I should have been clearer. I am also talking about moment-to-moment spectral complexity or entropy.

I agree that the point TFA is suggesting seems to be about the spectral complexity at any given moment in song - what you might call the timbre - and how nearly pure the tones in their spectrograms are. (They don't specify what species they're showing. Looks like several, but I can't ID them by eye.)

My point is that no, in fact, many bird species produce vocalizations that are indeed spectrally complex (beyond even just harmonic stacks) from moment-to-moment.

Take a look at song from a blue jay (https://www.remoteenvironmentalassessmentlaboratory.com/expl... ; not the best example, or one I produced, but an easy one to hand), particularly the syllables near the end of the clip. That's an example of a complex timbre.

And lots of species produce song and calls with features like this.