What I see are six or more distinct parallel lines, or overtones. There is significant energy throughout each of these lines. (When I try to whistle this call, I find I can usually only get energy in the lowest frequency range; above that is an amorphous cloud without the clearly-delineated lines in Buddy's vocalization.)
(I thought a piano chord might produce parallel lines like that, so I recorded a C chord; but parallel lines such as those in Buddy's spectrogram are not visible.)
Buddy's doing something different than I can do when I whistle; he's producing significant energy in distinct frequency ranges. The ranges appear to be (mostly) multiples of the lowest frequency. However in the fourth note, which is the loudest and longest and which bends, there are more than six distinct ranges. It's almost like he's producing two separate notes at once, and then bending them.
Note how the last note and the second note are the same.
This bird has perfect pitch; often when I'm using the microwave, he'll sing (before, after, or synchronously) the exact sound it produces to signal it's done.
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My hypothesis was that Armstrong's trumpet produces frequencies in parallel ranges, like birds do.
Here's a short section from about 0:23 of Nobody knows the trouble I've seen, as a spectrogram: http://subbot.org/misc/music/buddy/louis_nobody.png
There aren't distinct parallel lines as in Buddy's spectrogram. The main energy seems to be bunched up in the lower ranges, under 4k. Buddy can get high energy (the white parts of the spectrogram) up to 10k (on the fourth note), and his formants are clearly distinct and tight (in narrower ranges) up above 19k.
The resolution for Louis's trumpet sound doesn't seem too good. I'd like to continue playing around, see if I can get clearer lines, maybe on some of Louis's loud, high notes.