Here's Wynton's version (with Eric Clapton singing):
http://www.youtube.com/watch?v=fwz8kVO3i34
Note that Wynton doesn't recreate Louis's trumpet breaks. He sort of tries in the opening, around 0:33 to 0:41 or so. But Louis's breaks are louder, faster, and higher!
Clapton sticks pretty close to Louis's vocal, but at 2:28 his phrasing is cornier than the original.
Spectrogram and spectrum plot of Wynton's trumpet: http://subbot.org/misc/music/buddy/wynton_last_time1.png
The spectrum is taken from the high note just to the right of the plot, at about 19.65 seconds on the spectrograph. There is a lot of energy in the higher frequency ranges. Note the bump around 10k, and the regular sawtooth nature of the spectral profile.
Maybe because of the recording quality, the spectrographic and spectral analysis of Louis's trumpet does not show any energy above 5k or so. I have a recording of this tune; I might try to see if I can get a better quality recording to analyze.
The hypothesis is that Louis's distinctive tone (which Wynton in this recording is clearly trying to reproduce) has a lot of energy in the higher frequency ranges (like bird calls).
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Previous relevant diaries:
http://www.kuro5hin.org/story/2012/9/8/3212/27826 "Why do old rockers turn to jazz in the end?"
http://www.kuro5hin.org/story/2013/2/10/233747/866 "Spectrographic analysis of a cockatiel call"