In terms of sheer familiarity, this piece has the same place in Jazz that the opening notes to Beethoven's 5th Symphony (dut dut dut duhhhh) has in Classical Music.
One of the advantages the Jazz Idiom enjoys often, and the Classical Idiom rarely does, is its ability to reinvent the familiar, over and over again:
Usually, when a Classical composition is finished, that's it; as evidenced here, a Jazz Composition can be rearranged and re-conceived in as many ways as the composer is inspired to do it.
This particular arrangement of "Satin Doll" has been turned into a showpiece for the rhythm section, especially the bass player...
...and as many times as I've heard (to say nothing of actually played) this tune, this was brand new to me.
(Was there ever a more elegant stage presence than Duke Ellington?)
Addendum, nine months later:
I just noticed this...
Such a tight ensemble, such flawless precision in phrasing, and what do you not see?
MUSIC.
These guys are playing this superlative arrangement FROM MEMORY.
The Duke played at my 21st birthday party on the 30th of Sept. 1969. The next day I was on duty At Cherry point Marine Corps air base Where he was playing. I stood back stage until he saw me stopped the music to play happy birthday to me. He sent cards to my father 2 to3 time a year . The last was 3 days before he died .. He was a great man.
I came here because there's a tumblr post that mentions this song.
Post from ed-nygma-variations
"i have a friend who is colorblind.
i have another friend with synesthesia where she sees colors when she listens to music
my colorbind friend has always wanted to see color and because my friend with synesthesia and my colorblind friend have the same taste in music, she describes color to my colorblind friend by relating it back to music
like 'the sky is duke ellington’s satin doll'
and it is the purest thing this is what pure friendship is"