I guarantee I'll be back to right some wrongs here; I KNOW I'm leaving out some significant ones. But here's my first cut:
Additions in RED
- WC Handy
Scott Joplin
Eubie Blake
Louis Armstrong
Jack Teagarden
Tommy Dorsey
Glen Miller
Harry James
The Count (Basie)
The Duke (Ellington)
The King (Nat King Cole)
The Queen of Soul (Aretha Franklin)
Ella F
Lou Rawls
Ray Charles
Sarah Vaughn
Charles Mingus
Thad Jones
Lionel Hampton
Slide Hampton
B.B. King
Stevie Ray Vaughan
George Benson
Stevie Wonder
Stanley Clark
Chic Corea
Maynard Ferguson
Bill Watrous
Don Ellis
Joe Ely
Whoever played bass-bone for all those old Sinatra recordings (probably a lot o' George Roberts?)
Itzhak Perlman
Bing Crosby
Roger Whitacre
Robert Goulet
Roy Orbison
Marty Robbins
BJ Thomas
Karen Carpenter
Neil Diamond
Jimmy Buffett
Jim Reeves
Glen Campbell
Willie Nelson
George Jones
James Pankow (Trombone for Chicago)
Steve Perry (Journey)
Ian Anderson (Jethro Tull)
Don Henley (Eagles)
Alison Krauss
John Williams
Jerry Goldsmith
Jay Lerner**
Fredrick Lowe
Richard Rogers
Oscar Hammerstein**
Anthony Lloyd Weber
Bryan Duncan (Christian)
Stephen Curtis Chapman (Christian)
Keith Green (Christian)
Wintley Phipps (Christian)
** I realized after posting this that some people might think that these librettists (that means that guys that wrote the words, for those of you in publik skools) don't belong; but I argue that the words, in their cases, are so integral to the phrasing of the music that they have, in fact, been significant influences.
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Joe Baker, who reminds the reader of this list that when one describes another person's tastes, the word isn't "weird" but "eclectic"

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