The best!! The best of the best melancholic sax player ever is GATO BARBIERI,no doubt; the next 3 are??

Listen to this marvelous man and his particular sound....oh yes;my eyes....tears.

Gato is masterful on 'Europa' - that is one of my all-time favorites.
John Klemmer's 'Touch' is also an excellent 'melancholic' sound - check it out.
James Moody on 'Moody's Mood for Love' is legendary, as well as Phil Woods' alto on Quincy Jones' 'Quintessence'.

Paul Desmond
Candy Dulfer
Branford Marsalis

Non-Jazz :~

Dick Parry
Raphael Ravenscroft
Kenny G

Mindi Abair, Dave Koz, and Boney James.

Runner up: Richard Elliot, the late Grover Washington, Jr. and Najee

Ernie Watts, Wayne Shorter, Stan Getz.