The classic term might be melancholy, as it is used in this exchange between Amiens, who has been singing a sad song, and Jaques, who has been avidly listening, in As You Like It:
Jaques. More, more; I pr'ythee, more.
Amiens. It will make you melancholy, Jaques.
Jaques. I thank it ; I do love it better than laughing.
Amiens. My voice is rugged : I know I cannot please you.
Jaques. I do not desire you to please me; I desire you to sing.—I can suck melancholy out of a song, as a weasel can suck eggs. Come, warble, warble.
As Jaques says elsewhere in the same scene, his is "a melancholy of mine own, compounded of many simples, extracted from many objects; and, indeed, the sundry contemplation of my travels, in which my after rumination wraps me is a most humorous [that is, strongly felt] sadness." That is a pretty good description of the experience of luxuriating in the deep pathos of a heartfelt sadness.