I know the voices dying with a dying fall
Beneath the music from a farther room.

from T.S. Eliot – The Love Song Of J. Alfred Prufrock on Rap Genius

A reference to the soliloquy of Orsino, the lovesick duke, in Act 1, Scene 1 of Shakespeare’s Twelfth Night. The exact text is as follows:

If music be the food of love, play on;
Give me excess of it; that, surfeiting,
The appetite may sicken, and so die. —
That strain again; it had a dying fall:
O, it came oer my ear, like the sweet sound
That breathes upon a bank of violets,
Stealing, and giving odour! Enough! No more.
‘Tis not so sweet now as it was before.

“Dying fall” refers to notes, in music, that fade away. These voices are themselves obscured by music as they fade.

“Dying” can refer to reaching climax, as in the archaic phrase “the little death.” If we take Prufrock to be in a whorehouse, he is referring here to the sexual cries he hears beneath the music. By saying he “knows the voices” he may mean he literally recognizes their owners because he comes there so often (no pun intended).

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