Read the excerpt from Twelfth Night, by William Shakespeare. 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 o'er my ear like the sweet sound,
That breathes upon a bank of violets,
Stealing and giving odour!

Now read the excerpt from "The Love Song of J. Alfred Prufrock."

For I have known them all already, known them all:
Have known the evenings, mornings, afternoons,
I have measured out my life with coffee spoons;
I know the voices dying with a dying fall
Beneath the music from a farther room.

What does the phrase “dying fall” most likely mean in both excerpts?