Definition: EPIPHANY (eh-PIF-a-nee)
3b. A comprehension or perception of reality by means of a sudden intuitive realization: "I experienced an epiphany that would change the way I viewed myself." (Frank Maier)
"I had an epiphany that I would NEVER AGAIN spend so many hours sequencing a difficult or unique song like this." (Texas_PhoneMan)
"Epiphany" is when Sweeney Todd has just missed (what appears to be) his only chance of getting his razor at the lecherous Judge Turpin's throat. His mind snaps and his epiphany transforms him from an unjustly punished and vengeful man to a cold-blooded serial killer.
He vows to indiscriminately kill anyone in his barber chair until he finishes his "work". He even turns on the audience asking them, "How about a shave? No one in the chair--come on!"
The music is eerie, clanging and almost painfully dissonant (very Prokofiev-like) but makes for 3 minutes of extremely powerful theater.
This file even reflects how the music accentuates Sweeney's mind splintering.
Towards the end of the number, the orchestra begins to sound like "a bunch of broken cuckoo clocks" (a quote from a 'friend')-- after Todd's mental breakdown, he sings "...and I'm full of joy!", after which the orchestra seems to try to get him (vocally and mentally) "back on key" for a "satisfying conclusion" by blasting the resolved dominant chord while the strings eerily sustain the unresolved, dissonant chord. ("vanilla" description)
This served a dual purpose as the director wanted no break for applause between the end of the song and the next dialogue. By the time the audience realized the song was over and that chord was not going to be resolved, the scene had continued and it was too late to applaud. Besides, the next song is "A Little Priest" which is the finale of Act 1 and definitely brightens up the show after all that "gloom".