Inon Zur, composer of all of the Fallout games since Fallout Tactics, has worked his magic for Fallout 4, and Bethesda has a released a video showing him playing the game's main theme on piano.
In a post on Bethesda.net, the company said Zur suggested piano play a prominent role in the post-apocalyptic role-playing game because Fallout 4 offers a more personal story than previous games in the series. Fallout 4 features voice acting for the player character - a first for the series - and many more lines of dialogue than other Fallout games.
Present and correct within the Fallout 4 main theme is the two chord refrain Zur drummed up for Fallout 3. Here's an interesting tidbit: it was designed to reflect "the dualism in Fallout".
"...the despair of war," Zur said, "but also the hope for the future. In Fallout we're always torn between the despair and the darkness and all the dangers that are lurking in the world, and the hope to build a better world."
What we hear is a minor chord leading to a major chord. "These two chords combined - always the minor and the major together - give us this bittersweet Fallout feel," Zur said.
"It's the signature of Fallout. You start from the bleak and you go to the hope. Very simplistic but works like a charm every time."
For comparison, here's the Fallout 4 theme as it sounds on the game's trailer.