Formal, Laudatory, Pious, Mournful
The narrator of Beowulf uses several different tones over the course of this long epic poem, but throughout everything he is always super formal. This isn't a chummy, chatty, nudge-you-in-the-ribs kind of narrator. Instead, everything in Beowulf seems to be spoken with grave, calm, even stiff formality. We see this in the characters as well as in the narrator; even Beowulf himself announces his own name through an elaborate speech about his deeds:
"So every elder and experienced councilman among my people supported my resolve to come here to you, King Hrothgar, because all knew of my awesome strength. They had seen me boltered in the blood of the enemies when I battled and bound five beasts, raided a troll-next and in the night-sea slaughtered sea-brutes. I have suffered extremes and avenged the Geats (their enemies brought it upon themselves, I devastated them). Now I mean to be a match for Grendel, settle the outcome in single combat." (415-426)
Although his tone is always formal, the narrator of Beowulf does shift between three more specific tones, depending on what's happening at the moment in the story. When Beowulf or someone else is behaving especially heroically, the narrator becomes laudatory, or praising:
Thus Beowulf bore himself with valour; he was formidable in battle yet behaved with honour and took no advantage. (2177-2179)
In fact, we'd go so far as to say that this narrator does some real boot-licking. To listen to the narrator, you'd think that Beowulf was just the most awesome, honorable, powerful hero who ever lived—which is exactly what epics are supposed to be about.
But when Beowulf starts losing, the narrator becomes mournful, lamenting the hero's defeat and the suffering of the people, or pious, reminding us that all heroism is dependent on God's favor: