So say you're watching some TV and you turn the volume way down. You can kind of hear what's going on, but it's mainly background noise now. That's sort of the experience of reading One Day in the Life of Ivan Denisovich. The narrative often turns the volume down on emotions, so to speak, so that the tone becomes sort of quiet and muted in a way. This fits with the book's theme on futility, or the uselessness of doing much. Life in the camp is one of putting up with lots of injustice and the exhaustion that comes from that, which is reflected in the novella's overall tone.
But in the overall tone there's also lots of stress and anxiety (and sadness and anger and all the other things you'd expect people to feel in a prison camp). The emotion doesn't whack you in the face though. Shukhov isn't running around delivering anguished soliloquies or ranting and raving. The emotional outbursts we do get in the narrative are either pretty short-lived or are almost perfunctory, or delivered without any real sentiment behind them. Anger and violence seem to be how people deal with each other in the camp, and feeling anger and despair over life in the camp is also a normal state of affairs.
So what connects these deep emotions to the muted, exhausted tone often used in the narrative? That would be irony. Irony is a sort of black humor, a way of saying something that's funny but in a dry, dark sort of way. Irony can be a way to get a serious point across, or to highlight a serious situation, without being overly serious about it. So here's an example:
He's expected it, all right, but hearing it nevertheless cut him to the quick. Who wouldn't be sorry for his precious Sunday rest? Of course, what they were saying in the queue was true enough: your day off could be hell even in camp, they could always think up something for you to do [...]
Nothing seemed to upset them more than a zek sleeping after breakfast. (932-933)
While this scene starts out with some emotion (Shukhov is upset that he won't get Sunday off), it quickly switches over to a sarcastic list of how zeks usually get to "rest" on Sundays and ends with an ironic statement. Irony crops up all over the novel, in the narrator's tone, in Shukhov's thoughts and expressions, and often in the dialogue too.
During an angry scene at the mess hall, this exchange occurs, and Shukhov has a thought to add:
"104, form up in fives," Pavlo shouted down at them. "And you make way there, friends!"
The friends would be hanged first. (979-80)
Calling an angry mob "friends" is pretty funny in a dark sort of way. Sarcasm and irony seem to be good coping mechanisms in the camp, so it makes sense that the overall tone of the book reflects this, along with the emotional exhaustion and the periods of intense anger/sadness/stress that characterize a zek's daily life.