Cozy Voice for Catastrophes

The work you are reading deals with some dark, dark things. Distressingly unique methods for killing characters, living manifestations of dark psyches, and things that should traumatize every character in the story for life.

So, naturally, this should be treated with the deathly serious import such subject matter warrants, right?

No, actually. One school has it that if you're going to revolt your reader, you'd better do something to make your story easy to read. So the narrator or viewpoint character will speak of those horrific topics in a calm, sort of folksy way that both engages and detaches the audience. It's also applicable to audio and video.

Examples of Cozy Voice for Catastrophes include:

Film

Hitch Hikers Guide to The Galaxy's radio and television series both had a cheerful, soothing narrator, played by Peter Jones (succeeded for the revival of the radio series by William Franklyn). The Movie had the below-mentioned Stephen Fry.
- In one particularly stressful scene in the television series, he assures the main characters' safety in advance while pleasant images appear on the screen.
- 'And it has the words "DON'T PANIC" printed in large, friendly letters on the cover!'
The film of The Color Purple depicts things like a teenage girl twice pregnant by her father against a backdrop of lush, bright colors and a charming array of Southern accents.

Literature

The Green Mile is the epitome of this. People's faces are melted off more than once, but the tone is always that of an old man with good stories to tell.
- Stephen King novels in general have a very folksy, affable quality to the narration, no matter what nightmarish situation they're narrating.
Old Man's War is similar, right down to the, well, old man. The aliens they fight each have their own unique way of being horrifying, but the narrator's matter-of-fact tone sees you through.
This could almost be considered Amélie Nothomb's trademark style. Fear and Trembling is an excellent example.
Ender's Game is a borderline case - Ender is not exactly a poster child for Angst? What Angst?, but he's still a child discovering new things, affording the proceedings a kind of wonder.

Live Action TV

Mohinder Suresh from ABC's Heroes often spoke the opening narration in a tone that makes the show's techno-babble easier to digest.
A possilbe alternative name for this trope is "The David Attenborough Narration". Such a calm soothing voice, easing you through the violently graphic imagery of a seal being snatched from the beach and shredded by Killer Whale.
The narrator of Pushing Daisies was voiced by Jim Dale. Every episode we would hear him describing creatively violent murders in dulcet English tones.

Music

"Weird Al" Yankovic is notorious for this. A perfect example of this is "Good Old Days".

Video Games

GlaDOS of Portal isn't just a sadistic killer operating system - she's a really, really quotable sadistic killer operating system.
Vigil in Mass Effect. He lays it all out in a relaxed, calm manner.
Bastion applies this both visually (through a cute, childish art style) and aurally (Logan Cunningham, an actor with no previous major credits, has been noted by multiple reviewers to give very soothing narration even when listing off the names of all the dead people the protagonist finds in the street.)
Stephen Fry provides the voice over for LittleBigPlanet.

Voice Actors

Paul McGann has a soft, pleasant voice, and has said in an interview that for this reason he's often asked to narrate documentaries on frightening topics.
Referenced in this picture of Morgan Freeman. And this one.
- As shown by xkcd.
The British equivalent to Freeman, Stephen Fry, can also do this, and he in fact did with two very personal documentaries about very frightening things (HIV and bipolar disorder).
As referenced above, Sir David Attenborough has a calm, soothing voice that make the most heart-rending scenes in a documentary less awful.

Web Original

The Little Fears: a YouTube personality. Makes videos wherin she recites Creepypasta stories, 'true' accounts, and her own made up tales in this manner.

Western Animation

Oliver Postgate never used this in his many fondly-remembered cartoons, but Charlie Brooker invokes it in his glowing obituary for him:

There is no more calming sound in the world than the voice of Oliver Postgate. With him narrating your life, you'd feel cosy and safe even during a gas explosion.

In ThunderCats (2011) Court Mage Jaga (veteran voice actor Corey Burton) has an Opening Monologue wherein he describes the necessity of a kingdom's fall in a reassuringly pleasant tone.