Its called opera.

Tommy is the rock opera album by the who that is all one story

This question has some weird conditions on it - "doesn't repeat itself" is the most troubling one. Pi has an infinite number of sevens in it (so it repeats the same values quite often) but it's unique in its entirety - it also has infinitely long blocks that are repeated because, you know, infinity be weird like that.

I'd point you to a symphony like Vivaldi's Seasons or, if you're willing to substitute "words I can't understand" for "words" (and don't happen to speak German) Der Ring des Nibelungen. While the later does have talkie bits understanding those gives you barely any more context than the raw emotion of the music.

But, both of those (and all music that doesn't suck) relies heavily on repetition... but they're also unique overall (unless they don't have a strictly defined form aka jazz but now we're really in the weeds)

Thick as a Brick

Halloween by Helloween.

2112 by Rush.

Waters of Black Mesa https://youtu.be/NNJS0iO9uyo

I'm also ignoring the without words part to share Aesop Rock.

The Hurricane by Bob Dylan

https://youtu.be/bpZvg_FjL3Q?feature=shared

Not a song, but two whole "fuzz rock/metal" albums written to work as one long story: Howling Giant's Black Hole Space Wizard Part 1 and 2

The story isn't super direct, but it's about an escape ship fleeing the dying earth, crashing (Part 1) leaving one survivor, and him going on a maddened journey to become the earth wizard (Part 2).

A bit less obscure is the Protomen's Act 1 and 2, a rock opera fan fiction based off Megaman

Exquisite Corpse is ostensibly a George Watsky song but the featured artist list includes Adam Vida, Chinaka Hodge, Grieves, Wax, Rafael Casal, Daveed Diggs and Dumbfoundead

It's called what it is for a reason, and it's also a 10-minute long epic poem about the post-apocalypse. One of my very favorites.

It's all words though.

These have words but might still fit the other factors:

Bohemian Rhapsody - Queen Horses - Patti Smith

Aqualung by Jethro Tull may meet your needs. If you're Will ng to flexible in your definitions the the Crane Wife cycle by the Decemberists might also fit .

"The chances of anything coming from Mars are a million to one he said"

~ Jeff Wayne's War of the Worlds epic

We Lost the Sea had some songs that retell stories, mostly through audio:

• Challenger parts 1&2 are my favorite, about the Challenger disaster
• The Last Dive of David Shaw is also very good

Eminem - Stan

Olias of Sunhillow alternates between instrumental and lyrical tracks, and both tell the story of a bucolic species going to space in a wooden boat. It is the proggest of prog rock. If you enjoy anything by Yes, this is the main lead guy's solo debut, and it is right in the same notch as Fragile and Close To The Edge.

The Mystic Crystal by Ninja Sex Party is a great story song.

Also most of TWRP has songs that tell stories, like Starlight Brigade or Black Swan

(maybe without words)?

In the Hall of the Mountain King by Edvard Grieg. It's not that long though.

Light of Day, Day of Darkness by Green Carnation. Album length track that is a rock opera.

Its technically an album, but the "continuous mix" of Thomas Bergersens American Dream

Dream Theater does a really long song almost every album, but they all have words

A 5-minute long song, it has words but it kind of tells a story

Darkness Fell by Wolfgang(OPM Band)

Blues Traveler - Hook

Bowie - "Wild Eyed Boy From Freecloud"

Bowie - "Cygnet Committee"

Deathbed by Relient K. Used to be one of my favorites, very heartfelt and bittersweet.