The Great Below

For testing however, if you must visit the Dimension you can use "/execute in thegreatbelow:thegreatbelow teleport @p ~ ~ ~"

The Great Below plays Ancient City music from vanilla because it fits the theme perfectly and gives the player a sense of dread as they explore the dimension.

It also has a custom music track that can be found as a secret Music Disc!
The Great Below is an infinite mining dimension with giant open caves and a plethora of deepslate ores to excavate! (If you can avoid the warden that is...)
The Great Below itself is a direct  reference to the Nine Inch Nails track "The Great Below" and inspired the creation of the dimension. 

The Great Beyond is somewhat different, this dimension is meant to represent a sort of spiritual plane. The place where all souls are whisked away to as their final resting place. Except something is wrong, it isn't paradise, it's actually quite unsettling. There are these Soul Engines that seem to be using souls to power something, it feels desolate and ominous. 

There is a bigger picture here, one that you are not privy to. You are merely a living interloper. 

There are lost souls floating about and they are being harnessed by the Soul Engines. The lost wayward souls floating aimlessly through the endless abyss of The Great Beyond. 

What are these Soul Engines powering? You have far more questions than you have answers.

My personal headcannon is that every time a player or creature dies in Minecraft their soul is sent to The Great Beyond. 
But why don't you get sent there when you die? What makes you special? That is a mystery that is worth solving!

I wanted to pick a theme that would make the player feel small. As if they ended up in a place they really shouldn't have and looked behind the curtain to their despair.

Ghosts 1-1 is a track I adore by Nine Inch Nails, who are one of my favourite bands. What's special about this track and the entire Ghosts album is its license which is Creative Commons.
Trent himself even encouraged people to take album and use it for creative projects. 

Ghosts 1-1 is an incredible track and a masterpiece. 
You can find an altered version of the track in The Great Beyond, but as to how you get it? You'll just have to figure that out yourself!

(I have added a slight reverb, more distortion, slowed the track down and converted it to mono from stereo to support Minecraft jukebox playing)

My belief is the lost souls themselves are singing.. Or crying. It's up for interpretation.

I have plans to do a lot more with this dimension, but for now it's a bottomless abyss with no end in sight.

Credit: Nine Inch Nails  Ghosts 1-1
Credit: Mojang