The Enneagram is a system positing nine basic personality types in the human race. You can read more about it here. Type Five is the Investigator, the Observer, the Innovator, the Specialist - cerebral, perceptive and secretive. Two prominent Fives in music are Bjork and Tom Waits.

Fives don't follow the crowd. They pursue their own inclinations, usually outside of any kind of institutional learning (Fives are often intelligent drop-outs), self-educating, delving deeply into whatever interests them for hours, weeks or years at a time, amassing knowledge with no immediate practical value. They get off on explorations of unknown territory and neglected subjects.

Tom Waits said: "I'm interested in things when I don't know what they are. Like 'Hey, Ray, what the hell is this?' Oh, that's lipstick from the 1700s, that's dog food from the turn of the century, that's a hat from World War II. I'm interested in the minutiae of things. Oddities."

Bjork said: "I wouldn't mind working in a shop like 12 Tónar selling records, or having a radio show where I could play obscure singles. I would also like to teach music. It's weird the way they teach music in schools like Julliard these days. I know someone who graduated at age 20 as a classical composer, playing music the way they did a hundred years ago or more. I would take kids out into nature, and teach them that they can be right, and not just the teacher. I would let them lead the way. To some degree, at least…"

Fives don't avert their eyes from horror, chaos, destruction and atrocity. They look right at it, with straight-faced interest and appraisal. Check out Tom Waits's declaration that Misery is the River of the World, from his album Blood Money. He sings this with no sadness, the way a Four might. He's the carnival barker, the ringmaster, the coxswain on the boat, enjoining everyone to row…

The higher that the monkey can climb

The more he shows his tail

Call no man happy till he dies

There's no milk in the bottom of the pail

God builds a church

And the devil builds a chapel

Like the thistles that are growing

Round the trunk of a tree

All the good in the world

You can put into a thimble

And still have room for you and me

If there's one thing you can say about mankind

There's nothing kind about man

You can drive out nature with a pitch fork, baby

And it'll always comes roaring back again

Misery's the River of the World

God tempers all the winds for the new shorn lambs

The devil knows the bible like the back of his hand

All the good in the world

You can put into a thimble

And still have room for you and me

For want of a bird, the sky was lost

For want of a child, the knife was lost

For want of the toy, the child was lost

For want of a nail, a shoe was lost

And misery's the river of the world

Misery's the river of the world

Everybody row, everybody row

Everybody row, everybody row

There's considerable musical innovation in Waits's music. Blood Money's credits include bass clarinet, log drums, calliope, marimba, toy piano, pump organ, cello and tenor tuba.

Bjork shows a similar love of innovation in her newest album Biophilia - a Five project if there ever was one. It was released on CD and iPad, along with ten apps specially designed for the album, which lets the listener interact with the songs and even change them. Each app comes with a game related to the song, the song's score, animations, and a musical essay. The following video compiles various songs from the album and gives a taste of the animation for each one. Also note how different each song is in style. What's going on in Bjork's head?? Nothing anyone's ever thought before, that's for sure (one song chronicles the love affair between a virus and a cell, with the relationship consummating as the virus kills the cell). For a Five, that's exactly the point.

Fives are famously private, and as far as I know, Tom Waits has successfully kept where he lives a secret. He's curmudgeonly in interviews, deliberately keeping himself obscure. Bjork, unlike many pop stars, reviles the attention from paparazzi. She came face to face with a photographer at the Bangkok airport who said "Welcome to Bangkok." Bjork knocked her to the ground. She had a similar incident in Auckland, tearing the photographer's shirt down the back before sending her to the floor. Don't mess with a Five's privacy. Their ruling passion is avarice, which doesn't necessarily refer to a thirst for material acquisition. Fives are greedy about their personal resources. Don't let anybody in. If you tell people about your experiences, your feelings, your life story, they'll suck you dry, and leave you with nothing, not even the understanding of what you've given them. So Fives store up specialty information. They pack up a reserve of what they consider precious.

At their worst, Fives become alienated, antagonistic and arrogant. Haunted by insomnia as their brains never stop buzzing, they'll burn bridges and retreat further into nihilistic isolation. But at their best, as Riso and Hudson describe, they can let go of the conviction that they're separate from the world, that they're simply outside observers, and share the gifts of their unique perception and pioneering vision. I'd say both Bjork and Tom Waits have done this in abundance, releasing one innovative, original album after another, whether the world's ready for it or not. They've also let at least some people in. Bjork has mentored many musicians. And Tom Waits has co-written all of his songs with his wife for the last thirty years.