Tom Waits doesn't make a lot of albums, so the arrival of a new one is always cause for celebration.

His latest offering, Bad As Me, is the first collection of new studio songs since 2004's Real Gone. Prior to that it was Mule Variations in 1999. Three albums in 12 years doesn't seem like much.

There has been other stuff during that time: two albums of songs from older stage shows; a double live set; and a 3-CD collection of obscure and unreleased tracks.

But what us Tom Waits fans wanted was an album of new material, something to rock our worlds, and the maestro has well and truly delivered with Bad As Me.

There was a bit of a teaser on the internet a few weeks back.

Tom Waits was holding a ‘private preview session'.

It was as frustrating as it was funny. Tom was sitting at a table with an old gramophone player.

After saying hello he dropped the needle and the title track started playing in all its ferocious glory.

About 30 seconds in, a phone next to the record player rang and Tom stopped the music to answer it.

After hearing the message he indignantly announced that the ‘private' session wasn't so private after all: people were listening in from everywhere! So it couldn't continue and off he went.

But from that half minute of music it was clear that this album had something new to say.

And it does. I find myself again floored by the sheer overwhelming weight of Tom Waits' imagination.

After all, the guy's 64 now, not much younger than Bob Dylan. But while Bob's recent albums – enjoyable though they have been – have tended towards relatively lightweight versions of previous glories, Waits is still heading for undiscovered countries.

After 40 years or so in the biz you could forgive the man for repeating himself a bit, but I realised upon listening to Bad As Me for the first time that it wasn't until the eighth track that I thought ‘Oh, I think I've heard him do something like that before'. And maybe that was only because it was the same song I'd heard at the ‘private preview session'.

The album starts with an extraordinary rhythmic horn attack, saxophones and trombone playing aggressive single notes that together combine into a churning mass of sound. Setting behind them are guitars from both Keith Richards and Marc Ribot, Charlie Musselwhite's harmonica and the every steady bass of Canned heat's Larry Taylor. It's a breathless opening.

Tom Waits albums tend to do that I've found. The first track – often the first two – may be there to weed out the weak. ‘Big in Japan', which kicked off Mule Variations was like that, a sonic barrage which said ‘get on board if you dare'.

Of course, the whole thing isn't like that, it's just a little test.
Elsewhere there are gorgeous ballads, a brilliant monologue of a song, ‘Talking at the Same Time', sung completely in an otherworldly falsetto, an outing into rockabilly, which in Tom Waits' hands sounds like no rockabilly you've ever heard, but simultaneously seems to capture the essence of what all true rockabilly is, and then there's Keith Richards.

Tom Waits and Keith Richards have been mates a long time.

The Rolling Stone first popped up on Tom's classic Raindogs album nearly 30 years ago.

Waits has a knack of writing songs that seem perfect for the two of them.

One was ‘That Feel' with its refrain ‘There's one thing you can't loose and it's that feel', possibly the only true anthem any musician needs.

Here it's a ballad, and a lovely one too: ‘I'm the last leaf on the tree / the autumn took the rest but they won't take me / I'm the last leaf on the tree'. They sing it together.

You can't really call it harmony, and it's debatable exactly how much of a voice Keith still has, but it is a moment of heartfelt twisted beauty, the sort of thing that only Tom Waits can do and get away with.

And I haven't even mentioned the song where he segues into ‘Auld Lang Syne'. That's pretty wonderful as well.

As you can see, I like this album a lot. And, if you like Tom Waits, you will too.