Back in 2002, I made a seemingly bold prediction.

I suggested that, if they apply themselves, the then-semi-well-known British quartet Coldplay could one day be one of the biggest bands in the world. This was months before “Clocks” made them superstars, back when the band could simply release records, instead of creating worldwide messianic events. But there was always something there, some yearning for bigger and more epic mountains to scale.

The album I was reviewing at the time, A Rush of Blood to the Head, sounds so quaint and small now. My prediction was dead on – Coldplay got huge, and their sound transformed along with them. From “Clocks” to “Fix You” to “Viva La Vida,” they have evolved into a rare beast: a stadium-filling pop band that still cares, very much, about art. Coldplay traffics in singalong anthems, but they are on a mission to create the greatest singalong anthems ever belted out by 90,000 people at once.

Because here’s the thing about Coldplay: they don’t have to try new things. They could keep on pumping out the same rehashes of their older material and cashing the checks. (And with “Speed of Sound,” the first single from 2005’s X&Y, they very nearly did.) But they’re better than that. They’re restless, and while bringing in Brian Eno to shake up their sound certainly isn’t going to put to rest any of those U2 comparisons, the places they took that sound on 2008’s Viva La Vida were remarkable.

On that record, they pulled from a wide range of influences, from Radiohead to the Talking Heads, but in the process, gave up a little bit of their identity. Viva La Vida was a strikingly diverse piece of work, and pushed Coldplay forward in many important ways. It just didn’t often sound like them. Well, they’ve managed to rectify that without losing any of their experimental edge on their just-released fifth effort, Mylo Xyloto. It’s hard to explain what they did right here – this record still doesn’t sound much like Coldplay, but it feels like them.

Rather than running wild through a dozen different styles, the band has concentrated on the things they do best: hands-in-the-air triumphant rock songs, and peaceful, pretty ballads. These songs could easily fit on earlier Coldplay albums, but they’re produced like new-model Coldplay, awash in synthesizers and electronic beats and sparkling effects. I’ve heard this described as the band’s foray into pop, as if they’ve been playing some form of art-rock before this, and I think that’s a reaction to the heavy synth bass lines and computers on display. The songs, they’re pure Coldplay.

Eno is back, providing “Enoxification,” according to the liner notes, and whatever that is, I’ll credit it with making Mylo Xyloto the most relentlessly enjoyable Coldplay record ever. This thing apparently began life as a concept record about two lovers (named Mylo and Xyloto, natch) in a dystopian future burning down around their ears. Of course, that’s pretty much the plot of Green Day’s 21st Century Breakdown, so I’m glad it’s only hinted at on Coldplay’s disc. But this feels like a concept record, like a single piece carrying you through from first note to last.

It helps that all of those notes are really good. “Paradise” has already taken hold as one of my favorite Coldplay singles, with its dirty electronic bass and Chris Martin’s earworm chorus. “Charlie Brown” may be even better – it’s one of those songs like “Clocks,” on which the band hits upon an almost inhumanly catchy and memorable instrumental figure, and builds a whole tune around it. This is the band in full anthem mode, and is countered by the simple, fragile “Us Against the World.”

By this point, you’ll have realized that one of Coldplay’s greatest strengths is also its biggest weakness: Chris Martin. His voice is oddly compelling, his everyman style grounds this band effectively. But his lyrics are lead weights. They’re terrible. “Us Against the World” is exactly what you think it is – over an elementary guitar strum, Martin sings, “Slow it down, through chaos as it swirls, it’s us against the world.” That the song still works is a minor miracle.

Same with “Every Teardrop is a Waterfall,” a rousing, soaring piece loaded down with clunkers: “I got my records on, I shut the world outside.” “From beneath the rubble, sing a rebel song.” “I’d rather be a comma than a full stop.” But damn if it doesn’t rise above that, and connect anyway. Jonny Buckland pinches Big Country’s trick of making his lead guitars sound like bagpipes, and when he, bassist Guy Berryman and drummer Will Champion kick in full force about a minute from the end, it’s like listening to the puzzle pieces fall into place.

The band does take a few risks, like the complex and dark “Major Minus,” but none is more interesting than “Princess of China,” on which the boys welcome Rihanna to duet with Martin. Remarkably, this tune isn’t much more radio-pop than the rest of Mylo Xyloto – Rihanna confidently works her powerhouse voice right into the sound of this record. It works far better than you’d expect it would, and sets up the back third of the album nicely. Final track “Up With the Birds” is like the streamlined version of “Death and All His Friends,” sliding through movements and building up to a brief coda, before collapsing back to earth.

I mentioned that Mylo Xyloto plays like a single song, and one thing that helps that is the band’s restraint on individual tracks. Yes, they’re mainly stadium-sized things, but they’re relatively short – only a few tracks here break four minutes, and Eno and the band have sprinkled little interludes throughout. No other Coldplay album comes off as a cohesive experience quite like this one.

That’s a big step forward, I think, as is the fact that the band has figured out how to meld their restlessness to their core identity. Very little of Mylo Xyloto sounds like Coldplay, but in many ways, it’s the most Coldplay album they’ve made. It’s also one of the best. I don’t think Martin is right when he says his band is the most hated on the planet, but they certainly don’t get the respect they deserve, as record-makers if nothing else. Mylo Xyloto probably won’t change that, but for those of us who predicted an artistically and commercially successful career path like this one, it’s a sweet triumph.

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You couldn’t invent Tom Waits if you tried.

An old-time balladeer, part Gypsy, part Tin Pan Alley, with a voice like freshly ground sandpaper and a knack for telling darkly humorous, yet indescribably moving stories. Yeah, Waits is one of a kind. He’s been plying the same rhythmic, earthy yet otherworldly trade since he kind of went nuts on 1983’s Swordfishtrombones, so the only question that needs asking about a new Tom Waits album is, is it as good as the last one?

Yep, it is. Waits’ 20th record is called Bad as Me, and it’s full of the same ghostly shuffles, clattering grooves and glorious weepers as its predecessor, 2004’s Real Gone. I’m not really sure what took him so long, in fact – once again, Waits proves that he does Tom Waits better than anyone. There are some classics on here, like the organ-blasted “Raised Right Men,” on which Waits growls “Heavens to Murgatroid” and gets away with it, or like the absolutely crushing “Pay Me,” a doomed man’s lament, with accordions.

As always, Waits’ voice shouldn’t work with this material, and yet, I can’t imagine any other voice working quite as well. Take the sweetly-shuffling “Back in the Crowd,” as traditional a ballad as Waits has written: “If you don’t want these arms to hold you, if you don’t want these lips to kiss you, if you’ve found someone new, put me back in the crowd…” But he sings it like a drunken man teetering on a ledge, his gravely mumble suggesting the notes rather than hitting them, and it’s somehow so much more affecting than it would be with a straighter delivery.

Waits has pulled that trick off throughout his career, and he does it here half a dozen times. The rest of the time, he sounds like a lunatic, or a demon. The title track is a mesmerizing big-beat blues, Waits leaping for notes in an unhinged falsetto, and the incredible “Hell Broke Luce” is like a death march with Satan playing drill sergeant. “How is it that the only ones responsible for making this mess got their sorry asses stapled to a goddamn desk,” he barks, over a genuinely scary percussive soundscape, one that devolves into machine gun fire midway through.

This all works through sheer personality, and through the efforts of the amazing and like-minded musicians Waits has assembled. Guitarist Marc Ribot, Waits’ longtime bandleader, is superb here on every track. His subtle lines in “Face to the Highway” cannot be overvalued. Bad as Me also features Keith Richards, Charlie Musselwhite, Flea, David Hidalgo, Patrick Warren and Les Claypool. Yes, all on the same record. And what’s astonishing is, you’d never know it – they all just sound like the Tom Waits Band.

Bad as Me is just the latest chapter in a singular vision Waits has been playing out for decades. There’s not much new here – Waits’ even falsetto on “Talking at the Same Time” is new for him, but that’s about it. But hell, as long as nobody else is even attempting to be Tom Waits, Tom Waits can do it as long as he likes. He’s like no one else on earth.

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It took Tom Waits seven years to follow up his last album, but he’s got nothing on our other Tom this week, who has been away from store shelves for 19 years. I can’t speak for anyone else, but I missed him.

If people know Thomas Dolby, they likely only know him for one thing: “She Blinded Me With Science.” That a man this prodigiously talented is considered a one-hit wonder is practically criminal. I could probably fit everyone who heard 1992’s splendid Astronauts and Heretics into my basement. And it’s not a particularly large basement. The guy’s made some excellent music that has been woefully ignored, is what I’m saying. So much so that he left music sometime in the 2000s to concentrate on his ringtone company. Yeah, his ringtone company.

So the fact that there’s a new Thomas Dolby album at all is kind of amazing. And the fact that it’s as good as it is makes me a very happy music fan. It’s called A Map of the Floating City, and it’s tied to a video game Dolby also developed, which takes you through three areas of play: the mechanical Urbanoia, the dusty western Americana, and the vast and peaceful Oceanea. Songs on the album are split up into those three categories as well – the more electronic stuff first, the acoustic Americana stuff second, and the pretty and watery material last.

Oh, and it was all recorded on a solar-powered 1930s lifeboat, apparently.

If all this sounds too heady for you, take it from me: the album is a blast. Dolby makes polished, melodic, consistently enjoyable pop music, and while the extensive back story might be daunting, it’s completely unnecessary. The songs are immediate, and time has not dulled Dolby’s lyrical prowess. This is dark and cynical and just wonderful stuff, and it has a good beat, and you can bug out to it.

The first suite is along the lines of Dolby’s past work – computer-enhanced pop with swell melodies. Opener “Nothing New Under the Sun” is a mid-tempo singalong with pitch-black lyrics about music and fame: “Somehow the cancer found a lung, you woke up to hear your words on the tip of every tongue, now go learn to live with the legend you’ve become…” “Spice Train” takes the Urbanoia theme seriously, spinning an intricate web of synth lines and percussion with a nifty Middle-Eastern melody. And “Evil Twin Brother” pulses along nicely, with vocal contributions from Regina Spektor.

All of which makes the quick turnabout on the Amerikana music more jarring, and more fascinating. “Road to Reno” bounces along to a skipping drumbeat and an acoustic strum, Dolby telling the tale of a politician and a lingerie saleswoman who meet a sticky end in a hotel room. “The Toad Lickers” gets even more down-home country, with fiddle from Natalie MacMaster and Jew’s harp from none other than Imogen Heap. And the seven-minute epic “17 Hills” is mesmerizing, a soaring country ballad about lovers on the run: “We robbed a store and she shot an armed guard, but mine was the face on the DVR…” Like most of Dolby’s stories, this one doesn’t end well for our heroes. But Mark Knopfler adds some wonderful guitar.

The Oceanea material is my favorite. “Oceanea” itself is almost inhumanly lovely, Dolby showing virtually everyone else who has ever used Auto-Tune as a vocal effect how it’s done. Over a shimmering synth bed, he sings a song of freedom: “You’re soaring on a thermal wind, you’re learning how to shed your skin, you made it home to Oceanea…” Just when you think it can’t get any more beautiful, Eddi Reader adds her voice to the mix. It’s just terrific.

And it’s matched by the stunning closer, “To the Lifeboats.” The music is lilting, even pretty, but the words are black as midnight. “The superstitious sailors of old refused to learn to swim, but there’s no need to drown these days, ‘cause we’ve got lifeboats… Where are the lifeboats? There are no lifeboats, there are no fucking lifeboats…” It ends almost too quickly, the first Thomas Dolby album in nearly two decades shivering to a conclusion on the name “Caroline.”

Speaking for myself, I didn’t need further proof that Thomas Dolby is brilliant. But if you do, A Map of the Floating City gives it to you in spades. It’s a fine addition to his too-brief discography, a gently malignant piece of work that again establishes him as a tremendous songwriter and record-maker. Like a lot of artists unfairly dismissed as one-hit novelties, once you get past the surface of Dolby’s work, you’ll find it’s something pretty special.

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Next week, devil horns in the air, as I tackle metal’s Big Four. Leave a comment on my blog at tm3am.blogspot.com. Follow my infrequent twitterings at www.twitter.com/tm3am.

See you in line Tuesday morning.