It’s more than 40 years since Sparks appeared on Top of the Pops with “This Town Ain’t Big Enough for Both of Us”, one of a handful of hits from the brothers Mael, Ron and Russell, who grew up in 1950s and ‘60s LA detesting the “cerebral and sedate” folk boom and grooving to such British acts as the Who and the Kinks.

As pretty much everything but a plague of locusts is visited upon this grim old world, an evening in the company of Neil Sedaka is the greatest of pick-me-ups. At the Royal Albert Hall on Monday, as his UK tour drew to a close, the capacity audience clearly felt uplifted, borne aloft on a raft of enduring songs and the evident enjoyment of the man who wrote them.

Sixty years ago this year, Sedaka made his first appearance on Dick Clark’s American Bandstand and signed a recording contract with RCA. Since then he’s written some 600 songs, the latest so recent he needed the lyrics propped up on the piano. Not for him an autocue – Sedaka has it all in his head and under his hands. Here’s one man unlikely ever to suffer from brain fade. Only the knees and the hips have aged – when he gets up from the piano stool, occasionally for a little bop, you notice his stiff gait.

Sedaka's is still the voice of a young man, pitch-perfect and secure

In recent years, he has played with an orchestra. This time round he was completely solo, a man and his piano. Alone on stage, a screen projecting his image to those in what his friend John Lennon (for whom he wrote “The Immigrant”) would have called “the cheaper seats”, he cut a cheerfully unstagey figure. Sedaka is what an old-fashioned men’s outfitter would call “short and portly” – rather like Elton, who did much to rejuvenate his career in the mid-1970s, but the threads are more sedate: a blue sport coat atop an open-necked black shirt and slacks (as he’d surely call them) and comfy-looking shoes. His silvery hair is combed over and he has jowls – in other words, he’s happy to look onstage like the 78-year-old grandfather he is offstage. His eyes twinkle and when he refers to himself in the third person it’s mostly to poke fun.

The back projection offered close-ups of his hands and it’s fascinating to watch him play. For Sedaka is a real pianist, one who would most likely have pursued a classical career had he not heard the siren call of 1950s pop. He won a junior scholarship to the Juilliard when he was just eight years old, travelling to Manhattan from Brighton Beach for lessons. At 16 he played Debussy and Prokofiev for Arthur Rubenstein.

These days, he told us, his songs are written over a vodka martini or two, but those early hits which emanated from Broadway’s celebrated Brill Building were fuelled only by Coca-Cola and teenage effervescence as Sedaka teamed up with Howie Greenfield to write a string of hits that remain as fresh today as when they were written and which have been recorded by a roll-call of singers, from Frank Sinatra to Sheryl Crow via Elvis, Tom Jones, the Carpenters, Andy Williams, Peggy Lee, Rosemary Clooney and Connie Francis, and he’s featured in The Simpsons.

At the Albert Hall, the hits just kept on comin’: “The Queen of 1964”, “Breaking Up Is Hard to Do”, “Standing on the Inside”, “Our Last Song Together” (the last song he wrote with Greenfield following a 25-year partnership), “Solitaire”, “Where The Boys Are”, “Laughter in the Rain”, “Happy Birthday Sweet Sixteen”, “Next Door to An Angel”, “Love Will Keep Us Together”, “The Hungry Years”, “Betty Grable” and of course “Oh Carole”, written for his high school sweetheart Carole Klein, who the world came to know as Carole King. During a brief comfort break, a Cinebox video of “Calendar Girl” was played, Sedaka in red jacket and perma-tan, “the girls” in bikinis and furs: the American 1950s preserved in aspic. Returning, jacketless, to the stage, he quipped that “Miss January” had recently reintroduced herself to him in an LA club. “She looked so old,” he joked, pausing for a beat. “Of course I hadn’t changed at all!”

And vocally he hasn’t, for Sedaka’s is still the voice of a young man, pitch-perfect and secure, the tessitura and timbre as distinctive as ever. The audience would have had him sing all night – and he looked as though he’d have been perfectly able to oblige. Long may he play on, his perfect miniatures bringing joy to our lives. Michael Eavis should book him for Glastonbury.

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Overleaf: Watch Neil Sedaka play a medley of his greatest hits on BBC's The One Show

In the UK, the best-known version of “Shadows and Reflections” is by mod band The Action, who issued it as a single in June 1967. At that point, the north London outfit had merged their predisposition towards soul with a taste for American harmony pop and psychedelia. Covers of Byrds songs featured in their live set. The American song wasn’t originally theirs: it was co-written by Tandyn Almer, whose compositions were recorded by The Association, and had been issued in the States by Eddie Hodges and an obscure band called The Lownly Crowed.

Nine hours after meeting up in a Shoreditch courtyard to discuss her new album Music for People in Trouble, Norway’s Susanne Sundfør is on stage elsewhere in the district at a theatre called The Courtyard. It’s a sell-out and the room she’s playing is over-full and over-hot. A few days before the album’s release, most of the new songs are unfamiliar to the audience. Yet connections are made instantly.

The Some Bizzare Album was released in January 1981. Compiled by DJ Stevo, it featured twelve unsigned acts he felt represented a fresh way of approaching pop – one enabled by the availability of synthesisers and rhythm machines. Stevo was playing the new music at the nights he hosted, putting the bands on and compiling the electronic chart for the weekly music paper Sounds. After being inundated with demo tapes, he chose the ones he liked best and issued the album.

We are living, I think it’s fair to say, in troubled times. That is, if we’re living at all by the time of publication. Putting aside, for a second, the sabre-rattling of two monstrous egos, there is a need, in such dark days, of some light. Thankfully, Hard Lines, the third album from British pop act Lucky Soul shines with the force and intensity of the Sun – admittedly still not as hot as an exploding thermonuclear warhead, but let’s work with what we have.

For the last four years US pop superstar Kesha has had a huge but miserable media presence. Her bitterly fought court battle to be released from her contract with producer/alleged Svengali Dr Luke, which involved allegations of abuse and sexual assault, created reams of headlines and social media conjecture, but gave the lie to the notion that “all publicity is good publicity”. And there’s been almost no music in that interim. Now, however, minus the dollar sign that used to make up the “s” in her name, Kesha returns with all guns blazing, and the best of her third album takes the listener by surprise.

The mood of Rainbow is righteous fury, as might be expected. On the three opening tracks, this works brilliantly. The album’s opening lines, on the stadium-acoustic “Bastards”, are “Got too many people that I’d like to prove wrong/All these motherfuckers been too mean for too long”, and she doesn’t stint on the swearing from thereon. “Let ‘Em Talk” is an Avril Lavigne–style plastic punker and the cuss-crazed, Stax-on-speed “Woman” comes on like a rabid Amy Winehouse, courtesy of The Dap Kings’ horn section.

Kesha, however, also has a penchant for cheese and power ballads. Sometimes this works, as on the space-pop “Hymn”, but sometimes it’s less successful, as on the ultra-epic “Praying”. Dolly Parton pops in for the country waltz “Old Flames (Can’t Hold a Candle to You)” and Kesha let’s her hair down for a glam stomp on the “Monster Mash”-meets-Sweet “Boogie Feet”, but the best material arrives when she doesn’t curb her innate eccentricity.

There’s plenty of country flavour on Rainbow and it works well, from the kooky, albeit faintly stalker-ish “Hunt You Down” to the jolly, Eartha Kitt-goes-electro canter of “Boots”. The album’s closing tracks, the child-like, preposterous “Godzilla” and the excellent, five-minute cosmic strum of “Spaceship”, showcase a woman whose talent is only just starting to truly shine. In fact, turn this album into an EP of its best six or seven cuts and it would be 5/5 material, because Rainbow is a smart, sassy, well-calibrated return to the fray.

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Overleaf: Watch the video for "Woman" by Kesha

If you consider the fanciful notion that Arcade Fire are a kind of Canadian art house Dexys Midnight Runners who have substituted strained angsty soul for strained angsty rock, then the title track of their new album is their “Come On Eileen”. It’s got that same striving for some kind of transcendence beyond the boundaries of what is, after all, just pop music.

Back in 2013, Haim's debut seemed like the freshest breath of air in a slightly stuffy rock scene. The girls' inimitable musical style – a kind of blend of Stevie Nicks and Shania Twain – lit up any number of radio playlists. Equally important was their air of authenticity. These three musical prodigies from LA were literally sisters and literally doing it for themselves. But there were still nagging doubts – particularly after one TV performance which they, rather oddly, dedicated to David Cameron. For all their hippy hairstyles were the girls actually as free-spirited as they seemed? 

Something to Tell You indicates that the trio may not be quite as bohemian as they look. The guiding principle during the album's lengthy gestation seems to have been to iron out every inch of quirkiness. The result is an album which is mostly fine – sometimes even better – but which is also very middle-of-the-road. Gone are the off-centre melodies of "The Wire" and "Don't Save Me" and in their place we find hooks and choruses so polished you can practically see your face in them.

Of course, not everybody will consider this a bad thing. Fans of American FM rock, for instance, will love the Fleetwood Mac vibe on "Nothing's Wrong", an influence so strong you can hardly believe that Nicks and Buckingham aren't lurking somewhere in there. There are also a handful of tracks bound to delight TV producers looking for soundtrack material. "Little of Your Love" and "Want You Back" have a kind of summery feel that evokes the lives of beautiful people. It's achieved with a mix of power-pop and adult-orientated rock. And therein the lies the rub. Something to Tell You bids farewell to the girls' greatest asset. It is the work of slick, professional grown-ups. What made their debut so well-loved, on the other hand, was its air of gauche naivety.

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Overleaf: watch the video for "Want you Back"

The follow-up to Lorde's multi-platinum, Grammy-nominated album Pure Heroine has been a long time coming after the 16-year-old singer/songwriter withdrew from the limelight and beat a hasty retreat back to her home country of New Zealand.