Certain Nordic countries are identified with particular forms of music. Norway and Finland are the home to various strands of metal. Sweden’s pop songwriters and producers are world-renowned, attracting the likes of Britney Spears to Scandinavia. Iceland homes individualists like Björk and Sigur Rõs. Denmark’s influential Mew and Efterklang capture mood like no one else. But you won’t find any of this on the new three-CD set Beginner's Guide to Scandinavia.

The leap from BBC Four to Channel 4 is more than the flick of a switch. Migrating from the BBC’s digital channel to its terrestrial broadcast has transformed the Danish noir drama Forbrydelsen. It's now in English. It’s become American. Copenhagen has been banished. The alchemist responsible is US TV network AMC. Channel 4’s screening of the US remake of The Killing will attract more viewers than BBC Four ever could, but it’s impossible to watch the Seattle-set makeover without thinking back to the original

One of the great strengths of Manfred Eicher's ECM label is the way in which it has encouraged and documented many unlikely yet fruitful musical collaborations throughout its thousand-plus discography. First assembled for her season as artist-in-residence at Norway's Molde Jazz Festival in 2008, percussionist Marilyn Mazur's Celestial Circle quartet brings together stylists as individual as pianist John Taylor, bassist Anders Jormin and vocalist Josefine Cronholm (who makes her ECM debut here).

On the Jutland coast, Aarhus is Denmark’s second largest city after capital Copenhagen. Its attractive continental atmosphere is amplified by the presence of this week’s temporary population, which includes visitors from Britain, Estonia, France, Germany, Luxembourg, the US and the other Nordic countries. They’re here for SPOT, Denmark’s annual festival showcasing homegrown music. It’s a good moment as electro-popper Oh Land is making significant waves in the States. Bands like Efterklang, The Ravonettes and the seminal Mew are embedded in the international musical landscape.

Drummers that sing lead are rare. Ones that sing while pounding away like Keith Moon are even rarer. Denmark’s Treefight for Sunlight are a talented lot, a four-piece who all sing, with three taking the lead. These are the vocals that drive the band and their melodies. Chuck in a wodge of psychedelic nous and you have an art-pop combo that can raise smiles and even the odd scream in hyper-cool Shoreditch.

The Royal Opera has announced that Kasper Holten, artistic director of the Royal Danish Opera, has been appointed Director of Opera at Covent Garden, to succeed Elaine Padmore at the end of this season.

Oslo’s annual by:Larm festival celebrates Nordic music. Over the three days, just under 180 acts play Norway's capital: 142 are Norwegian, 15 are Swedish, with single figures each for Iceland, Denmark, Finland and even Greenland. Time presses, and hard choices have to be made about what to see. This year, by:Larm also hosted the inaugural Nordic Music Prize, awarded to Iceland’s Jõnsi, for his recent album Go. Overjoyed, but overwhelmed, in reaction he said little more than, “Thank you so much, I’m really bad at this.”

If you've just come back from a taxing, tiring orchestral tour, as has the London Philharmonic, the last thing you want to face is a programme of four tough works which demand, at the very least, bright-eyed vigilance but more often a tense, finger-wrecking articulation. So the players must have been relieved to find firm hands on the wheel in the shape of the electrifyingly assured Finnish master Jukka-Pekka Saraste and that most intelligent, repertoire-curious of solo violinists, Frank Peter Zimmermann.

Although Danish singer-songwriter Agnes Obel has professed a kinship with Roy Orbison and his grand musical dramas, it’s John Cale that she covers on her debut album. Choosing the slow-burning “I Keep A Close Watch” from 1975’s Helen Of Troy (Cale re-recorded it in 1982 on Music For A New Society) is telling. Not only does Obel look for and seek to telegraph emotion, she is allying herself with performers and songwriters recognised as passionate and heartfelt. After her openness, it’s fair to ask whether Obel is similarly affecting.

The National Theatre’s new production of Hamlet is both a very good Hamlet, yet also a somehow disappointing one. For a work so rich in possibilities, with so much emotion, so much superb and intricate engineering, it is often like this, in England or anywhere else - inspiring and unconvincing at once.