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Forwards? Backwards? Upside down? All three at once? From Machaut to Pärt, Ensemble 360 considers the relationship between musical structures and varieties of mathematical pattern.

A perfect triple bill became a less perfect quadruple bill. Brilliant performances by dancers from Gibney, kNoname Artist, Paris Opera étoiles rarely seen in New York and – a rarity these days – live musicians. 

The JACK Quartet frames its recital at Symphony Space on Manhattan’s Upper West Side around the Pierre Boulez centennial. 

Musical cross-pollination came to life in London Sinfonietta’s electrifying performance, in a seamless blend of theatre, history and virtuosic playing.

Silliness can find a place in art, as we see in some of Erik Satie’s work titles, but sometimes it is just silly. 

Patricia Kopatchinskaja and Aurora Orchestra serve up an over-the-top confection at Purcell Room in Southbank Centre. 

One minor Balanchine, elevated by commanding performances; a rare Albert Evans; Peter Martins at his most compelling and Jerome Robbins at his funniest.

François-Xavier Roth and the Gürzenich Orchestra tear up the traditional concert programme to celebrate the 250th anniversary of Beethoven's birth. 

Amala Dianor and CNN Ballet de Lorraine channel the US choreographer in two UK premieres and a Cunningham classic, all brilliantly performed.

Despite the uneven performances, the evening offered a painful reminder: the future of Cunningham's opus is fragile and delicate. With his own company disbanded, his future is in the hands of dancers who are not trained in his technique and did not have the good fortune of working directly with the great choreographer.

Thrilling and spellbinding experimental music for harpsichord and electronics, performed by Mahan Esfahani. 

Since its inception in 1986, the Davos Festival has given a platform to more than 2,080 young artists of promise. This 33rd festival year is no exception. 

Hugo Ticciati and Víkingur Ólafsson explore notions of time, but a lesson in mindful performance comes from the gravity-defying Sanddorn Balance act.  

This program was a good one to inspire your confidence about the future of choreography.

Michael Tilson Thomas and the San Francisco Symphony Orchestra, joined by cellist Gautier Capuçon, presented modern, post-war masterworks in their first of two nights in Stern Auditorium.

A commanding performance of six pieces from as many composers – all either new, nearly new or rare classics. 

I definitely recommend Empty Moves but you have to come to it with an open mind, ready to see something completely different.

Peter Martins's greatest legacy at New York City Ballet is his tremendous eye for talent and it was on full display at this matinee show.

With a programme spanning from Bach through Schumann, Cage, all the way to Lera Auerbach and David Lang, Hilary Hahn shows she is on top form alongside pianist Cory Smythe.

James Levine led the MET Chamber Ensemble through a remarkable performance of Carter's The American Sublime, whose scattered yet distinct clouds of sound evoked the warmth, irony, and philosophical musings of the texts.

Cage hoped that the change from “pinch-penny mental attitudes to courageous wastefulness” would become as prevalent in the arts as it is in nature. Along those lines, his late choral music is spare, seemingly simple: quiet, almost fragile sounds scattered over silences.

Where lies the boundary between musical performance and performance art? With more and more musicians choosing to incorporate digital or multimedia elements into their performances, concerts are increasingly defying easy categorisation.

The penultimate concert for the 2014 season featured new choreography for Tan's ritualistic work, as well as a brilliant performances of percussion works and Shostakovich's second Piano Trio.

David Lang’s curated series collected stories drew to a close with three works by John Cage, including his autobiographical lecture Indeterminacy of 1958, performed simultaneously, and the world première of Lang’s own mystery sonatas, the only work of his own to be programmed for the series.

Choreographer and composer duo Jonathan Burrows and Matteo Fargion perform a pair of beautifully bizarre duets involving cows, chaos and Cage. At The Nightingale Theatre, Brighton.

New York City Ballet present Mauro Bigonzetti’s Vespro, Angelin Preljocaj’s Spectral Evidence and Liam Scarlett’s Acheron in New Combinations. At David H Koch Theater, Lincoln Center. 

Silence spoke volumes in this tribute to John F. Kennedy at the Nasher Sculpture Center, Dallas, which contained pieces by Messiaen, Steven Mackey and John Cage.

The centrepiece of Nonclassical’s “Pioneers of Percussion” festival was a rousing marathon of a concert at Scala, a large (mostly) rock venue near King’s Cross. It was a rich, varied, high-energy, happily chaotic affair that lasted into the wee hours of the morning.

The contemporary music festival Milano Musica is this year dedicated to the works of Morton Feldman, a man who professed to be more influenced by contemporary art and Persian rugs than he was by other music. The concert took place in Gallerie d’Italia, a former bank now a contemporary art gallery, and pulled together pieces for violin and piano by Feldman and his American contemporaries.

Irvine Arditti is turning 60 this year, but the real landmark perhaps comes next year, when his eponymous string quartet turns 40. The astonishing amount of good they have done contemporary music in this time deserves a ton of celebration in 2014.

It can be said that New York offers arts enthusiasts an embarrassment of riches. It’s a veritable cultural Mecca.

What drew John Cage and Frank Zappa into the same programme was their mutual admiration of Edgard Varèse, at its most striking in their use of percussion. Somehow I feel Cage would have been delighted to be the one out of step with an otherwise perfectly symmetrical programme. Flanking the interval were performances of Varèse’s Ionisation (1929–31).

Before diving into a performance of John Cage’s Sonatas and Interludes for Prepared Piano, New York pianist Marc Peloquin explained a bit of the background behind the sounds we were about to hear. As the story goes, John Cage was commissioned to write a dance piece in 1938, and was accustomed to working with different combinations of percussion instruments for these sorts of works.

This Sunday, pianist Karim Said returned to the Southbank Centre to put Arnold Schoenberg under the microscope for a third and last time. Performing as part of the International Piano Series 2012/13 and the cataclysmic Rest is Noise festival, Said’s concerts have focused on the genesis of the Second Viennese School.

This past Saturday, I spent five hours in a great big room with a cold concrete floor that was brimming from end to end with sounds and images and people.

On Thursday night, I reviewed the vast forces of National Youth Orchestra, playing big colourful works by European exiles in 1930s America.

While you wouldn’t have guessed from her performance, Margaret Leng Tan did not look happy before she played John Cage’s Four Walls in the Barbican Centre’s Art Gallery this Thursday.

There was no doubt that for this concert, one had to enter the front door with a completely open mind. The aim of the Contemporary Music Venture is to promote contemporary music to a wider audience, in an hour and for free – an honourable challenge.This was set to be their first concert of the year.

On Thursday evening, the American Symphony Orchestra bid an effervescent farewell to 2012 and thereby rounded out a year-long celebration of the centenary of John Cage’s birth.

Anyone who worries for the health of contemporary composition obviously wasn’t at the Southbank Centre this Sunday, where the London Sinfonietta presented a whole afternoon and evening’s worth of new music in and around the Queen Elizabeth Hall.

The fragile, stuttering tones died away, and pulling the instrument away from her lips, the trumpeter looked uncertainly around the group of instrumentalists sat with her on the stage.“What I loved about that was the way that the music started to breathe when you yourself had to take a breath. Think about how important silence can be when we improvise.

They say you should never meet your heroes. But they don’t say anything about them meeting each other, so I had very little idea of what to expect at Kings Place on Monday night when comedian Stewart Lee performed John Cage. In the event, this was a hugely enjoyable short recital, though I do wonder if it wasn’t a bit funnier than should really be expected from a Cage gig.

Now they know how many cacti it takes to fill the Albert Hall. Last night’s marathon John Cage Prom finished up, over three hours after it had started, with a wonderfully cactus-heavy performance of Branches (1976).

To judge by the continued chatter, no-one noticed 100 metronomes on stage being set in motion, signalling the beginning of György Ligeti’s Poème symphonique (1962). Even when the lights were dimmed it only dawned on people slowly that the concert had actually already begun.

Gloria Cheng is an uncommon artist. A specialist in contemporary piano literature, she has made a career championing new music and performing programs of adventurous (which is to say, esoteric) works. She is a frequent collaborator with some of the leading lights of contemporary music, including Pierre Boulez and Esa-Pekka Salonen.

Contemporary classical music is happening in all manner of unexpected venues in London at the moment, from Peckham car parks to pubs. But it isn't just getting edgier – it's also getting more respectable, if last night's suave affair in the Royal Albert Hall's Elgar Room is anything to go by.

Dance GB is a collaboration between the UK's three national dance companies, Scottish Ballet, National Dance Company Wales, and English National Ballet.

Could there be a more perfect setting for Sounds of Venice, harpist Rhodri Davies’ contribution to Gregynog Festival 2012 (“Venezia”), than the Impressionists gallery in the National Museum of Wales where the Gregynog collection’s paintings of Venice now hang? Apart from the city itself, you would be hard pushed to find one.