Between the ages of 27 and 33, Beethoven wrote nine of his 10 sonatas for piano and violin.

Hitherto, the violin had been the poor relation in such a musical partnership, by no means an equal partner. “The prototype Mozart sonatas can almost be played without the violin,” says pianist Daniel Tong, one half of a chamber music duo completed by violinist Krysia Osostowicz. But in the hands of the revolutionary young composer, a new meeting of instruments was born, one in which virtuosic playing was expected of both musicians.

To give a new dimension to these endlessly revealing works, Tong and Osostowicz have dreamt up Beethoven Plus, inviting 10 composers, including Judith Bingham, Huw Watkins and Jonathan Dove, to write a companion piece to the sonata of their choice. Their responses will be performed by Tong and Osostowicz in a series of individual concerts, and then all together during a Beethoven season in London next year. Several of the composers already had a favourite, while others were allocated one of the remaining sonatas. And while each writes for 21st-century audiences, each is unstinting in their admiration for a composer who, more than 200 years on from the debut performance of the Sonata No 1 for piano and violin, still takes us by surprise.

“When I work on a piece I like to look into it from the composer’s point of view,” says Osostowicz. “to work out why a piece is written as it is. It seemed a small step to talking about how a living composer would respond to it.” The 10 commissioned pieces will be played alongside the sonatas, before or after. “Traditional concert audiences will be pleased because the responses are short,” says Osostowicz, aware that new music can alarm ticket-buyers. “The difference between the original and the response will be like the difference between a novel and a short story. It’s like a crucible: you have to boil everything down.”

The sonatas fall into pairs, Beethoven often composing two completely different pieces at the same time. Osostowicz compares Nos 1 and 2, for example: “In No 1 Beethoven is saying, ‘I can write a classical sonata’ – it starts with a fanfare; ‘Here I am!’ It’s like a having a really delicious glass of sparkling water. No 2 starts with a spiky pattern and the piano hasn’t even got a tune. It’s a Tardis – quite small, but once you get inside there’s a lot there.

“No 4, and No 5, ‘the Spring’, are, again, opposites,” she continues. “No 4 is very dark and troubled apart from the quirky second movement. The Spring is radiant, open, and leisurely – and he wrote it straight after. Beethoven is saying, ‘I can do this, and I can do that’.” From his writings, we know that he was aware of posterity – that he was both leaving his calling card and writing for future audiences.

The players are sure that Beethoven would approve of their commissions, and of the more sophisticated instruments available to today’s players. “He would have been the first to embrace new developments,” says Osostowicz. “He would have written a saxophone concerto if the instrument had existed!” As for today’s composers, meanwhile, here four explain their responses:

Matthew Taylor: Tarantella Furiosa

In answer to Beethoven: Sonata No 9 in A minor, ‘the Kreutzer’

“Beethoven has been my god since I was small and The Kreutzer has always been my favourite sonata. I love it because it’s so big: it’s a good half an hour long in most performances and it’s incredibly intense and emotional. I chose to respond to the last movement, which is one of those fast, galloping movements that Beethoven does so well.”

David Matthews: Sonatina

In response to Sonata No 10 in G major

“I was able to choose the last sonata, my favourite. It’s written in Beethoven’s later style, which is more refinedand mature: the melodic material is more concise. It doesn’t start like any of the other sonatas – it starts with a wonderful trill on the violin, which I have used. My piece is very short but also has four movements. It is an extreme example of concision: the scherzo lasts one minute.”

Elspeth Brooke: Work in progress

In response to Sonata No 3 in E flat

“Beethoven’s Sonata No 3 was written in 1798 and dedicated to Antonio Salieri, who taught Beethoven, but who for me conjures up the dark figure in [the play and film] Amadeus. The piano part is virtuosic – there are tons and tons of notes. My natural tendency would be to zoom in and pull something out and elongate it, but I’m going to try to suggest the energy of the Beethoven. My piece could be an echo or an explosion of the original.”

Kurt Schwertsik: Unterwegs nach Heiligenstadt

In response to Sonata No 6 in A major

“Living in Vienna, I pass the many houses where Beethoven lived. He wrote this sonata in the spring of 1802, and in the autumn, having moved to the village of Heiligenstadt, he wrote his moving [letter to his brothers] Heiligenstadt Testament, in despair because he was losing his hearing. He even considered suicide, but he could also be very funny and sarcastic. My composition is to do with trying to understand his extraordinary handling of the [experience]. [The sonata] reminds me of his last period: in the other early pieces he is quite logical and very understandable.”