He was known for his modern and avant-garde works, but his most famous piece was a simple, haunting lament for solo piano - Farewell To Stromness.
"He was, right to the end, a pioneer," Stephen Lumsden, Managing Director of music agency Intermusica, said.
The Salford-born musician, who had leukaemia, died at home in Orkney.

• Obituary: Peter Maxwell Davies

Famous for pushing boundaries, Sir Peter's earlier works have been described as unplayable, generating controversy amongst audiences and critics alike.
He often referenced plainchant and medieval music, which he incorporated into challenging, serial compositions.

In 1969, people shouted "rubbish" at the premiere of his opera Eight Songs for a Mad King; while the inaugural performance of Worldes Blis caused a mass walk-out at the BBC Proms.
"Most of those who stayed booed," Sir Peter later observed. "[It] was very upsetting."
But over his career, he made it his mission to connect with as many audiences as possible, writing pieces for children, ballet, theatre and string quartet.Known to most as Max, he composed some 300 works, including 10 symphonies, 10 so-called Strathclyde Concertos and the operas Taverner and The Lighthouse.

He moved to the Orkney Islands in the early 70s, leading to a calmer style of music, which often incorporated Scottish motifs.
In 1987 he was knighted, and in 2004 he became Master of the Queen's Music - a post considered to be the musical equivalent of the poet laureate.

 The holder is expected to write music to commemorate important royal events, and the appointment of a self-confessed republican raised many eyebrows.
But Sir Peter told The Daily Telegraph in 2010 that he had become a monarchist after meeting and working with the Queen.

"I have come to realise that there is a lot to be said for the monarchy," he said. ""It is a better system than having a president and frankly I have been disappointed so much with our dishonest politicians