The last of the Culture books and Banksie’s SF books, both at all, and that I had only read once.
The odd one about this, as a Culture book, I realised only very late on, is that neither Special Circumstances nor even Contact are involved, directly. Just a random grouping of ships who take an interest in the matter.
The matter in question being the decision of a species called the Gzilt to sublime, or leave the material realm for higher dimensions. This a common endpoint (or new beginning) for civilisations in the Culture universe, and I wonder whether, had Iain lived, he would have taken us to the point where The Culture itself was making that decision.
Anyway, the sonata in question is one that is barely playable because it was written for ‘an instrument not yet invented’, which turns out to be be the Antagonistic Undecagonstring, or Elevenstring. An instrument with some 24 strings (some not counted in the name, because they are not played, they just resonate) designed to be played with two bows simultaneously.
Our hero — or at least, the main humanoid viewpoint character — Vyr Cossont, has been surgically adapted to have an extra pair of arms to allow her to play it. It is still next to impossible, but she has made it her ‘life task’: something to do while waiting for the day when your civilisation sublimes. The decision for them to go was made long before she was born.
But her playing the sonata is only a side issue. The real problem is that maybe someone is trying to sabotage the sublimation. Or maybe not, but odd things are afoot, and various people and ships get involved, and it’s all a whole shitload of fun.