I read this really well written story years ago:
It opens in England. There is a musician directing his orchestra. He has a musician friend and a mathematician friend.
He visits California.
Eventually, the world splits, fractured timewise. Each region is in a different era.
The protagonist voyages to Ancient Greece with his piano in a ship.
He also flies over Russia, which is in a future wherein it has has turned to solid glass.
Germany is in the World War era, and the PM of Britain calls for an immediate truce explaining that the world has fractured, and Britain has incredibly powerful weapons(nukes!)
A sea captain from the past turns up on the British shores asking for the War Office.
While in Greece, the musician challenges "Angels", he on his piano, they on a (lyre?) who happen to be from a Utopian future society in Mexico.
The mathematician and musician end up there, the mathematician deciding to go back, the musician deciding to stay.
I remember neither the title nor the author... please help me find it!!!