I haven't seen my take written anywhere, so here goes. I think Colm struck a deal with the devil ( or the witch) to become famous, at least in legacy, musician. To do this he had to give up the person he cared for most, Pad. After he tells Pad off, giving a pretty weak explanation, these music students appear for no apparent reason in this isolated village and start gathering around Colm. He begins to write his masterpiece. But Pad won't leave. He cuts off a finger, threatening his dream, to drive Pad away, but is relieved to see he can still play. Presumably, killing Pad would also fulfill the deal, but he is unwilling to do this. When he cuts off all of his fingers, he has broken the deal. He will not be a famous musician, but Pad will live.