To suggest new unfamiliar content to a user, the general approach is to use machine learning, specifically collaborative filtering, which is often used for recommender systems. The idea is to use the knowledge of the crowd, and finds people (or groups) that have similar taste to yours, and recommend new items that they tend to like.
An alternative is creating a classification algorithm for like/dislike, but that might require extracting features from each song that will describe the essense of the problem, and that's usually not trivial at all.
Some classification algorithms you might want to try are SVM, Naive Bayes, neural networks, Decision trees and more. The real challenge, as I mentioned would be to find the right features for the problem.