How can I get an objective measure of song similarity? I was browsing through ML project ideas and found an interesting one (just the problem statement ) which was: detecting if two songs are similar using lyrics. I found it to be an interesting idea but Im not quite sure how I'd go about getting a score of similarity for the songs. For my dataset, I have features of genre, artist and lyrics. What is a potential method of scoring the similarity considering there is no such 'training data' to begin with.

I have come across word embeddings and stuff but their working isnt completely clear to me. Moreover, I think they dont take the song-like features that are available into account: things like type-token ratio, sentiment rating, word density(average number of words per sentence)etc. 

Could an approach where first the songs were first clustered based on "high level features" such as type-token ratio, sentiment etc followed by a semantic similarity measure i.e. something like a cosine similarity metric on the word embeddings of songs in the same cluster make sense? How would I validate the usefulness of such an approach?
Two songs are two separated documents which have characteristics that make them similar or non-similar. There are plenty of techniques to determine similarness between documents:

How to compute the similarity between two text documents