- You have heard the piece and would recognize it on hearing it again
- You have heard it a lot of times and could sing along or hum some or all of the melody
- You have followed it in the score and could say what key it was in and perhaps describe the form (when I attended concerts in London a number of years ago I noticed that music publishers set up tables in the lobby where you could purchase the scores to the pieces being played)
- You have analysed the piece in some detail from the score
- In a slightly different direction, you are a player and have played through the score
- You can play the piece from memory
- You can write out the piece from memory
- You are very familiar with how the piece was constructed and could write a new piece using the same form and style
- You can place the piece within its historical context and describe its relationship with other music before and since
These are all the levels I can think of, off the top of my head. In some genres of music, there could be additional ones. For example, in jazz, another level would be the ability to improvise convincingly on the piece.
Now the sad thing is that I strongly suspect that the writers of many books on music don't get much farther than level two or perhaps three. Journalists are probably confined to level one! No wonder the general level of musical understanding is low.
Notice that everything on my list is related to the music itself, either in performance or score form. There is nothing there about the composer's biography, political leanings or favorite color. So many books on music contain little about the music and a great deal on these peripheral matters. The interesting thing is that there are quite a few composers about whom very little is known. And that little is known by very few people. Pérotin is an example. We don't even know the dates of his birth and death. But he wrote some fine music: