No, I'm not talking about a broken analytic approach (though that's compelling...) but rather an "Analysis Break," which is a chance for you, dear reader, to take a break from the rest of the internet, and walk with me through a somewhat in-depth discussion of a piece of music.
You may rightly ask: "Why analyze music at all?"
Analysis is an attempt to achieve a better understanding of "what's going on?" When you think about it, the set of expectations we bring to the musical experience is similar to the set of expectations we bring to the movies, for example. When we're watching an action film, we expect certain plot conventions: maybe a bad guy (or girl), a tense part of the film where we think all is lost, followed by a triumphant victory in the end. A major deviation from this plot format might strike moviegoers as odd or unusual, and people will probably not like it much.
Even at the micro-level, there are expectations for our movie experience. I would be surprised to see Samuel Jackson angrily hurling frozen fish sticks at his assailants. I wouldn't expect Bugs Bunny to randomly appear and start piloting the Millennium Falcon. Our enjoyment of the experience depends, to a degree, on the artist matching our expectations. Some unexpected events or situations may add "spice" to a film, but if you have too many surprises, the film becomes unbearable and difficult to understand.
Or if you can stand another analogy, a good musical analysis may be likened to a food item's nutritional analysis. Your Nutrition Facts label on your cereal box tells you the ingredients, calories, cholesterol, vitamin content, etc. Perhaps music analysis can also tell us what the "nutritional content" of a particular piece might be.
For us to really understand Music, we need to spend some time with it. This understanding makes us better and more astute in our listening, which in turns improves our ability to enjoy first-class music!