Also, my interest in analysis is not "academic" or "theoretical", but completely pragmatic.
The main problem facing students of any subject, is that as they are introduced to their subject of study, they are being given a solution, but for most of the time, the problem it solves is not at all clear. “Why am I learning this?” “Why do I have to do this?” are usual voicings of this dissatisfaction, which is mostly experienced as a lack of direction, a lack of meaning.
Although there are other problems that are solved by analysis, my interest in it is purely pragmatic: I do it – and suggest that my students do it – solely in order to better perform a piece. So the analysis that we do on pieces is neither complete nor necessarily correct from an academic point of view. I suggest my students to use it for the problems it aims to solve, and if their interest runs deeper, that they use it as a starting point in their theoretical interests (for instance, Schenkerian Analysis is mostly useless for the pragmatical aim of performing a piece - even though it is a very interesting theoretical tool - so I rarely use it). In short, I expect the students to delve deeper and complement and correct the analysis we go through initially as their musical knowledge increases.
A parallel I often draw is with Mathematics. When, as a child, you are first taught to count and add and subtract, you are told that you cannot subtract a larger number form a smaller number. 3 – 5 makes no sense. However, on the next year, you are told that such an operation is indeed possible, and that it creates a whole new set of numbers: the relative numbers. You are then shown how to operate in this new field. Later you will learn that square roots of negative numbers are impossible, just to be told that they are in fact possible and that a whole new set of numbers – complex numbers – is needed to operate on square roots of negative numbers.
It is not that your first teacher “lied” to you, or that he taught you wrong. Rather, he limited your field of learning, so that you would ingrain the basic rules. These basic rules are still valid as subsequent teachers expanded the field. The rules of subtraction and addition still hold with relative numbers.
Likewise, students are given a limited view of the field of analysis. They may come across statements that may prove to be limited and limiting (and even false) when they get more knowledge (“you cannot subtract a larger number form a small number” when in fact you can). The reason the subject in imparted in this way, is that otherwise, one may get the impression, both in music as in mathematics, that “anything goes”, when the very opposite is true. Both music and mathematics are highly organised fields that are constantly expanding and yet keeping the basic rules.
Different pieces will respond better to certain kinds of analysis than others. As the variety in your repertory increases, so should the analytical tools at your disposal.
Just to give you an example of the "problem/solution" approach, consider harmonic analysis. If I do a harmonic analysis of a piece, this analysis should be/provide a solution for a set of problems. These are the problems I set ou to solve with my harmonic analysis:
i. Name and recognize all chords in the piece, as well as their inversions. (Why? because it is a great way to learn about chords in general. It also furthers sight-reading through pattern recognition. And finally, being able to name is the first step to knowing what you are naming).
ii. Recognize recurring chord progressions. (Why? Because it shows that any piece is highly repetitive and patterned. Soon you will recognize that particular chord progression in other pieces and this will accelerate learning. The same chord progression can now be used in free improvisation and composing, and both activities are going to give you the greatest insight possible into the mind of a composer).
iii. Identify the underlying keys (scales) in the piece. (Why? Because in tonal music the notion of key is fundamental. Besides, it also shows which scales one should practice in tandem with the piece so that everything ties up: learning the piece, the practice of scales and the understanding that notes in a piece are not the fancy of the composer, but rather come form a hierarchically organized set of sounds: the scale).
iv. Identify the scale degrees from where the melodic notes and chords are derived and by so doing make explicit the degree hierarchy at work in the piece. (As above. Notice that atonal music poses a different set of problems, and trying to find out about underlying keys is going to be the inappropriate approach - a different sort of analysis is needed)
v. Identify modulations, the place where they occur and the means by which the composer made the transition from one key to the next, keeping in mind that in most cases composers intentionally aim to hide and disguise such transitions. (Modulation is the major compositional tool employed since equal temperament became available and all keys became equally usable by the composer. Identifying the places where modulation occurs has direct import on interpretation - are you going to call the attention of your audience to those points, or are you going to hide them? Often composers change keys in a subtle way. They hide the harmonic structure of their pieces, so to speak. This kind of analysis makes such structure visible. You are now in the position of using this knowledge to make informed choices - the alternative is to have an "intuitive"intepretation where you play in a certain way guided by your "emotions", and you do not have a clue why your emotions are taking you in that particular direction).
vi. Identify cadences – since they signal the phrase structure of the piece – a major consideration for interpretation. (as above)
Now I suggest that you start making a similar list of problems for other kinds of analysis (e.g. modal analysis, motif analysis, counterpoint analysis, fugue analysis, etc.). Further I suggest that you restrict such problems to the ones that will have a direct import on the performance of the piece (at least that is my interest). A musicologist will come up with a very different set of problems, and therefore his analysis is bound to answer those problems, which most likely will not be a performer’s problems. Hence however "useful" the analysis maybe from a musicological point of view, most likely it will have no relevance for a performer trying to tackle the performer´s , main problems:
i. learning the piece;
ii. memorizing the piece;
iii. acquiring the technique to play the piece;
iv. making interpretative decisions in relation to the piece.
Any analysis that helps with these problems should be actively pursued. Likewise, any analysis - however interesting from other points of view - that does not, should be ignored. It is simply an issue of time and efficiency. If your goal is to acquire repertory on the most efficient and rapid way, analysis should be a tool to that end.