Sometimes I'll be working on a group of pieces and realize that I'd like to experiment with abstracting some of the musical ideas (rhythms, harmonies, etc) into a musical vocabulary that I could use for my own improvisations or compositions. Has anyone here ever tried this? How could I methodically break down these classical piece(s) into a musical vocabulary?
FYI, I'm a fairly advanced, amateur classical guitarist/pianist with experience playing music spanning periods from Gaspar Sanz to J.S Bach to Villa-Lobos. For the purpose of this question, if you'd like to use Erik Satie's Gymnopodie's as an example, that would be a bonus for me as these are an example of the kinds of pieces that I'm talking about.
I don't know if you can find a methodic formula to do this that is that detailed. But as overview, you might consider this process:
Pick a piece, or group of related pieces
Do various analysis of the pieces. Analysis such as harmonic, rhythmic, structural, motivic etc might be useful depending on the piece. You can also look for papers that have already done this for the same piece or other pieces by the same composer/period to give you ideas.
Try to compose a short piece in that style or that includes an aspect of what you learned from your analysis. Or maybe improvise on what you have learned.
Classical Music (the genre, not the period) covered a lot of periods of music. Different periods and composers have different analysis techniques so there isn't going to be One Formula to Rule Them All. But this is a general framework you can use to study this.
In a similar way to what has been suggested before, you could try writing variations on some part or parts of these pieces. You could even take rhythmic ideas from some of the pieces, melodic from others (or the same), and harmonic ideas from others (or the same again.) "The Technique of Variation" by Robert Nelson gives examples of how this has been done over the last few centuries.
I'm suggesting variations in order to concentrate the parts being used.