Tonal Movement through Development Sections

This was a topic that I came into by way of a lecture I heard in my undergrad by Dr. Steven Lubin. He had written a dissertation on the topic of how composers moved through tonal centers in the development sections of First-Movement Form of the Classical Era. He viewed the possibilities of keys as kind of a landscape, upon which the themes set out on their journey before arriving home in the recapitulation sections.
He began by drawing up a small diagram demonstrating a key (in this case, C) and its closely related keys. On either side of C (no flats and no sharps) are the two keys immediately next to it in the circle of Fifths - F (one flat) and G (one sharp). Above and below C are listed the tonic minor (c minor) and the relative minor (a minor). And above and below F and G are their respective tonic and relative minors. From here keys can be continually added on either side along with their respective tonic and relative minor keys. Finally, those keys can begin to repeat vertically as well in a sort of pattern.
Using this method, Dr. Lubin created a 3-Dimensional sort of globe upon which one could visually map-out the progression through tonal centers. I have, as an example, mapped out the tonal progression through the development section of Beethoven's Piano Sonata in E-Flat Major, Op. 31, No. 3. So here, we have Beethoven beginning in E-flat and immediately progressing through c minor, to C Major, to F Major, through b-flat minor and E-flat Major, going a little to far to A-flat Major before returning to the home key of E-flat.

This is exciting in that it gives me a way to do some visual analysis on these Beethoven Piano Sonatas.

-Taylor