Composer and musicologist Kyle Gann has an interesting post citing David Fanning’s quotation of Russian musicologist Mark Aranovsky’s classification of the movements of the typical symphony, a classification which runs as follows:

• Movement #1:  Homo agens: man acting, or in conflict (Allegro)
• Movement #2: Homo sapiens: man thinking (Adagio)
• Movement #3:  Homo ludens: man playing (Scherzo), and
• Movement #4:  Homo communis: man in the community (Allegro)

This makes immense sense, and provides a neat explanation of the structure of symphonic form.  Many of my long-standing questions are answered with this classification.    Why normally 4 movements?  Why is the first one normally louder and faster and more serious than the next two?  And why does the first movement often seem more like an ending movement than a beginning one?   In other words, why is the climax to the first movement so often more impressive and more compelling than that for the other movements?  Why is there usually a middle movement that is noticeably less serious than the outer movements?  Why is the last movement often in rondo form?  Why do some composers (eg, Mozart, Mendelssohn) include a fugue in their last movements?  Why do some composers include a song to brotherly love  (Beethoven) or a hymn (Mendelssohn)  in their last movements?

Of great relevance here is that the German word for movement (of a musical work) is Satz, meaning “sentence”.  In the German art-musical tradition, a musical work first makes some claim or states some musical position, and then (in Sonata form) argues the case for that claim by exploring the musical consequences of the theme (or themes), or of its  component musical parts, before returning to a re-statement of the initial claim (theme) at the end of the movement.  In this tradition, the theme, being a claim which is developed, does not have to be very interesting or melodious in itself, since its purpose is not to please the ear but to announce a position.   Beethoven, for example, was notorious for not writing good melodies:  his most famous theme, that of the first movement of the 5th Symphony, has just 4 notes, of which 3 are identical and are repeated together.  But he was a superb developer, perhaps one of the best, of themes, even of such apparently insignificant ones as this one.

The distinction between writing good melodies and developing them well strikes me as very similar to that between problem-solving and theory-building mathematicians – both these cases essentially involve a difference between exploring and exploiting.