Hey fellow YCs,
I've got a question begging me and I thought this was a good place to ask.
What are the limits of counterpoint?
By that I mean 18th century counterpoint, the one Bach and Beethoven knew of. I've been reading Fux but I know that his contemporaries used a freer style of counterpoint, especially regarding voice movement, counterpoint that evolved beyond Palestrina's style. The Art of the Fugue is certainly magnificent although I haven't yet looked at it closely. Especially Contrapunctus XIV.
This piece is very likely an (actually unfinished) quadruple permutation fugue - that means it has four subjects and four voices and states one in each voice. This already makes it incredibly complex owing to the form and the quadruple counterpoint. Amazingly enough, one of the subjects' inversion fits in with the whole as well.
Most of us also know of the finale of Mozart's 41st Symphony, the Jupiter - a Fugato consisting of five previously-stated themes in quintuple counterpoint.
One thing that's obvious is though that there are limits. The five themes in Mozart's Jupiter Symphony are quite simple and obviously constructed to fit with each other, being not as melodic as Mozart usually is. Bach didn't have a lot of freedom left in constructing his subjects either. Five- and six-voice fugues are incredibly rare and contrapunctally very dense so many voices rest a lot and move very slowly - kind of like elephants ;)
So, ultimately, how far could one go? Would it be possible to write a quintuple, even a sextuple permutation fugue and who would be able to do so? What about a fugue subject that goes with its inversion, its retrograde and its retrograde-inversion in fully invertible counterpoint? I haven't had a closer look yet due to my lack of knowledge, but is it mathematically possible to construct such a subject of reasonable length considering all CP rules (regarding dissonances and invertible counterpoint especially) that does that? Is there anything left out there that surpasses Bach's AoF or Musical Offering in sheer complexity?
Just curious.