Limits of traditional counterpoint

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.

Is it possible? Sure. Should you? Depends on how much of your life you want to devote to a single form of compositional theory.

I think in terms of complexity, the fugue might be one of the most complex devices from a "horizontal" viewpoint, with Bach's creations being at the pinnacle of counterpoint. Of course, the only limitations are those that the classical "rules" place on it - in fact, I have jotted down a few lines of a jazz fugue, with piano accompaniment. This allows for much more freer dissonance and voice treatment. If you're talking about pushing a fugue beyond what Bach might have done, go ahead and try it - who knows what the result might be?

Part of me just wants to find five or six subjects that go together and make something out of it but I'll stick to easier things first :) As Tokke said, I don't want to spend my whole life figuring out one single thing even if I'm just not capable of it.*

A Jazz fugue also sounds interesting - but jazz doesn't quite have the concepts of consonance and dissonance that common practice music is built on. AFAIK 7th chords are the new triads, so they would have to be consonant. That means sevenths above the bass would be consonant, but on the other hand, why not seconds then? And fourths are more consonant than both so that would only leave a tritone as a possible dissonance but not by much compared to major 7ths and minor 2nds. Alternatively, 7th chords could be passing chords except at cadences, where they can stand on their own. How did you go on for your attempt at a fugue, Paranoid?

I'm not an expert but it seems to me that fugues tend to "fall apart" more easily the more they depart from the strictest rules of harmony and counterpoint so it might be a challenge to bring that to work but that's exactly why I created this topic, to see what could be done to further push the CP rules.

I think I'll get a bit more acquainted with all the nuances of the rules first. Then I can go on about breaking them. Bit of experimentation can't hurt anyway.

This is interesting as post-Bach fugues are something very different. Bach himself began exploring with the shifting paradigm of blurring the lines between exposition and development, as well as extremely large subjects (BWV 543 circa 1730, for example.) Mozart (KV 608, for example) favored double fugues, but continued the late Bach tendencies but mixed a series of styles. The 608 Fantasia in F is in the form of a Buxtehude toccata with the northern subject patterns with repeating notes that Bach also adopted in many of his works.

After the baroque period Fugues were seen as very "old hat," and no composer really wanted to do style copies for the sake of doing them. Instead, what we get is pushes in different directions that attempt to combine various elements of the new forms and materials into the fugue culminating into the paradigm that the entire canon of western music can be divided into two major points: the Fugue and the Sonata.

Beethoven's fugues are attempts to combine techniques from sonata (the development and motive economy) as well as form structure into fugues, while retaining the exposition but blurring the line between the development and further expositions leading to fugues where it's hard to tell if a subject's being exposed or it's simply motive development.

Later composers pushed further and further, notably during the late 19th century composers like Grieg (Fugue in F minor for SQ) even further experimented turning the subject into a flexible thing that could also serve as accompaniment (one of the major characteristics of the romantic) as opposed to being the focal point of attention. By Grieg's fugue it's easy to identify an exposition that has more in common with a sonata exposition with two themes, which alternate in a bizarre mix-form of both.

Later, with Hindemith, Stravinsky, Schostakovich, etc the fugue becomes again a focal point, being re-interpreted over and over this time including many new elements and theories, sometimes building further from the romantic mix-forms, others adhering to strict baroque tendencies with new sound models (Durufle's fugues, Ludus tonalis by Hindemith, Schostakovich's 24 preludes and fugues.)

And even to this day, there's so much that can be done with the simple ideas presented in a fugue. Because, when it comes down to it, a fugue is a free form composition with very barebones rules that only relate to aesthetic elements in the counterpoint and very little to the form, leaving much room to add and substract things while retaining the "fugue-like" characteristics. Bach's experiments with form in his fugues are nothing but legendary in this regard, each tackling different problems and finding different solutions.

So yeah, I hope this gives some historical overview of the topic.