A Counterpoint & Fugue-Related Question

Here are three fugue subjects from an old competition I've been playing around with lately (see attached image).

The given task is to write four-part fugues upon them, either with one or two <invertible> countersubjects. I found it relatively easy to design just one CS that works; however, no matter how hard I tried I haven't been able to find a way to introduce a second CS (so that the musical texture would be in triple counterpoint).

Does anyone familiar with the topic have any suggestions how this problem could be solved?

I am not a pro in this subject but I try to share my ideas. I think you are only asked to make 2 separate countersubjects. They don't need to be invertible by each other but only with the subject (two double cp. instead of one triple cp.)

Anyway, writing a triple (invertible) counterpoint is far more complicated than a double one but provides 6 different positions instead of 2. If I were you, I would use very long notes for the 2nd countersubject to avoid parallels more easily.

Máté

Thanks for the reply.

I think you are only asked to make 2 separate countersubjects. They don't need to be invertible by each other but only with the subject

At first I had the same thought; however, the competition rules explicitly hinted at triple counterpoint. The jury must have known how difficult it would have been to accomplish this feat, so possibly that's why the 2nd CS was optional (for some extra score points, I guess).

In case of the G-major theme your suggestion of using long notes yielded an initial solution which was technically more or less correct (save for the last measure) but musically very dull.

Here is another fugue-related problem for which I'm looking for advice here (I didn't want to post it under a brand new topic since it's similar to my previous question.)

I took an old subject (see attachment) on which I intended to make a textbook-fugue. Having found the correct tonal answer I started to devise the countersubject that would harmonize with the main subject. However, in the 3rd measure that A flat caused me some headache. My first thought was that this lowered II. scale degree implied a Neapolitan harmony. But in school during classical harmony lessons I learnt that Neapolitan chords functioning as subdominants are followed by dominant harmonies - yet in this g-minor fugue theme, the A-flat is immediately followed by a G so there isn't any 'space' for a harmony of dominant function. At present I cannot think of a better solution, even if this current one doesn't sound very convincing for me.

Maybe some forum members who have encountered a similar problem could suggest something how to deal with that A-flat?

Do whatever you did for the first instance of the chromatic passing note.