Counterpoint question: Fux, First Species, Ex. 1

Hi all!

It's been a while since I've been on... and I'm returning with a question about Fux's counterpoint from Alfred Mann's The Study of Counterpoint:
Are the solutions to each of Aloysius' examples (with corrections) the only acceptable solutions?

In attempting to complete the very first exercise (first species counterpoint on the given cantus firmus, in the bottom voice, in dorian mode), I find there are good reasons to rule out most of the consonances that could be considered. However, I don't know if there are hard and fast rules which make the answers that Joseph gives the ONLY possible answers.
Anyone have experience with this problem or insights?

Thanks!

There are almost always more solutions possible. Fux just didn't see the point of writing down all solutions, because it would be a never ending project. 

I saw the given solutions more as standard formulae, which I analysed both in intervals as in melodic progressions. 

If you have any questions, please ask! 

Another important point is what you see as accepted. 

Even in Mann's edition there are footnotes, which say that other theorists do or do not allow the things Fux does or does not. 

If I remember correctly, Fux sort of forbids lower neighbour notes, whereas Palestrina does write them. It is also a matter of personal and stylistic taste. 

Awesome, thanks! I happened to read the introduction to Schenker's Counterpoint yesterday and he criticizes Riemann for encouraging students to find the best possible counterpoint for a given line -- so, you must be right about multiple solutions. Everyone I've read seems to agree that learning counterpoint strengthens the way you think about music and, most admit that informed, artistic choices are ultimately the takeaway.

I think you need to think in terms of historical context. The solutions and options you have are only limited by what kind of style you're attempting to copy. Considering vocal counterpoint goes back to 1400s (and even earlier if we're going to take into account ars antiqua guys!), it's fair to say that you have quite a lot of options if you pick and choose from different periods. Fux himself was trying to copy Palestrina's counterpoint, but that's far from the only way to do it.

I think it helps, if you're doing historical exercises, to pick a very specific timeframe or composer to emulate, that way you can establish rules much easier.