what was a skip according to fux and what is it in general

Question

I wonder what a skip actually is for Fux. Because, in Gradus he says a reversal is needed after a skip but then he does something like that:

To clarify, I've no problem with how it sounds, it sounds perfect to me but felts a disappointment after compared it with my counterpoint because I thought this ending too but did not write as he already wrote it is illegal. So Mr Fux, why don't you follow your own rules.

I'd appreciate a clarification please, thank you!

Note: It's from Alfred Mann's trans.

Answer 1

Nothing in music is illegal, you won't go to jail!

A skip is any movement that isn't step-wise motion of whole or half steps.

It's just triadic arpeggiation in the passage you pointed out. Something that works musically, but isn't the point of the Gradus, so Fux glossed over it.

Don't miss the forest for the trees. The Gradus isn't 100% consistent or meant to explain everything. Follow his instructions as closely as possible, and understand that the occasional deviations like this (and those in m.2, 5, and 6) illustrate some artistic license is OK provided you try to diligently follow the point of each species.

Are far as the artistic license thing goes, keep in mind there is often a trade off between options, like concern for line over harmony or vice versa, and it can be good to examine the possibilities. In m. 9 if the c.p. had resolved the skip by a step in the opposite direction, it would have landed on a tritone on a strong beat. We don't want that dissonance so we do something else despite the general rule to resolve skips with a step in the opposite direction. Also, m.9 is about harmonizing the F of the c.f. Notice how Fux handles all the bars with F in the c.f. All of them arpeggiate the minor tonic chord. I know we aren't supposed to think of species counterpoint in harmonic/chord terms, but it's hard to not admit what's going on in those bars.

It's wrong to read the Gradus as rules and laws of music. The aim is to follow the graded species and develop a disciplined craft along with an appreciation for the overall aesthetics of counterpoint. In other words it is not a complete composition manual. It's more of a disciplined training program for the essentials of counterpoint.

Answer 2

Your understanding of Fux is correct. He does indicate that a skip of a fourth or larger should be followed by a return in the opposite direction. However, Fux throughout the book does make room for exceptions to rules, though he doesn't always explain them when they appear.

In this particular case, the exception may be the octave displacement. Since he moves from F down to C then down to the lower F, it may be that he considers this "the same" as if he had moved back up to the higher F, as he does on the following note. He employs a similar move in measure 6.

It also may be that the particular sequence of notes — down a perfect fourth, then down a perfect fifth — is sufficiently idiomatic, that Fux does not consider it as breaking any rules, but rather an allowed movement unto itself.

Bottom line: Fux is not always consistent, but the rules he lays out are still useful in terms of understanding basics of counterpoint.