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I'm starting to work through Fux's Gradus ad Parnassum. For the two-voice, first-species, Phrygian-mode, lower-voice exercise (p. 36 on the first Google result for "Fux Gradus"), Aloys says that he allows the voice-crossing

because otherwise [he] would have had to use direct motion up to this point, which would have resulted in less satisfactory voice leading.

What's he talking about?

What makes this composition

Fux's example

more acceptable than, say, this? (edited to correct some of the extraneous errors pointed out in the first answer)

My example

To be clear, the upper voice in both is the cantus firmus, which I can't change. Also, both voices I think are assumed to be adjacent since we're only considering two parts for now.

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Your solution broke the rule given half way down the previous page:

Therefore, if a composition of this species, being otherwise very simple, should contain very many perfect consonances, it would necessarily be lacking in harmony.

Apart from the mandatory unison on the first and last notes, you used two perfect consonances, a fifth and an octave. Fux's version uses only imperfect consonances.

(And I assume your B natural was a typo for a B flat!)

Keep in mind that Fux's approach to counterpoint is not so much "musical composition" as solving a complicated puzzle. Artistic creativity is not allowed ;)

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In the first example, you have counter movements throughout the piece, something which good voice leading comprises off. The soprano voice encompasses a seventh which is good enough movement, the bass encompasses a sixth which is OK

In your example, you start with a good form with something that resembles a passing 6/4 chord progression, but by bar 6 -7 you jump much too large intervals, too many times in a row.

Also if your bass line is really high then your Soprano voice needs to compensate for it by also being high on the treble clef. There simply would be no place to harmonize that chord for four voice, if the outer voices are so close to each other.

Lastly, for the most part, your outer melodies drone on the same notes. Your Soprano voice for the most part only operates between the D above middle C and the fourth above it. (Only two notes not featuring in that interval.)

That is one of the most important parts of harmonizing a melody. You can have all the correct notes, but if the outer voice you write does not have movement of roughly an octave, then it is boring and uninteresting.

The moment when you start to approach harmony exercise in the manner of writing a melody with the harmony the question provides, then you will start getting good marks.

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  • Have you ever actually read Fux, or at least understand what the book is intended to teach? Giving general advice about writing common practice harmony (even if it is good advice) doesn't answer the question.
    – user19146
    Aug 17, 2016 at 20:06
  • This is a good and helpful answer. The prevalence of counter-movements is exactly what Aloy prefers to "direct motion". And Fux most definitely prefers a well-formed line to one with too many repeated notes or too many leaps in one direction, etc.
    – Phil Freihofner
    Aug 18, 2016 at 1:36
  • This gave me some good feedback on my composing, but I corrected the mentioned mistakes, and my question remains to be directly addressed.
    – Sarkreth
    Aug 18, 2016 at 3:48
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"What's he talking about?"

The term "direct motion" refers to two voices moving in the same direction at the same time, e.g., both rising or both falling. This may be less of a problem than "parallel motion" where the interval between two voices remains the same. But it still does not result in as clear a perception of two separate lines as does having lines move in opposite directions.

I think it is useful to think of "good counterpoint" as that in which simultaneous lines are both well formed and easily distinguishable from each other. There are musical situations where it is okay if lines fuse perceptually (as can happen with direct motion). But when studying counterpoint, the goal is to become more aware of the degree of fusion and to be in control of when and where, not leave it to chance.

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