Cantus Firmus Question

Hi everyone,

I'm studying counterpoint, and I'm using Alfred Mann's translation of the Gradus ad Parnassum. I have a question about cantus firmi.

In my music history classes from college, and in some of the books I've read, a cantus firmus is derived from chant. My question is: HOW is a cantus firmus derived? The melodies I have in books of chant are very, very different from the cantus firmi in the Gradus ad Parnassum. Did Fux use a particular method to modify or rework existing chant melodies in order to use them as cantus firmi? If anyone can help me or point me in the right direction, let me know.

Thanks in advance,

Clayton

I guess I assumed that certain melodies are more suitable than others for that kind of thing. I was just curious. I thought it might be cool to be able to utilize other material from the chant repertoire, just for variety.

I'm pretty sure (most) cantus firmi aren't actually derived from specific, individual chant melodies (although you could do it with certain kinds of ones); it's just the melodic principles (pertaining to what kind of motion is considered consonant, melodic shape, &c.) which are derived.

If you wanted to do it, you could do it like this:

This is basically just a decorated cantus firmus: each beat (two semibreves in a bar) contains and, except for the opening bar and the latter half of the final one, decorates a note of the cantus firmis. The dotted slurs link notes to the next 'main' note of the melody; the ones in between just dance around or lead to that note with characteristic melodic decorative patterns—suspension, decorated suspension, passing note, consonant leap, cambiata. The CF you get from this is a pretty poor one, though, because raising the seventh degree to create a leading note at the cadence will result in a cross relation with the G in the CF, and the range outlines an augmented fourth; but the point was just to show how it's 'under' the surface of the music (and how, as far as the melody is concerned, it doesn't actually matter all that much that it's a weak CF 'underneath'; so, if you could literally derive one from a melody, like this, it won't necessarily provide a good one, because the outlined tritone isn't in the actual melody itself and the composer, as can be seen from the melody, obviously wanted a natural seven at the cadence anyway).

This is just the same idea, except it's longer, looks more like a real melody, and the structural notes don't fall uniformly, rhythmically. The dotted slurs, again, link structural pitches, if they're not consecutive, and these become the whole-note outline at the bottom. The regular slurs, there, show the segments that you might use as cantus firmi, and the dotted slurs show segments you might add as a kind of appendage to them (or just mini cantus firmi).

The only dodgey bit was the first two bars of the second line. I didn't put the A B♭ A (which is kind of a characteristic Dorian figure) into the CF because it's just a biggish auxiliary to A, and you generally don't want chromatically altered tones in your CF anyway. The second bar is essentially made up of a G that goes to F in the following bar; but you can only allow your CF to become so dull before you start hacking at your throat with a rusty piece of tin, so I put the E in there to delay the move to F and save us all some throat slashing; you could put the second G in, if you were so inclined, but it sounds foolish.