Devising A Cantus Firmus

I am studying Fux's Gradus Ad Parnassum, and I've gotten to the end of the first species. Before I move on to the second, I'd like to try and write a bunch of cantus firmi that I can then harmonize, for practice. The book left me with many questions about how this might be done, so I looked at a few other books and websites. Now I'm sifting through that information (not all of which is in agreement) and trying to put together a set of guidelines. I still have questions, however, and I'm hoping you can help me with some of them.

The first deals with outlined intervals. I have read that augmented, diminished, and seventh intervals are not to be outlined, but the Lydian cantus firmus by Fux outlines an ascending minor seventh between notes 5 and 8:

Does this mean the outlined m7 is allowed, but not the M7?

Another interval allegedly forbidden in outline is the d5, but there's one in Salzer & Schachter's C Aeolian cantus (figure 1-21c) between notes 5 and 8:

Is this a mistake? Or is it just that the CF was purposely not written according to "strict" rules?

I've carefully analyzed the cantus firmi of Fux, Jeppesen, Salzer & Schachter, Schoenberg, and Schenker, and these are the only questionable outlined intervals I could find. At this point I am leaning toward formulating my rule for outlined intervals as follows: no augmented intervals, no diminished intervals, (even the d5) and no major seventh intervals, but minor seventh intervals are allowed. Does that seem reasonable? Thanks in advance!

Hello,

To make things clear, instead of modern major/minor 7-degree scales, old music used three overlapping 6-degree scales:

1.) normal hexachord: C ut, D re, E mi, F fa, G sol, A la

2.) soft hexachord: F ut, G re, A mi, Bb fa, C sol, D la

3.) hard hexachord: G ut, A re, B mi , C fa, D sol, E la

"Mi contra fa" was considered bad, and usually avoided between different hexachords, both melodically and harmonically: E mi contra Bb fa, B mi contra F fa, B mi contra Bb fa. (Note that C, D, G and A exist in all hexachords.)

E-Bb and B-F are diminished 5ths (or augmented 4ths) while Bb-B is an augmented prime.

So while they were bad intervals, I think 7th was not, especially when using slow (long) notes.

Here is an example of a Ionian cantus firmus outlining a major 7th (lower notes in capital):

C, G, A, G, F, G, c, e, d, c

About your second cantus... In later music (~1600-) diminished intervals and 7-degree scales became more and more common, so later theorists usually allow those intervals. They sound better in downward direction, and can be resolved by a rising semitone, as in Salzer's Aeolian cantus. Anyway, "strict rules" are very arbitrary and differs from theorist to theorist.

Good luck!

Máté

PS.: Please use cut time for Fux's examples, otherwise 2nd species won't work (no weak beats).