I was going through the ligatures in 4 parts exercises from Fux's Gradus. On page 133, Aloys says, "Finally, in the sixth measure of the same example the fourth is doubled, although as a rule one doubles the second rather than the fourth":
When Josephus asks for clarification, Aloys presents the answer as a matter of complete harmony (a third, fifth, and octave) in the second half of the measure. However, his correction (below) does not double any note. Instead, he understandably opts to use a C so that it leads up to D, forming a complete harmony in the second half:
I'm still a bit confused about the reasoning for doubling the second over the fourth since Fux did not provide any other detail.
- Why is doubling the second much more preferable than doubling the fourth? I know that when the bass descends by step a fourth will become a fifth and a second will become a third. This means that doubling the second would result in doubled thirds, which could be problematic if the thirds are major. Or does this rule only apply when the resulting thirds are minor?
- Are there any instances/examples where you would need to double the second?
Thanks in advance and sorry for the long question.
Edit: After doing more research, I have found this section about 4-part ligatures in Louis Van Beethoven's Studies in Thorough-bass, Counterpoint and the Art of Scientific Composition:
From this I can assume that (correct me if I am wrong):
-Minor thirds on the upbeat (meaning second on the downbeat) can be doubled.
-Major thirds can be doubled only if
- The third is a third tone
- The doubled notes are are in the middle parts
- The third is not a leading tone
What is a third tone in this case? I don't think it is a tritone since that would mean it is a leading tone, which is forbidden.