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I am working my way through Gradus ad Parnassum (Mann translation). The chapter is: third species in three voices. At page 92, I see an example (Fig. 130) that ends like this:

example

I cannot understand the closing formula of the Counterpoint. It is 6M 4 5 6M from the Cantus Firmus, but earlier in the book (two voices) we were told that the closing formulas in third species (with Cantus Firmus on the lower part) were (p. 52):

  • 8 7 5 6M or
  • 3 4 5 6M

I feel I am missing something.

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The key point is that you are now in three voices as opposed to just two. You're correct that page 52 lists Fux's recommended cadential formulas in two voices. But recall one of the main points of three-voice counterpoint as mentioned by Aloys on page 51:

Here it is to be observed first of all that the harmonic triad should be employed in every measure if there is no special reason against it.

The cadential formulae in three-voice counterpoint are a bit different than those in two voices because, with three voices, you can make the harmonic context more clear. Notice, for instance, that your penultimate bar is just an A-major triad, which is the dominant will later become known as the dominant of D, the tonic final.

  • Just to clarify for those who might be reading, Richard is alluding to the voice underneath the Cantus Firmus filling out the remaining member of the A triad, notably the root, before resolving to the final. On an unrelated note, I think that if the lower voice were an octave lower in the penultimate measure, the voice-leading would be more pleasing to the ear. – jjmusicnotes Apr 13 '18 at 5:33

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