Gradus Ad Parnassum question

[RobXGal]

Hey guys this is my first post...

I’ve been driving myself crazy for a couple of days trying to work out something in figure. 6 (page 31)

I don’t understand why the fifth Joseph chose for the first bar was a wrong movement as it was a perfect fifth, like he did in figure 5. Aloys says that he forced himself out of the mode because the cantus firmis is in D (la,sol,re) and he started with G (sol,re,ut). As the key is in C major and the Cantus firmus is in the mode D Dorian, why is a -octave G wrong. I don’t really understand the purpose of the hexachord and there relation to modes... Mabye I’m overthinking it but I would really appreciate a simple explanation as to what exactly went wrong. Also when aloys mentioned the degrees in brackets eg. D(la,sol re) and then G (sol,re ut), why did he choose this order for the degrees as D is soft-hard-natural and G is natural-soft-hard. Is this important ? Can the mistake Joseph made only happen if the counterpoint is below the Cantus firmus because he didn’t mention it in the first excersise!

Thanks guys!

[jancivil]

https://www.britannica.com/art/hexachord

[Gamma-UT]

The footnote in the Alfred Mann translation does a really pisspoor job of explaining what the issue is. Though it might be a problem of brevity. Mann chooses to explain the hexachord arrangement in a footnote but I don't think it was meant to explain the actual problem to which Fux alluded.

What's left unwritten is in the structure of the Church modes that Fux is using. G/D as a fifth is OK but the fourth interval of D/G is, believe it or not, considered a dissonance. So A/D only a page or two earlier is just fine but this interval is bad. However, it's good if the mode is actually that of G and so considered as really being a fifth, albeit in the wrong octave. Not only that, D in the G mode is the important reciting note. These effects I think leading to Fux describing the effect as "forcing it out of mode". The hexachord footnote is, to a large extent, misdirection.