counterpoint question

[ShadowName]

This is a page from The Study of Counterpoint from Johann Joseph Fux's Gradus Ad Parnassum.

 

I find confusion in this page where it explains that the second should be doubled rather than the fourth. "As a rule one doubles the second rather than the fourth". In Figure 197 bar 5, "the second is doubled while the sixth which is required for an absolutely perfect harmony is missing.".... I do not see a second, what are they referring to? In bar 5 I see on the downbeat (from Bass upward): F, D, G, and B, and on the upbeat E, E, G, and C; I do not see how E is second to any harmony expressed here, if that is the doubled second they refer to?

 

Thank you.

 

[john]

On 9/12/2018 at 7:29 PM, ShadowName said:

This is a page from The Study of Counterpoint from Johann Joseph Fux's Gradus Ad Parnassum.

 

I find confusion in this page where it explains that the second should be doubled rather than the fourth. "As a rule one doubles the second rather than the fourth". In Figure 197 bar 5, "the second is doubled while the sixth which is required for an absolutely perfect harmony is missing.".... I do not see a second, what are they referring to? In bar 5 I see on the downbeat (from Bass upward): F, D, G, and B, and on the upbeat E, E, G, and C; I do not see how E is second to any harmony expressed here, if that is the doubled second they refer to?

 

Thank you.

 

 

 

Hmmm. I don’t see the notes you see. You seem to be misreading the octave down tenor part. These are the notes I see, going from highest on the left to lowest on the right, using the bass note as the chord root you can see:

 

BGG F

4 8 2 R

note the 2nd and 8th

 

and the second half of the measure

CGG E

6 9 3 R

 

 

then looking at the 6th measure:

 

6th Measure

AFA E

4 2 4 R

Note the doubled fourth, relative to E, the root.

 

and the 2nd half of the measure:

 

AFA D 

5 3 5 R

 

note the doubled 5th, and the missing octave.