The Allegro, BWV 998 by J.S. Bach, was next on my list of things to do. I wanted to work on this before taking on the Fugue. Below is my analysis of this work. I hope you find it useful.
As with the Prelude to this set I used a reduction method which is shown on the lower staff. The idea here is to more or less reduce the piece to its fundamental contrapuntal structure.
Notice again, as in the Prelude, the long descending and ascending step-wise lines in the soprano and bass that are easy to follow in the reduction staff. For example the opening thirty-two bars can be seen essentially as an elaboration of simple descending and ascending D and A major scales.
Part One-Measures 1-32:
Follow the upper voice beginning on the second D above middle C and notice how it first descends an octave into measure three after which it ascends an octave back to where it began (the high D) by measure twelve.
This is the start of an interval pattern (10-5) which takes the D ultimately down to A in measure twenty-one. The A then travels back up to D in measure twenty-four, down to A again in measure twenty-seven, and finally all the way up to the high A in measure thirty-two at the cadence. We can look at this entire section harmonically as a move from tonic to dominant as is typical in most binary forms.
Part Two-Measures 33-96:
We begin in the dominant (A) and immediately return to tonic (D) in measure thirty-six, followed by a transposed restatement of the previous four measures now in the subdominant (G).
The next sixteen bars take us into the supertonic (E minor). Notice again the descending parallel tenths, then thirds, in the reduction staff between the soprano and bass in measures forty-one through forty-eight.
Following in measures forty-nine through fifty-two is another of Bach’s beautiful sequential lines based on descending parallel tenths leading to the cadence in E minor at measure fifty-six.
This E minor harmony is then converted to E major in measure fifty-seven (functioning as the V/V in D major) resolving as it should to A major (V) in measure sixty, which returns us to tonic (D) in measure sixty-four. Notice the ascending parallel tenths that underlie this passage (mm. 57-64) in the reduction staff.
In measures sixty-five through seventy-two Bach inverts the previous soprano line (mm. 57-60) to create this next sequence which is now based on descending parallel tenths (thirds).
Finally Bach gives us two beautiful melodic sequential patterns based on the two interval patterns shown below the reduction staff. The melodic patterns sometimes terminate before the interval pattern does as in the second example (mm. 81-89). In measures seventy-three through seventy-nine we have the interval pattern 10-7 followed by the interval pattern 3-5 in measures eighty-one through eighty-nine. Notice how we end up at the finish of these interval patterns exactly where we started, on the tonic (D) with the same D and F# in the outer voices.
The final section (measures eighty-nine through ninety-six) wrap things up with the additional interesting move to V/IV in measure ninety-four accomplished via the step-wise ascent to C-natural in the soprano shown in the reduction staff.
Harmonically this second part can be seen as having the following harmonic plan:
V-I-IV-ii-V/V-V-I
As a footnote I would like to mention that many sequential patterns are based on what Heinrich Schenker calls linear intervallic patterns or LIPs for short. I have pointed out a few of these in the analysis using numbers below the reduction staff showing the intervals involved.
Of course, as with other contrapuntal analyses, the harmonic designations are what I believe are implied by the counterpoint. You may or may not agree.
There is also a great deal of contrapuntal technique involved with this little piece that I have yet to look into. I am sure I will discover many more amazing things over time as you will too. At least this gives us some basic insight into the genius of Bach’s compositional technique.