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The Prelude from J.S. Bach's Prelude, Fugue and Allegro, BWV 998 has always interested me. Actually everything Bach has ever written has always interested me. But since I have only one lifetime (so I think) I will have to select a few of his works for study and this one I think is especially beautiful.
I have set up the analysis using two staves, the upper containing the actual music along with the harmonic analysis using chord symbols and Roman numerals and the lower staff showing the reduction in a way similar to what Heinrich Schenker (1868-1935) would do. As I have said before, Schenker is a strong influence on my analytical technique.
I hope most of the analysis is self explanatory with the use of the pdf file above. I would like to take a closer look at some of the most interesting features.
The most prominent and ingenious feature of this piece can be seen in the reduction staff. Almost the entire piece can be seen and heard as a series of ascending and descending step-wise lines in the soprano and bass. Notice the long step-wise descending line in the upper voice which begins on the high D in measure one and descends (with two, one octave displacements in measures eleven and nineteen) to the B in measure twenty-seven. The bass support for this line is usually a tenth, sometimes a sixth, which descends step-wise right along with it after the pedal point breaks in measure four.
Once the B is reached (third of subdominant) in measure twenty-seven we have a short ascending line moving from the B to the F# in measure thirty (third of tonic) forming another tenth with the bass. This begins the next descent from F# down to C# in measure thirty-three with bass support a tenth below.
An arpeggiation to the high A begins the next descent back to the F# in measure thirty-six. This time the bass ascends step-wise in contrary motion with the soprano voice.
Once this is reached an ascending step-wise line occurs in the soprano along with a descending step-wise line in the bass, taking us to the G and Bb in measure thirty-eight (minor subdominant, a high point harmonically).
After the Bb descends as it should to the A in measure forty, the final step-wise descent begins, taking us from the high A in measure forty all the way down to the final tonic D at the close of the piece (again with octave displacements occurring in measures forty-two and forty-six). The bass this time is a tonic (D) pedal point beginning in measure forty-two through the first half of forty-six with the traditional cadential 4-5-1 bass line occurring at the close.
If possible, play the reduction staff along with a recording of this prelude and you will hear the underlying voice-leading clearly. With a bit of experience this reduction method developed by Schenker will allow you to see and hear this deeper structure which seems to exist in all music by the great composers of the tonal era. For further study please read Introduction to Schenkerian Analysis by Allen Forte and Steven E. Gilbert, W.W. Norton and Company, New York, NY.
The harmonic plan is also quite interesting and a bit unusual. Notice how all closely related keys are touched on in the course of this prelude.
Beginning with tonic (D major) we move into the dominant (A major), then the supertonic (E minor), then the submediant (B minor), the mediant (F# minor) before returning to tonic in measure twenty-three. Notice how these key areas are arranged in descending fourths rather than the more common descending fifths.
We finally get the subdominant key area (G major, measure twenty-four) before the final return to the tonic key in measure twenty-eight in which we stay to the end. This final section contains a most striking harmonic feature, namely the minor subdominant (Gm) in measure thirty-seven and thirty-eight which morphs into an even more striking Neapolitan Sixth chord (Eb/G) in measure thirty-nine.
Then, as if that isn't enough, Bach resolves this Neapolitan Sixth chord in a most unusual way. Rather than moving directly to the dominant (A) he first moves to the V/V (E7) in third inversion with this great appoggiatura in the upper voice on beat one of measure forty. You can see how the two active notes (Bb and Eb) resolve up by half-step to the B-natural and E-natural and the G moves first to A and then resolves to G# to form the V/V. Then of course we finally get the dominant (A7) in the same measure. That is what I call cosmic!
Note: This may be helpful in understanding the function of the Neapolitan Sixth chord. Think of it as a variation of the minor subdominant (iv) chord. Raising the fifth of the minor iv chord one half-step as Bach does will form the Neapolitan Sixth chord. In the key of D major the minor (borrowed) iv chord (G-Bb-D) becomes the Neapolitan Sixth chord by raising the D to Eb (G-Bb-Eb). The Neapolitan Sixth usually prepares or precedes the dominant. This is the reason it is usually in first inversion. The fourth scale degree is in the bass which then moves up to the fifth scale degree (dominant) while the other voices resolve in contrary motion.
This sets up a restatement of the opening two measures beginning in measure forty-two before the final wrap up in the tonic key.
One more note: The m7b5 chord is known more commonly in classical analysis as a half-diminished seventh chord. I prefer to use m7b5 as it is more descriptive of this chord type.
I always find the most interesting and surprising things in Bach's music. I hope you will too. Enjoy this one!