Harmony
As you can guess from the title, this work is written in the key of B-Flat major. For transposing instruments, it's written in C major for B-Flat instruments, G major for E-Flat instruments, and F major for F instruments. However, this work doesn't remain in B-Flat major for the entire piece.
In the prelude, we start off the first section in B-Flat major then sequence through various key areas and modulate to F major. This first section cadences in F major (a half cadence) before going back into B-Flat major for the repeat. The second section of the prelude starts off in B-flat major, sequences through various keys while sounding in g minor (the relative minor of B-Flat major), then goes back into B-Flat major where it repeats back to measure 25 and ends at measure 58 in B-Flat major on a perfect authentic cadence.
The fugue is in B-Flat major for the most part, relying on sequencing to explore various key areas while remaining in the key of B-Flat major. There are several prominent cadences presented in the fugue: an authentic cadence at measure 70 in the oboes, English horn, B-flat clarinets, alto saxes, and cornets; a half cadence at measure 83 right before the cornets enter with a modified version of the subject; an authentic cadence at measure 90 in the cornets; a deceptive cadence at measure 99 before the tonal answer in the trombones; and a perfect authentic cadence at measure 110 to conclude the piece.
There are two important compositional techniques that Bach employs in this piece. The first is the use of sequences, which are restatements of a motif or longer melodic passage at a higher or lower pitch in the same voice. In other words, a sequence is taking an existing theme or motif and transposing it up or down to create a longer melodic line. One example of this is found in the oboe parts at measure 29:
The other important compositional technique that Bach uses is suspensions. No, I'm not taking about getting sent home from school, but musical suspensions. A suspension occurs when the harmony shifts from one chord to another, but one or more notes of the first chord (what we call the preparation) are either temporarily held over into or are played again against the second chord. This creates a mixture of non-chord tones with harmonies from the second chord, creating a suspension. This suspension is then resolved by moving to a chord tone through stepwise motion (what we call the resolution). Suspensions always resolve downward or else they are not a suspension. Suspensions may be further described using the number of the interval forming the suspension and its resolution. For example, a 4-3 suspension is the 4th resolving down to the 3rd, a 7-6 suspension is the 7th resolving down to the sixth, etc. There are several prominent instances of suspensions used in this piece. Here are two examples from the prelude:
Here are the alto clarinet and bass clarinet lines from pick-ups to measure 22 to the first note of measure 23.
Here are the horn and trombone parts at the 2nd ending of the prelude
(measures 57 & 58).
(measures 57 & 58).