The lower-case letters a, b, c refer to distinctive melodic ideas, all of which move in more or less continuous sixteenth notes. Idea "a" is a initially vaulting stepwise rise of parallel thirds that later float downwards; variants on this are more wave-like. This idea serves as the ritornello that articulates the tonic chord of each new key, and the return to the main key of B-flat at the end. Its four statements divide the music into four different rotations.
Idea "b" uses chromatic half-stepping neighbors harmonized in parallel sixths. Idea "c" alternates between harmonic third and sixths as each interval descends by step. The reuse of idea "b" divides the prelude into two parts, each with two rotations.
The notated key-signature changes are Szymanowska's, which partition the prelude into four parts as shown with the blue brackets on the left. The proximity of systems to one another in my layout reflects the rotational form, which begin in alignment with the tetrapartite key-signature form, but then cut across it toward the end.
While the first and last rotations unsurprisingly start in B-flat major, the main key of the prelude, the second is in C major and the third is in E major. These are unusual, even audacious, subordinate keys to be thematically and formally articulated in such a small-scale piece like a prelude, perhaps even the two most unusual of such among classical tonal works if we categorize relations to the main key regardless of mode and direction but simply by one of the six interval classes: minor second, major second (B flat to C), minor third, major third, perfect fourth, and tritone (B flat to E). (Root motion by major second and tritone is also the largest distance between the roots of consonant triads in this space.)
Also, m. 29 has a curious pivot chord. Its curiosity can be understood by first recognizing that the interpretation of tonal materials is often hierarchical, sometimes deeply hierarchical, empowered by the preposition "of," and that this hierarchy has the potential for rearrangement. For example, the highest note in the first chord of Beethoven's First Symphony can be interpreted as the third of (the chord built on) the fifth (scale degree) of the (scale whose tonic is a) fourth of (the scale whose tonic is) C. Sometimes the ordering of the intervals in the hierarchy is permuted, creating a different interpretation of the same note, chord, or key. For example, the fourth note of the famous G-G-G-Eb motive at the beginning of Beethoven's Fifth Symphony in C Minor is typically heard as ^3 in i ("three of one"), but, when conductors repeat the exposition, which ends in E-flat major, one can hear this same Eb as ^1 in III ("one of three"). The chord at the end of a typical sonata-form exposition is I of V (V:I), but the same chord at the end of a typical sonata-form development is V of I (I:V).
In Szymanowska's prelude, an F-sharp minor chord sounds in m. 29, which is very close to exactly halfway through the 56-measure prelude. In a larger formal context, this chord's root is the tritone above the formally articulated tonic of C, which is in turn a whole step above the prelude's tonic of B-flat. But Szymanowska recycles a technique from mm. 18-20, reinterpreting a triad as a supertonic in the following key. This puts m. 29's root a whole step above the next key of E, which is in turn a tritone above the prelude's tonic of B-flat. (Szymanowska achieves the modulation from E to B flat in m. 41: the German sixth in E becomes a V7/V in B flat. This enharmonic pivot is quite common to modulate up or down by semitone, but it's much less common to use it to modulate by tritone.) The tonal hierarchy of the F-sharp minor chord in m. 29 has been turned "inside out," as the roman numerals and the pivot-chord analysis in red show above.
Also, m. 29 has a curious pivot chord. Its curiosity can be understood by first recognizing that the interpretation of tonal materials is often hierarchical, sometimes deeply hierarchical, empowered by the preposition "of," and that this hierarchy has the potential for rearrangement. For example, the highest note in the first chord of Beethoven's First Symphony can be interpreted as the third of (the chord built on) the fifth (scale degree) of the (scale whose tonic is a) fourth of (the scale whose tonic is) C. Sometimes the ordering of the intervals in the hierarchy is permuted, creating a different interpretation of the same note, chord, or key. For example, the fourth note of the famous G-G-G-Eb motive at the beginning of Beethoven's Fifth Symphony in C Minor is typically heard as ^3 in i ("three of one"), but, when conductors repeat the exposition, which ends in E-flat major, one can hear this same Eb as ^1 in III ("one of three"). The chord at the end of a typical sonata-form exposition is I of V (V:I), but the same chord at the end of a typical sonata-form development is V of I (I:V).
In Szymanowska's prelude, an F-sharp minor chord sounds in m. 29, which is very close to exactly halfway through the 56-measure prelude. In a larger formal context, this chord's root is the tritone above the formally articulated tonic of C, which is in turn a whole step above the prelude's tonic of B-flat. But Szymanowska recycles a technique from mm. 18-20, reinterpreting a triad as a supertonic in the following key. This puts m. 29's root a whole step above the next key of E, which is in turn a tritone above the prelude's tonic of B-flat. (Szymanowska achieves the modulation from E to B flat in m. 41: the German sixth in E becomes a V7/V in B flat. This enharmonic pivot is quite common to modulate up or down by semitone, but it's much less common to use it to modulate by tritone.) The tonal hierarchy of the F-sharp minor chord in m. 29 has been turned "inside out," as the roman numerals and the pivot-chord analysis in red show above.
