I am trying to analyze a Bortkiewicz prelude, op. 40 n.4 in F# major, but I have some doubts.

I divided the prelude into three parts:

  • part A (bars 1-11)
  • part B (bars 12-20)
  • part A' (bar 21-29)
  • coda (30-41)

Moreover I don't understand the harmonies of the last part, the coda (bars 30-41). Do you think there are any modulations?

One last question: Is polyrhythm (used in part B) intended to accelerate the progress of musical discourse?

music score

  • What do you mean by "accelerate the progress of musical discourse"? The cross-rhythms in Part B preserve cohesion by continuing the trend from the cross-rhythms in Part A, I'm fairly sure, but what progress is there to accelerate if we disregard the tempo increase?
    – Dekkadeci
    Oct 5, 2021 at 15:43
  • I think that with the use of the polyrhythm there is a nautral "accelerando" in the execution. I don't know if this is only my impression or if the author used the polyrhythm to achieve this goal
    – m_art_ina
    Oct 6, 2021 at 8:27

1 Answer 1


I'll get the shorter discussion point out of the way first: as far as I can interpret, the polyrhythm used in Part B is not intended to accelerate the progress of musical discourse. That 2-against-3 polyrhythm is already used in Bars 1-4 in Part A, so Part B merely takes that use further. In fact, right before Part B, there is an 8th-note triplet in the melody. The melody, in fact, slows down its note rate right when Part B starts instead of speeding it up because it now uses regular 8th notes instead of 8th-note triplets. It is the animando expression marking that does all the work of accelerating the progress of musical discourse there - given the rit. later in Part B, the animando is implied to indicate an increase in tempo.

Now for the harmonic analysis of the coda:

The entirety of the coda can be explained as being in F sharp major with modal mixture and tonicization of IV.

Bars 30-38 all have a F♯ pedal note at the start of each measure in the left hand.

Bar 30 roughly uses only I - the tonic chord.

Bar 31 is easier to explain as V13/IV by taking the pedal F♯ note into account along with the right hand's E-G♯-A♯-D♯ chords, even if the right hand never plays F♯.

Bar 32 is similarly easier to explain as IV13 by taking in the left hand's F♯ and B along with the right hand's D♯-G♯-A♯-C♯ chords.

Bar 33 starts with vii°7 (E♯-G♯-B-D) and changes to V13 on Beat 3. Note that vii°7 is borrowed from the tonic minor - F sharp minor.

So, the chord progression of Bars 30-33 is I-V13/IV-IV13-vii°7-V13.

Note that Bars 34-37 repeat the same chord progression as Bars 30-33.

Bar 38 is an almost exact quote of Bar 30 that uses the same chord: I.

Bar 39 starts with a D7/C chord, which can be interpreted as a re-spelled German Aug. 6th of F sharp major (or F sharp minor) or as V7/♮II, except it resolves like neither of them. It proceeds to a more bizarre A♯7 chord on Beat 3, which at least can be explained as a chromatic mediant of F sharp major and shares A♯ in common with the tonic chord.

Bars 40-41 all use only I (barring non-chord tones) and end the piece with the tonic chord.

Given how often the coda returns to the home key of F sharp major (even if the beginning of Part A obscures that home key quite hard), taking only 1-measure breaks at longest, I cannot say that the coda modulates.

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