I am trying to analyze the harmony in Bortkiewicz prelude, op. 40 n.3 in E major, but I have some doubts.

I put under the arpeggios the romanic numbers of the harmonies. In the first part, even if there are a lot of passing notes, the chords are quite clear but, from the 8th bar, I don’t understand the harmonies of this piece.

I think there is a modulation in A# (as I wrote in the first and second movements) and then in G-, even if there is no B flat. In the next bars I don’t understand the meaning of “B flat” and “E falt”. Is this a modulation in B flat major?

Moreover, from the 11th bar, there is a chromatic progression. How do you think it can be analyzed?

Bortkiewicz prelude complete score


Bars 9-10 are fairly clearly in G major (the rough LH chord progression of Bars 9-10 is I6-V7-I6-V7 in G major). Note the many naturals there.

Bar 8 prepares Bar 9 pretty badly, though. It starts off with a "changing notes" figure in the right hand that obfuscates the left hand's vii°6/4-V7 of V (note that the right hand clashing harmonically with the left starts right in Bar 1 with the C♮-G♮ dyad and repeatedly reappears). The left hand goes viiø4/3-V7, this time in the home key of E major, in the second half of Bar 8, but is obfuscated again by the right hand's "changing notes" figure of E♯-G♯ in Beats 3 2/3 to 4. The best way I can describe the B7-G transition between Bars 8 and 9 is a chromatic mediant (with the B's of Beat 4 2/3 of Bar 8 as the shared pivot notes).

The second half of Bar 9 is a transposed version of the second half of Bar 1, and Bar 10 strongly resembles a transposed version of Bar 4 (again, Bars 9-10 are in G major). Note the heightened chromaticism of the passing notes (C♮ and G♮ in Bars 1 and 4, E♭ and B♭ in Bars 9-10) in all 4 bars.

Bar 11 slams right back into several-sharp territory with a F♯-B♯ø7 chord progression. This looks like I-viiø7/V in F sharp major, but it looks like keeping the chromatic descent in the bass is more important than adhering to common practice period harmony here. The previous G major harmony can be interpreted as a long tonicization of the Neapolitan of F sharp major.

Bar 12 more clearly uses i-V6 of B minor, but obviously, the B♯ø7-Bm chord progression between Bars 11-12 is problematic and aims to preserve the chromatic descent in the bass over adhering to common practice period harmony.

Bar 13 uses an again-problematic D-G♯m7 chord progression. At least D is III in B minor, but how it got there from V6 of B minor is another baffling use of a chromatic mediant. Note the strong resemblance of the first half of Bar 13 to a transposed version of the first half of Bar 11, though, along with a weaker resemblance of the second half of Bar 13 to a similarly transposed version of the second half of Bar 11 - i.e. Bar 13 sounds a lot like a transposed version of Bar 11. The G♯m7 chord can be argued to be ii7 of F sharp major when taking Bar 14 into consideration (so we get a ii7-V7-I chord progression in F sharp major in Bars 13-14).

Bars 14-15 use a fairly straightforward V7 of -> V(7) of -> V7 chord progression in E major, but this is obfuscated hard in the right hand, including nonchord tones in the first half of Bar 14 that provide resolution as maddeningly delayed as in Bar 19.

(Bars 16 and later, which are in E major, grow obsessed with I and a mystery chord with C♮, E, G♯, and A♯ that shares characteristics with ♮VI and V/V, with only Bar 19 breaking that up with a rough V7 with heavy chromaticism in the right hand, so I won't go into play-by-play detail there.)

  • This is an interesting interpretation. I'll think about it. Thanks a lot!
    – m_art_ina
    Oct 4 '21 at 13:50


The passage from measure 8–15 is a highly altered / disguised / chromatic version of the following progression in B major (with copious modal mixture):.

m8 m9 m10 m11 m12 m13 m14 m15
V → I bVI → V/bVI % V → bii i → V bIII → vi II → V I

Seeming modulations to A# and G-: These are actually F#7 and B7.

Inexplicable Bb and Eb: These are chromatic passing tones over a D7 harmony. They function in exactly the same way as the G and C naturals in the piece's first measure.

Literal analysis

Here's a literal breakdown of the chords involved from mm. 8–15.

measure 8 9 10 11 12 13 14 15
chords F#7 → B7 G → D7 % F# → (B# = C)m7b5 Bm → F# D → G#m7b5 C#7 → F# B7

Initial interpretation

So one way to analyze would be

measure 8 9 10 11 12 13 14 15
chords F#7 → B7 G → D7 % F# → Cm7b5 Bm → F# D → G#m7b5 C#7 → F# B7
key E–B pivot G major B minor F# minor F#–B pivot
RNA (V7/V → V7) or (V → I) I → V7 % V → bii7 i → V bVI → ii7 (V7 → I) or (V7/V → V) I

This is fine as far as it goes, but it begs the question of the relationship between the key changes: E G Bm F#m/F#M B.

Better interpretation

My feeling is that the most straightforward analysis of this highly chromatic, not-at-all-straightforward passage, is to look at it in the key of B major, with a healthy dose of modal mixture.

First, note that B is the dominant of E. At that level, it makes sense analytically as a main target of modulation. Furthermore, all of the various modulations make sense in B: G = bVI (from minor); Bm = parallel minor; F#m = v (from minor); F# = V. This analysis gives

measure 8 9 10 11 12 13 14 15
chords F#7 → B7 G → D7 % F# → Cm7b5) Bm → F# D → G#m7b5 C#7 → F# B7
RNA V7 → I1 bVI → V7/bVI % V → bii7 i → V bIII → ii7/v2 V7/V → V (I = V7/E)3

Other interpretations

This passage could also be explained in terms of (chromatic) mediant modulations, contrapuntal movement of voices, neo-Riemannian theory, and perhaps other methods. I've chosen this particular interpretation only because it's the one that best matches my own theory background.

1 As noted earlier, this measure serves as a pivot between E major and B major. The B7 chord, V7 in E major, although not strictly from B major, does serve as the "jumping off point" aurally for the change. In that regard, it can be viewed as a "surrogate" I chord.

2 Notice that

  • bVI in F# minor is also bIII in B minor;
  • ii7/v in F# minor (G#m7b5) is an altered version of vi7/I in B major (G#m7); and
  • V7/V in F# minor (C#7), is an altered version of ii7 in B major (C#m7).

Thus in measures 13–15 we have a disguised/altered version of the very conventional III → VI → II → V → I progression. (See note 1 regarding the use of B7 in place of B as the I chord.)

3 Here is the pivot back to E major, which returns in the next measure.

  • I personally don't buy either your all-B-major interpretation or your "E G Bm F#m/F#M B" one. I haven't listened to or played the piece yet (I just looked at it and heard some of the notes in my mind's ear), but I've already picked different and more intermediate keys for the passage, and from experience listening to similar passages, I know I'll interpret Bars 9-10 as a full-blown tonicization to modulation upon listening to it. Also, I don't think F# → Cm7b5 is in B Minor at all - what piece goes straight from the dominant to the dominant of the dominant of the dominant?
    – Dekkadeci
    Oct 4 '21 at 13:05
  • This is an interesting interpretation. I'll think about it. Thanks a lot!
    – m_art_ina
    Oct 4 '21 at 13:50
  • @Dekkadeci You've hit on the limitation of my interpretation. It's not so much that it's "in B" as that I find it easier to relate the various chords in terms of B. I allow that might be a distinction without a difference. Regarding the Cm7b5, I'm considering that as bII rather than V/V/V. One of the reasons I chose this way of expressing the harmonic relationships was to avoid multiple layers of applied chords.
    – Aaron
    Oct 4 '21 at 15:13

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