For information on the composer, Sergei Prokofiev, and the general overview of the entire flute sonata (Op. 94) you should check out my analysis of the first movement before reading through the analysis of this movement. Understanding the background – including the conditions – Prokofiev was writing under will help inform the analysis of this movement:
IV. Allegro con brio (♩=112)
This is the final movement of the sonata, and comparatively has much more diverse and virtuosic material. The general form is a rondo (which can be more specifically narrowed down to Sonata Rondo form) which I’ll break down more in depth later. The main characteristic of a rondo is the repetition and recycling of the ‘A’ material. Generally speaking, a rondo in its most simple layout can be reduced to ABACA. The development of the ‘A’ section is up to the composer and in this case Prokofiev demands more virtuosity from the performer with each recap of the ‘A’ section.
Let’s compare what sonata rondo form looks like (generally) as well as how Prokofiev adapts this form in the fourth movement:

The key difference between these two models if Prokofiev’s repetition of the A and B before the C section is stated. However, remember that in Sonata form the Exposition can be repeated; sometimes you may see this when the length of the exposition is shorter than the combined development and recapitulation. I regard Prokofiev’s decision to include the A’ and B’ sections before the ‘development’ or C was used to this effect especially considering the slowness/major character shift that makes the C section feel much longer than the lively allegro ‘A’ section we hear interspersed throughout the fourth movement.
To make sense of what we are seeing in the diagrams let’s break down what defines each section – in particular look at the model for Prokofiev’s adaptation in dark grey we see one of the links to sonata form is the use of sections with the A and B parts: primary (1) theme, transitional theme, secondary (2) theme, and closing theme.
‘Exposition’ – A: primary and transitional themes
The first theme spans m. 1-16 and is in DM (both the first movement and fourth movement are centered around the same tonic, D). It is characterized by a pickup of four 32nd notes that has an upbeat, lively rhythm such as the arpeggiated 16th note triplets – as well as the other 16th triplet figures – eighths and embellishments (such as the one 16th two 32nds and the dotted eighth sixteenth).

While the opening is in DM, 6 measures in the theme is transposed down a whole step into C – however, Prokofiev quickly takes a detour in m. 8 (the 3rd bar of the transposition) which takes us to this G#-G-G# 16th triplet figure. He does so route us back to D Major; in m. 9 we are still in C, but by oscillating between G-G# he is able to fill in the Major 2nd (a whole step) back to D as he finally does in m. 12 on beat 3. He gives as an exact copy of the opening theme to springboard us into the transitional theme.

The transitional theme spans m. 17-29, still in DM and ends with a HC – AM (V). This theme presents a new rhythm with the driving 16th notes especially in the ta di-mi rhythm on a low D4 which appears first in m. 17 and then again in m. 21.

We also see a return of the 16th triplets.
And we see ambiguity to the tonal center. In m. 25 Prokofiev begins his DbM arpeggios on sixteenth notes, by m. 27 we have some dm arpeggios, and then a sequence of descending Major and minor 3rds which end with the half cadence on A.
‘Exposition’ – B: secondary and closing themes
The secondary theme spans m. 35-39 and is in AM (with some tonicizing of the new dominant E). This theme is completely new material the syncopated rhythm (SLS) with large intervals and arpeggiated grace notes.

The closing theme is a bit of a misnomer since similar to the primary theme it does a recap that is reminiscent of ternary form. This theme spans m. 40-53 and starts in f#m (the relative minor to A) and ends in AM. There are steady eighth notes with four 16th notes that pickup into the next phrase group.
We can establish the f# more solidly when we consult the piano score:

Repetition of the Exposition – A’ and B’
Prokofiev made the choice to extend the ‘exposition’ of this sonata rondo form with truncated versions of the primary theme, transitional theme, and secondary/closing theme.
What is absent from A’? The D Major 16th triplet arpeggio in m. 60 into 61 is in a bar of 2/4 (NOT 4/4) and does not take us into C as the opening did. We are taken directly to the transitional material sans the grace not flourishing, this version goes straight into the 16th triplets, DbM arpeggios, and descending 3rds.
And what about B’? There is just one subtle difference in the flute material which is the final sixteenth of m. 71 being changed to a G-natural (originally a G3) as the flute transitions down to F rather than up to A.
The transition into the development is set up by the piano’s eighths that establish the new key – originally the piano is giving us downbeat Fs in the left hand before leaning into the instability with first inversions (A-C-F) with A being the lowest note in both hands.
‘Development’ – C
The material being ‘developed’ is very clearly the material from the B theme – characterized by the steady eighths and the group of 4 pickups – Prokofiev uses various techniques to make the theme more robust/complex such as varying rhythms, new tonal areas, and adding piano interjections.
There can be many arguments made for what Prokofiev is tonicizing/modulating in this development however there are pillars that I think are solid (and would generally be recognized) these are as follows:
- F – m. 87
- Ab – m.107
- F# – m. 116
In the diagram at the top of the post, I gave some further tonal areas that I believe Prokofiev plays around with:
- F – m. 72-86
- (C) as the dominant of F there are short motives interspersed throughout the C section
- m. 87-89
- g which is the dominant of c, with a lowered 3rd… however this could be argued to be an extension of the C/dominant
- m. 90-91
- A – a whole step up from g, as well as, the 3rd of F
- m. 92-94 – plus the pedal C is used to modulate into other tonal areas with that common note
- (C) again m. 95-97
- And a combo of both C and G (the dominant and secondary dominant)
- m. 104-106
- Ab – m. 107-110
- Db – the predominant which is leading us up to when Prokofiev changes the key to reflect D (however he is using it in it’s parallel minor b)
- m. 111-112
- F# (mostly likely being used a dominant within bm to end in a HC before the recapitulation)
- From key change to bm, F# is already being established as the dominant m. 113-121
‘Recapitulation’ – A” B” A”’
When A” is restated there is a demand for more virtuosity – the sections of the primary theme are transposed up an octave. Likewise parts of the transitional theme are transposed down an octave. Rather than ending solidly there is a slow quarter note ascension to the secondary theme in the tonic (D Major). A” spans m. 120-143.

As per sonata form, the recapitulation is solidly in the tonic/home key (both A and B sections, whereas in the exposition the B section is a new tonal area). That being said, B” presents the secondary/closing theme in D major – transposed up a m6. Prokofiev also switches up the order that he presents this material: rather than starting with the syncopations and grace note arpeggios, he starts with the steady eighths and pickup four 16ths and THEN goes to the syncopation and arpeggiated graces in DM. B” spans m. 145-160.

The final statement of A”’ begins in m. 161; has a fake out opening that like A” is partially transposed up the octave before repeating and moving into completely new material that is mainly flashy flourishes to demonstarte ultimate virtuosity.
What do you think of this final movement? And what do you think of the Sonata as a whole? Let me know in the comments!