Piano Sonata No. 31 (Beethoven)


The Piano Sonata No. 31 in A major, Op. 110, by Ludwig van Beethoven was composed in 1821. It is the central piano sonata in the group of three, Opp. 109–111, which he wrote between 1820 and 1822, and the thirty-first of his published piano sonatas.
The work is in three movements. The moderato first movement in sonata form, marked con amabilità, is followed by a fast scherzo. The finale comprises a slow recitative and arioso dolente, a fugue, a return of the arioso lament, and a second fugue that builds to an affirmative conclusion.

Composition

In the summer of 1819 Moritz Schlesinger, from the Schlesinger firm of music publishers based in Berlin, met Beethoven and asked to purchase some compositions. After some negotiation by letter, and despite the publisher's qualms about Beethoven's retaining the rights for publication in England and Scotland, Schlesinger agreed to purchase 25 songs for 60 ducats and three piano sonatas at 90 ducats. In May 1820 Beethoven agreed, the songs already being available, and he undertook to deliver the sonatas within three months. These three sonatas are the ones now known as Opp. 109–111.
Beethoven was prevented from completing all three of the promised sonatas on schedule by several factors including a bout of jaundice, along with rheumatic attacks in the winter of 1820 ; Op. 109 was completed and delivered in 1820, but correspondence shows that Op. 110 was still not ready by the middle of December 1821, and the completed autograph score bears the date 25 December 1821. Presumably the sonata was delivered shortly thereafter, since Beethoven was paid the 30 ducats for this sonata in January 1822.

Form

characterises the main themes of the sonata as all derived from the hexachord – the first six notes of the diatonic scale – and the intervals of the third and fourth that divide it. He also points out that contrary motion is a feature of much of the work, particularly prominent in the scherzo second movement.
Another unifying feature is the fact that the main themes of each movement begin with a phrase covering the range of a sixth. There is also the significance of the note F. It forms the peak of the first phrase of the sonata, acts as the tonic in the second movement, and a pronounced F marks the commencement of the Trio section. The third movement also begins with F at the top.

Moderato cantabile molto espressivo

Duration of roughly 7–9 minutes.
The first movement is marked Moderato cantabile molto espressivo. Denis describes the first movement as in "orderly, predictable, sonata form", and Charles Rosen calls the movement's structure Haydnesque. Its opening is marked con amabilità. After a pause on the dominant seventh the opening is extended in a cantabile theme. This leads to a light arpeggiated demisemiquaver transition passage. The second group of themes in the dominant E includes appoggiatura figures, and a bass which descends in steps from E to G three times while the melody rises by a sixth. The exposition ends with a semiquaver cadential theme. Beethoven does not ask for the exposition to be repeated.
The development section consists of restatements of the movement's initial theme in a falling sequence, with underlying semiquaver figures. Donald Francis compares the artful simplicity of the development with the entasis of the Parthenon's columns.
The recapitulation begins conventionally with a restatement of the opening theme in the tonic, Beethoven combining it with the arpeggiated transition motif. The cantabile theme gradually modulates via the subdominant to E major. The harmony soon modulates back to the home key of A major. The movement closes with a cadence over a tonic pedal.

Allegro molto

Duration of roughly 2–3 minutes.
The scherzo is marked allegro molto. describes it as "terse", and as "humorous", even though it is in the minor key. The rhythm is complex with many syncopations and ambiguities. observes that this ambiguity is deliberate: attempts to characterise the movement as a Gavotte are prevented by the short length of the bars implying twice as many accented beats – and had he wanted to, Beethoven could have composed a Gavotte.
Beethoven uses antiphonal dynamics, and opens the movement with a six-note falling-scale motif. finds that Beethoven here indulged the rougher side of his humour by using two folk songs, Unsa kätz häd kaz'ln g'habt and Ich bin lüderlich, du bist lüderlich. However, Tovey earlier decided that such theories of the themes' origins were "unscrupulous", since the first of these folk songs was arranged by Beethoven some time before this work's composition in payment for a publisher's trifling postage charge – the nature of the arrangement making it clear that the folk songs were of little importance to the composer.
The trio in D major juxtaposes "abrupt leaps" and "perilous descents", ending quietly and leading to a modified reprise of the scherzo with repeats, the first repeat written out to allow for an extra ritardando. After a few syncopated chords the movement's short coda comes to rest quietly but uneasily in F major via a long broken arpeggio in the bass.

Adagio ma non troppo – Allegro ma non troppo

Duration of roughly 10–13 minutes.
The third movement's structure alternates two slow arioso sections with two faster fugues. In Brendel's analysis there are six sections – recitative, arioso, first fugue, arioso, fugue inversion, homophonic conclusion.
The movement uses the scherzo's concluding ritardando bass arpeggio in F major to resolve to B minor, forming a seamless bridge between the rough humour of the scherzo and the doleful meditation of the Arioso, in A minor. Commentators have seen the initial recitative and arioso as "operatic". The recitative, whose tempo changes frequently, leads to an extended arioso dolente, a lament whose initial melodic contour is similar to the opening of the scherzo. The lament is supported by repeated left hand chords.
The arioso leads into a three-voice fugue, whose subject is constructed from three parallel rising fourths. The opening theme of the first movement carried within it elements of this fugue subject and sees a foreshadowing of it also in the alto part of the first movement's antepenultimate bar. The countersubject moves by smaller intervals. Kinderman finds a parallel between this fugue and the fughetta of the composer's later Diabelli Variations, also finding similarities with the Agnus Dei and Dona Nobis Pacem movements of the contemporaneous Missa Solemnis .
The subject of this fugue opens with three ascending fourths and then goes downwards in gestures outlining fourths. The counterpoint has two themes working together to highlight the fourth.
At the point where Beethoven introduces a diminution of the subject's rising figure the piece comes to rest on the dominant seventh, which resolves enharmonically onto a G minor chord in second inversion, leading into a reprise of the arioso dolente in G minor marked "ermattet". contrasts the perceived "earthly pain" of the lament with the "consolation and inward strength" of the fugue – which points out had not reached a conclusion. finds that G minor, the tonality of the leading note, gives the arioso a flattened quality befitting exhaustion, and Tovey describes the broken rhythm of this second arioso as being "through sobs".
The use of G minor comes to something unusual: it acts like a "closely related key" of A major. The closely related keys come from the chords of a diatonic scale, and in the original "tonic" key of A major, the "actual" closely related keys follow as:
The arioso ends with repeated G major chords of increasing strength, repeating the sudden minor-to-major device that concluded the scherzo – now a second fugue emerges with the subject of the first inverted, marked wieder auflebend. There are many performance instructions in this passage that begin poi a poi and nach und nach. Initially the pianist is instructed to play una corda ; ascribes an unreal, illusory quality to it. The final fugue gradually increases in intensity and volume. After all three voices have entered, the bass introduces a diminution of the first fugue's subject, while the treble augments the same subject with the rhythm across the bars. The bass eventually enters with the augmented version of the fugue subject in C minor, and this ends on E, the work's dominant. During this statement of the subject in the bass the pianist is instructed to gradually raise the una corda pedal. Beethoven here relaxes the tempo and introduces a truncated double-diminution of the fugue subject; after statements of the first fugue subject and its inversion surrounded by what Tovey calls this "flame" motif, the contrapuntal parts lose their identity. sees the following, final section as a "shaking off" of the constraints of polyphony, while goes so far as to label it a peroration, calling the closing passage "exultant". It leads to a final four-bar tonic arpeggio and a last emphatic chord of A major.
Matthews writes that it is not fanciful to see the final movement's second fugue as a "gathering of confidence after illness or despair", a theme which can be discerned in other late works by Beethoven. describes the coda as "passionate" and "heroic", but not out of place after the arioso's distress or the fugues' "luminous verities". Rosen states that this movement is the first time in the history of music where the academic devices of counterpoint and fugue are integral to a composition's drama, and observes that Beethoven in this work does not "simply represent the return to life, but persuades us physically of the process".