Beethoven's Op. 31 No. 2 opens with a question it takes 232 measures to answer, and answers only once. The first movement is a sonata form in D minor whose exposition, fifty-bar development and recapitulation run their course without an authentic cadence in the home key — until eleven bars from the end. What holds it together is not cadential closure but a single recurring gesture.
The sonata begins on its own dominant. The first bar is an arpeggiated A major triad spread across two octaves, rolled, marked pp, and sounded alone in a tempo that will not last the bar. An Adagio answers it. Then the Allegro breaks in. Three tempi in six measures, and no tonic yet.
D minor arrives in the third bar, but as a sound rather than a conclusion. Nothing has cadenced, and nothing will for a long time. At m. 7 the arpeggio returns transposed to C major — the subtonic, arpeggiated and rolled exactly as before, pointing toward a relative major the movement never visits. The gesture is already doing what it will do for the rest of the piece: marking a boundary, and refusing to close one.
The transition ascends rather than modulates. It is continuous, it gathers register and volume as it goes, and it reaches the second group without a cadence to hand it over. Arrival here is a matter of force, not of harmonic argument.
The subordinate key is A minor: the minor dominant, not F major. F major is raised once, at m. 8, where the applied dominant of the mediant sounds explicitly, and then dropped. Of the two standard destinations for a minor-mode sonata exposition, Beethoven takes the darker, which means the exposition can end no brighter than it began.
One chromatic inflection persists across the movement. The flattened second degree colours the second group in both rotations — B♭ in the exposition, E♭ in the recapitulation — at the same position each time, so the colour is written into the form rather than into the moment.
Fifty measures, and not one cadence of any kind. The arpeggio opens the development three times in close succession, but not as it stood: the rolled six-voice chords become grace-note runs with nothing held underneath. Same outline, no weight.
From there the music turns to the sharp side — D major, a diminished seventh, F♯ major, and then a long oscillation between a bare dyad and octaves above it. None of these is a key area. They are functions passing through, coloration rather than tonic, and the development gives none of them a cadence to stand on.
The retransition builds a dominant pedal and then walks away from it. The recapitulation arrives on the dominant, exactly as the movement began. Before it does, the arpeggio surfaces once more at m. 141, reduced to two grace notes — the last trace of the gesture before it returns whole.
The arpeggio comes back unaltered: rolled, sustained, six voices, pedalled. What does not come back is the first theme's Allegro continuation. In its place stand two unaccompanied recitatives, single-line and unmeasured in effect, the texture emptied out at precisely the point where the exposition was most active.
The recapitulation is otherwise a movement of adjustment. The transition is shortened. The second group is re-registered, turning up a fourth where the exposition turned down a fifth. And the second group is at last resolved to D minor, across the long stretch that carries the movement to its close. Its cadences gather in the final bars, as the exposition's did — and the last of them, at m. 221, is the only perfect authentic cadence the home key receives in the entire movement. Eleven bars later the coda ends the piece.
Beneath the surface the structural soprano is more disciplined than the writing suggests. The same descent is stated twice, once at the exposition's cadences and once at the recapitulation's more than a hundred bars later, transposed from the subordinate key into the home key and otherwise unchanged. In both rotations the line is carried by the upper voice of the right hand, identifiable by rhythmic profile rather than by pitch height. The study guide sets the two statements out side by side.
The damper pedal is notated in this movement almost nowhere except at the arpeggio. Every statement of the gesture carries it; so does the coda; nothing else does. pp behaves the same way, marking the Largo statements and the close and effectively nothing between them. Both markings track the gesture rather than the phrase, which makes the arpeggio audible as a structural signal and not merely as a theme.
The gesture's texture is determined by section rather than by position. At the heads of the exposition and the recapitulation it is a rolled chord in six voices over a sustained bass; in the development it is a grace-note run with nothing held. The notes are the same. The weight is not.
Register describes an arch that does not close. The span between the outer voices widens across the exposition to a peak the movement never exceeds again until the very end, contracts through the whole development to nothing at all in the unaccompanied link bars, where a single line is left alone, and reopens in the recapitulation slightly wider than the exposition managed. Above it the ceiling is rationed: the development never rises as high as the exposition's peak, and the coda stays lower still. ff is spent at a handful of points only, and the movement's two fp markings are the openings of the two second groups.
| Section | Range | Tonal area | Function |
|---|---|---|---|
| The two openings | mm. 1–20 | D minor, opening on V | First group |
| The transition | mm. 21–40 | Moving toward A minor | Ascent to the second group |
| The second group | mm. 41–84 | A minor | Subordinate key established |
| The exposition's cadences and closing area | mm. 85–96 | A minor | Exposition closed |
| The gesture destabilised | mm. 97–102 | Unstable | Development opens on the gesture |
| The Allegro core and the retransition | mm. 103–146 | Sharp-side coloration | Development body; dominant preparation |
| The arpeggio restored and the recitatives | mm. 147–174 | D minor, opening on V | Recapitulation opens on the dominant |
| The second group recapitulated | mm. 175–222 | D minor | Subordinate material resolved to the tonic |
| The coda | mm. 223–232 | D minor | Close |
Forty measures of theme and ascent pass without one, and the second group is reached by register rather than by resolution.
The exposition's authentic cadences all fall in A minor and all gather in its closing bars. The imperfect ones resolve to complete root-position triads. The perfect one, at m. 87, arrives on bare octaves and states no third.
Fifty measures without a cadence anywhere in them. A dominant pedal is built and then abandoned rather than resolved.
The corresponding cadences resolve to D minor. The imperfect ones are again fully voiced; the perfect one, at m. 221, is the home key's only PAC in the movement and again states no third. The coda that follows adds none.
The movement contains two structural arrivals commonly heard as cadences that are not. One reaches the dominant without a cadential progression; the other reaches the tonic without closing a formal unit. Both are discussed in the analysis and identified in the study guide.
Confirmed cadence locations, with progressions and bass and soprano scale degrees, are set out in Appendix B of the study guide.
Analysis and study materials published as they appear.