It is in ternary form.

• Introduction [measures 1-8]
• A [a (measures 9-12) + b (measures 13-16)]
• B [b (measures 17-24) + Transition (measures 25-28)]
• A1 [a1 (measures 29-32) + Coda (measures 33-40)]

The main key is G major, but a church mode (Lydian mode) is partially felt. The introduction begins with a minor second dissonant interval between the raised fourth scale degree (C to C-sharp) and the dominant (D), which blurs the sense of tonality. When the open fifth of the tonic chord (I) appears in measures 3-4, the entire phrase suggests a Lydian mode with G as the final. This combination of Lydian mode and the sound of open fifths evokes folk music, reminiscent of Bartók.

From measure 9, it is in Lydian mode with D as the final, which corresponds to the dominant key in relation to the introduction. In measure 16, an octave on A appears, and no chord is formed. Considering this progression, A is likely the dominant rather than the tonic, suggesting that measure 16 is a half cadence. On the other hand, if the G-sharp from measure 13 is interpreted as a leading tone to A, it could also be considered a perfect authentic cadence. In any case, due to the sparse texture, these are mere conjectures, but the determination of tonality varies depending on how harmony is perceived. Therefore, we aim to synthesize interpretations while considering all such possibilities. Since these four measures from measure 9 are later recapitulated in the main key of G major from measure 29, this is considered the theme.

Measures 17-18 feature a doubly diminished fifth of the dominant in A major (an augmented sixth chord). This descends chromatically to resolve to the dominant seventh of G major. From measure 21, the progression is also descending, but a single figure repeats in descent, making the horizontal flow created by this figuration more prominent than the harmonic sense. Measures 25-28 constitute a transitional passage, commonly found before the recapitulation in sonatinas and sonatas. This is, in fact, a classical structure for returning to the tonic key or theme, also observed in Bach's Inventions.

The four measures from measure 33 differ from the four measures from measure 13 in that a two-measure chromatic progression is repeated. An 'accelerando' is indicated here, leading towards the conclusion. Overall, the piece is characterized by prominent dissonant intervals of minor seconds and diminished thirds, and the power of open fifths, seemingly expressing the irascible character of Mr. Punch, as suggested by the title.