No. 3 "Etude for both hands, with similar and perpetual motion" Presto C minor–C major 2/4 time  

An etude in unison at two octaves. "Similar motion (movement semblable)" refers to unison, and "perpetual motion ([mouvement] perpétuel)" refers to a "never-ending" melodic movement that continuously moves at the same tempo and figuration (in 19th-century French vocabulary, this term also had other meanings such as "a person with excessive physical activity," "perpetual motion machine," and "the search for a solution to an insoluble problem"). In music, this term was established early on, used by Mendelssohn in his Perpetuum mobile, Op. 119 (composed 1826), and the final movement of Weber's Piano Sonata No. 1, Op. 24, was published in Paris in 1853 under the title Mouvement perpétuel. The style of playing the same passage with both hands can be seen in training exercises found in official piano methods of the Paris Conservatoire at the time, but it was also becoming established as a compositional technique for piano pieces in the 1830s. For example, No. 15 of Zimmermann's 24 Etudes, Op. 21 (1831), is largely written in octave unison. Alkan used unison for 10 measures in No. 2 "Le Vent" (The Wind) from his Trois Morceaux dans le genre pathétique, Op. 15, published in 1837, as an expression of raging wind. In May 1840, when Alkan published his Trois Grandes Etudes, Chopin published his Piano Sonata No. 2, Op. 35, in Paris. As is well known, Chopin wrote the entire final movement of this sonata in one-octave unison. By 1840, the sound of unison had been integrated from a mere exercise into a means of expression. Alkan, in particular, created a dynamic sound in this work by forming unison at two octaves. The following year, in 1841, he would also use unison writing in the finale of his Piano Trio, published that year. No. 3 is written in a kind of rondo form, with five different episodes (B, C, D, E, F) inserted between the recurring main theme (A), totaling 420 measures. The formal diagram of No. 3 is shown below.   Here, the work will be explained by dividing it into the following three parts: Part 1: measures 1–129, Part 2: measures 130–245, and Part 3: measures 248–420.

Part 1

  The tempo is quarter note = 160. The main theme consists of two musical ideas (A and B). The upper voice of theme A is placed in the middle register, appearing twice with a dull murmur at p, forming a balanced phrase of 8 measures + 8 measures.   B consists of 17 measures, introducing variations with borrowed chords from related keys, leading to the dominant chord, and then guiding back to A at pp. The first return of A is followed by B, exactly as at the beginning, resulting in a direct repetition of 31 measures. This repetition not only foreshadows the subsequent brilliant sonorities but also instills in the listener the expectation that "B will follow A" in the recapitulation of Part 3. In the third return of A (A2), the same theme is traced for 10 measures, but from measure 11, it deviates to form an arpeggio for the first time (measures 79–82), leading to a dominant seventh chord and entering C, resolving to the tonic chord with a rapid four-octave ascent at ff, building the first climax.   Theme C appears twice, in measures 83–96 and 97–110, presented in C minor and G minor respectively. From measure 111, it transitions, forming arch-shaped arpeggios spanning two octaves with a Neapolitan second, a double dominant ninth chord, etc., simultaneously sounding the dominant chord of C minor and a chromatic scale, leading into Part 2.

Part 2

  In D in E-flat major, a new theme is presented at ppp. The melody is formed by eighth notes placed on the beat in the uppermost voice (for only 3 measures), while other sixteenth notes accompany it as broken chords. Despite being in unison, the roles of the voices are clearly separated here, and the "expressive (espress.)" melody contrasts with the rough theme of the opening.   A unified phrase is formed over 16 measures from measures 131–146, and when it reappears in measures 147–158, it shifts to G minor within 12 measures. The third presentation, starting from measure 160, begins in G major, but G major is quickly evaded by borrowed chords, returning to E-flat major and entering a new section, E.  E consists of a phrase sounding an ascending E-flat major scale in the high register, followed by G minor and its Neapolitan second. This 8-measure theme is repeated once more, but this time, it passes through the Neapolitan second of the tonic key and enters F in C-flat major.   F begins in a brilliant high register, and similar to D, a melody is sung at p in the uppermost voice. This musical idea gradually lowers its register over 14 measures from measures 199–212, and from measure 213, the melody shifts back to the middle register, appearing in C major, where it is varied and shortened. This phrase is traced from measures 221–230, and from measure 232, the dynamics gradually diminish, leading to the return of A.

Part 3

  The third return of A begins in the same register as the opening, but at ppp, sounding as if from a distance. The recapitulation of A3, appearing after the long Part 2, creates an expectation for the arrival of B, but before B, Alkan places D in A-flat major to subvert this expectation. D is directly recapitulated, this time in A-flat major (measure 261). Subsequently, B appears in the tonic key at measure 285 (B2), but at measure 300, D reappears in the parallel major of the tonic key (C major) (D3). The frequent appearance of D in Part 3 creates a device that subverts the listener's expectation twice by inserting D twice into the basic framework of A-B-A-C-D from Part 1, resulting in A-[D]-B-[D]-A-C-D. After A reappears in C minor, C and D follow, similar to Part 1. Since D has already appeared twice in Part 3, the final presentation of D is varied by placing the melody on the second sixteenth note instead of the beat, and its length is shortened to 16 measures. The dynamics here are also ff.   Finally, A returns once more at measure 376, but it is recapitulated in A minor instead of the expected C major. The right hand is in the high register and the left hand in the middle register, starting quietly (pp), but from measure 384, where the theme appears in C major, it gradually crescendos, entering the coda at measure 404 and building to a fff climax. In the coda, utilizing broken octave figures, it intensely sounds across a wide range, rapidly ascending the keyboard with a glissando, and grandly concludes the piece with the subdominant and tonic chords.