Composed in 1840, this work is dedicated to Hulin, a renowned Parisian violinist and violist who was a close friend of Liszt. It can essentially be considered a violin sonata in three movements. This is a work from Alkan's twenties, a period of prolific creative drive. The first movement is in a compressed sonata form, the second in ternary form, and the third a rondo. While it appears to adopt somewhat classical forms, Alkan's radical compositional language is evident in the unexpected modulations and expanded instrumental writing.

First Movement: As animated as possible, F-sharp minor – F-sharp major, 4/4 time

It begins with the first theme in F-sharp minor, the second theme is in C-sharp major. In the development section, the II degree of F-sharp minor is reinterpreted as the V degree of G minor, leading to D minor. Then, in the next moment, within just three measures, it modulates suddenly yet naturally from D minor to C minor → B minor → G-flat major. From the degree of G-flat major (reinterpreted as the IV degree of F-sharp major), it modulates enharmonically to the V degree of C-sharp major, returning to the second theme. In the coda, Alkan changes the key signature to F-sharp major for the first time, develops the eighth-note material subtly hinted at in the exposition, and then recapitulates the first theme in this key, bringing the first movement to a close. It is noteworthy that he achieves such a vibrant palette through extensive modulations within such a short movement.

Second Movement: "L'enfer" (Hell), Slow, A-sharp minor, 6/8 time

The second movement bears the title "L'enfer" (Hell). The opening features major triads chromatically oscillating around two C-sharps. However, the dissonance C-sharp-F-sharp-A-D is not randomly constructed; it becomes clear that it combines the tonic chord of the first movement (F-sharp minor), F-sharp-A-C-sharp, with the opening motive F-sharp-D, thus establishing a clear consistency with the first movement. By placing this in the bass, Alkan masterfully expresses a growl emanating from the depths of hell. Soon, a chromatic violin melody in D-sharp minor and B minor appears, marked "plaintivement". This melody, combined with the instruction, allows the performer to evoke faint screams and groans heard from the depths of "hell." In contrast, the middle section, far from hell, evokes the kingdom of God through the instruction "evangeliquement". Following a piano chorale, the violin, muted, plays a beautiful celestial song. Here, the tremolo-like usage in the piano plays a crucial role in creating a solemn atmosphere. The ending, once again, thickens the opening cluster to emphasize the contrast with the middle section, and the groans are swallowed by a low piano trill, bringing the movement to a close.

Third Movement: Finale, As fast as possible, F-sharp major, 2/4 time

Here too, the movement begins with a unison passage starting with the motive F-sharp-D, which is the theme of the first movement. Although this introduction is in 2/4 time, from the second measure for approximately ten measures, it is written as if it were in 3/4 time. In this movement, not only rhythm but also frequent key changes further enhance the vividness of the colors. Most of the 24 keys are used in this movement alone. The motives he employed are not limited to F-sharp-D; he also rhythmically develops the melody that appears in the piano underneath it at the beginning of the first movement.

Thus, it can be said that this work is a very elaborately constructed sonata overall. It is particularly interesting that D major, the most resonant key for the violin, does not appear throughout any of the movements. Since Alkan gave a public violin performance at the age of seven, this is by no means due to his ignorance of the violin. Rather, he deliberately pushed into directions that had never been explored before. Another important point to note is that all movements of this piece are constructed around the unifying motif of D-F-sharp. While the unification of a work through a motif is also a characteristic of his Piano Sonata, Op. 33 (1847), throughout the 1850s, he moved away from such motivic unification of the overall structure, adopting a unique form that juxtaposes different musical elements.