Kodály was already an avid folk music collector when he began writing this sonata, and the work's melodies are redolent of Hungarian folk song, while the harmonies evoke the Impressionism of Debussy. Kodály intended this sonata to fall into the usual three movements, but he withheld the first, with which he was never satisfied. About a decade later, he fashioned a new first movement, but felt it didn't fit stylistically with the older material, so he left the sonata in two-movement form.
The opening Fantasia (Adagio di molto) begins with a meditative recitative for solo cello. The piano eventually creeps in and spurs the cello on to the main sonata-form matter of the movement. Kodály does not quote folk songs here, but he liberally employs fourths in his melodies, which are characteristic of Hungarian music, and he gives the work a rhapsodic nature, full of rubato. Also, the piano often finds itself imitating the undampened sound of the cimbalom. At the end, it's the piano that quotes the initial theme.
Kodály credited Beethoven as the inspiration of the animated main theme of the Allegro con spirito, but its repetitive patterns, modal harmonies, occasional use of drones in the cello, and stamping exuberance are straight out of Hungarian folk dance. Here the cello and piano are true partners, trading off the primary material. The dance rises to an exuberant conclusion, but after a brief pause the piano leads the cello into a long reminiscence of the Fantasia's opening theme, bringing the work full circle.