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There is a period of ten years between the conception of the two movements of the Second Sonata for Cello and Piano. Vermeulen started the work in the spring of 1927, shortly after the premiere in Paris of the First Cello Sonata, published by Senart. That summer Vermeulen was forced to put aside the composition of the new sonata when he was in the middle of the first movement, as he was fully occupied with journalistic work. It was not until January 1937 that he resumed composing. On 9 August he got to the end of the first movement; the second movement was only completed on 29 August of the next year.
The high register of the cello part in the second movement is remarkable. Vermeulen was inspired to use this register of this instrument by the Dutch cellist Henk van Wezel, who he had heard playing the concerto by Saint-Saëns in a French radio broadcast in March 1937. Van Wezel's tone proved to him that it is possible "to sing and to be expressive in every register" of this instrument. Vermeulen dedicated the work to Van Wezel.
The more tonal slant of the second movement no doubt has something to do with the criticism on the 'dissonance' in his Third Symphony that Vermeulen had received from Pierre Monteux (expert on new music) in 1929. The score of De Vliegende Hollander (1930) also shows that Vermeulen had consciously started to try to integrate tonal elements in his music.
Like the Violin Sonata, the Second Cello Sonata is infused with a single motive. Here it is the so-called crosswise second relation that can manifest itself in four ways: as a whole tone in one direction (ascending or descending) followed by a semitone in the other direction (descending or ascending) or a semitone in one direction (ascending or descending) followed by a whole tone in the other direction (descending or ascending). Vermeulen used this motive as a means of producing unity while creating a great variety of free melodies.
The first movement is a sequence of segments each built around a different theme. It can be represented in the following way: theme A and development; theme B with a repeat and a development; theme C with a repeat in the form of a canon; theme D and a transposed repeat; theme E, etc. Just before the end of this movement Vermeulen breaks the pattern by repeating nearly all of the first theme, most likely in order to underline the melodic unity.
The second movement of the sonata is a rondo with a refrain that suggests the key of C major. It ends with a strong passacaglia-like finale in which the cello and the bass line of the piano in turn play 12-tone-rows:
 So in the end, even in this work which is symphonic in character, Vermeulen shows himself to be an atonal composer.
The first performance by Paul Tortelier and Lia Palla took place in Paris on 21 June 1943.
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