page_title: String Quartet No. 1 (Gerhard)
section_title: Moviment I (Allegro assai)
hierarchical_section_title: String Quartet No. 1 (Gerhard) / Analysis / Analysis of the movements / Moviment I (Allegro assai)
caption_attribution_description: English: Example from the 3rd movement of Gerhard's Quartet for strings n. 1: relation between series and their transformations
context_page_description: The String Quartet No.1 is a piece for two violins, viola and cello, composed by Robert Gerhard between 1951 and 1955, premiered at Dartington in 1956. This work marks a turning point in Gerhard's style and composition processes, because in one hand, he recovers some old techniques such as the sonata form in the first movement, along with others not as old like the 12-tone technique. Gerhard brilliantly develops, combines and transforms these resources along with new systematic processes created by himself, so that it leads to a new and broad theoretical framework that will be essential to his music thereafter.
context_section_description: Gerhard worked hard to reinvent the application of the sonata form by mixing it with the stylistic resources that he uses in his compositions, and this movement is a clear example of this. However, outside tonality, it was necessary to define new musical processes that would allow structuring a sonata within thematic and harmonic parameters. Because the thematic element is preserved within the twelve-tone ideology, it is not necessary to change the technique in this regard beyond the use of the kind of melodic lines of its own. As for harmony and the lack of tonality, he divides the tone-row of heights into two Hexachords and uses this duality to achieve the harmonic contrast that previously was marked by ancient modes and tonalities. Hexachords are a resource Schoenberg had used before, and Gerhard is known to have spent some time studying his master's compositions such as Von Heute auf Morgen.
  The division of the tone-row into these two complementary hexachords at the beginning of the quartet predisposes the importance that the hexachordal relationship plays in this work. In addition to this, each hexachord in the original series is part of the SC 6–22 (012468), which is complementary in itself. As a result, each hexachord, either extracted from the beginning or the end of the row, is related by its transposition and retrograded inversion. Gerhard takes this a step further by choosing to relate hexachordal tone-rows that share five pitch classes in common. This means that for each hexachordal row there will be two other hexachords that share five pitch classes among each other. Since Gerhard exploits these relationships exclusively quartet, we will refer to hexachords who manifest this relationship as "closely" related.
  While each hexachord in its prime form has only one related companion who shares the six pitch classes, there are two hexachordal transformations for each of the related six-note segments. This ladder-shaped relationship can be seen in Figure 2, which features a "hexachordal matrix", where each prime shape of the series is reordered from lowest to highest (from the order of pitch class) within its two hexachordal limits. Lines drawn from each hexachord to the other are paired with their nearest relative.
  Due to this relationship, Gerhard can move perfectly between multiple transformations of the series keeping at least five notes in common between each hexachord, resulting in clear and uninterrupted harmonic coherence.
  Regarding the use of these hexachords in the themes, he develops the relationships between these two structures, using retrogrades and inversions to develop the areas that correspond to exposition, development, recapitulation, and primary and subordinate themes. Thus, for example, he can only present one hexachord (with its respective transpositions) in the exposition, and reserve certain combinations of transpositions for occurrences of very specific motifs. The following schema refers to the association of these traditional segmentantions and how Gerhard implements seire transpositions and hexachords (encoded with P and H respectively).
  This new perspective of the harmonic structure is largely consistent with Babbitt's thinking, that the fundamental idea of 12-tone technique is a reformulation of the principle of tonality. In fact, it is inferred in Gerhard's writings that he was very much aware of Babbit's research.
  In addition, this first movement features "echoes of primitive Iberian rhythms". Specifically, some of the polyrhythms in the ostinato refer to the Charradas of Salamanca, and at some rate, to the Fandango.
caption: Figure 4. Pairing of two series related by inversion and retrogradation[28]
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