Haydn is the Father of the String Quartet. He did not compose the first one, however. That honor likely goes to Alessandro Scarlatti, who composed six works called Sonata a Quattro per Due Violini, Violette e Violoncello, senza Cemballo (i.e., a quartet comprised of 2 violins, 1 viola and 1 cello, without keyboard). While Haydn may not have invented the format, he was the first to master the form. And he was prolific–his 68 quartets number more than Mozart, Beethoven and Schubert managed, combined.
The string quartet was a perfect vehicle for the emerging Classical homophonic style. Typically led by the first violin, which Haydn used to establish the tonal center of the composition, the other instruments, playing in lower registers, were used to provide harmonic support. While Haydn’s early quartets vested responsibility for melody with the first violin, Haydn soon began giving the other voices a crack at melodic development. This technique of passing the melody around the band would find its most dramatic home in symphonic works–the sharing of melody would become a hallmark of the Classical style, all thanks to Haydn.
Haydn relied increasingly on the sonata form in the first movement of his quartets. In short, the sonata form presents the theme in an exposition section, develops the theme by exploring its harmonic possibilities in a development section, before restating itself, more or less intact, in a final recapitulation section. As the sonata form was typically found in fast–or allegro–movements, the form is frequently referred to as “sonata-allegro”.
Following a slow movement and a movement based on dance forms (such as a minuet or scherzo), the final movement would recap the theme in a dramatic way. Haydn relied on a vast array of forms in his final movements, including fugue and rondo (a form of theme and variation). Invariably, these final movements are the ones that catch my ear.
Here are two of my favorites. First, the last movement of his Op. 20, No. 5, proving that the fugue was not completely dead in the classical period. Second, a later work, the finale of his “Rider” Quartet:
Franz Joseph Haydn, String Quartet Op. 20, No. 5 “Sun”, IV. Finale, Fugue:
Franz Joseph Haydn, String Quartet in G minor, Op. 74, No. 3, “The Rider”, IV. Finale, Allegro:
A Gertus History of Music 