The Danish String Quartet brought Haydn and Beethoven classics to Rockport Music’s Shalin Liu Performance Center on Sunday, along with an early work by their fellow Dane Hans Abrahamsen, who has more recently become internationally known for works like Schnee and let me tell you (which Andris Nelsons brought to the Boston Symphony in 2016).

The tuneful refinement of Haydn’s String Quartet No. 25 in C Major immediately showed the Danish’s strengths. This quartet—comprising violinists Frederik Øland and Rune Tonsgaard Sørenson, violist Asbjørn Nørgaard, and cellist Fredrik Schøyen Sjölin—sounds as a quartet should: in fact, uncannily close to some ideal of string quartet blend and unity. They deployed vibrato strategically, projecting a fairly pure tone most of the time. The unison beginning of Haydn’s Adagio movement arrived scrupulously together, as if the quartet existed as one large instrument. But everything stayed on the pretty side: no grit made it through on this concert. The impression was a quartet with all its edges polished smooth.

Abrahamsen’s Quartet No. 1, from 1973, shows just how far this composer has come. A subtitle like “Ten Preludes,” especially when added to a work in a major genre, is often a composer’s hint to the listener not to keep expectations too high. And so it was: this piece read like a student sketchbook, none of the preludes was developed enough to stand alone, and somehow they felt even flimsier in each other’s company. The kernels of ideas were often inventive, though in a baffling range of styles from high modernism, to minimalism, to Vivaldi. I missed any sense of a composer’s unique presence or point of view: something Abrahamsen has found in his more recent music.

Following intermission and the first violinist’s brief backstage search for his part, the Danish played Beethoven’s first “Razumovsky” Quartet, Op. 59, No. 1, in F Major. Like the opening Haydn, this came close to an ideal performance, if not quite an interpretation. The Adagio suggested profundity, but most remarkable was the attacca transition to the Russian-folksong finale, which the group navigated with unusual sleight, slipping the listener delightfully into a new sound world. The Danish encored with a fiddle-tune they wrote themselves (they all have an interest in Scandinavian folk music). Certainly the suavest fiddling you’ve ever heard.

It’s clear why the Danish Quartet is a rapidly up-and-coming group, popular with presenters: they sound really good, and seem like an affable bunch, too. There is something familiar and very of-the-moment about their playing I couldn’t quite place until it occurred to me later: even live, they sound like a digital recording, edited, mixed, and mastered.

Benjamin Pesetsky is a composer and writer based in Boston.