The Guardian (London) calls them “peerless” and “the greatest string quartet in the world,” and the Takács Quartet, performing Sunday afternoon, was clearly the finest ensemble yet to appear at the Lied Center. They displayed strength and delicacy, passion and languor, joined to singleness of interpretation and unparalleled communication with one another.

Opening with Franz Josef Haydn’s charming “String Quartet in F Major, Op. 74,” the group demonstrated such mutual sensitivity that they sounded like a single instrument. Each member maintained constant eye contact with the rest, and clearly all aimed at the same effect.

They produced a buttery-smooth tone, with remarkably fluid and delicate transitions in tempi and dynamics. Entrances, except when meant to be accented, were so soft and precise one could scarcely hear them initiate.

Bela Bartók’s “String Quartet No. 5,” next on the program, was, of course, a natural choice for this quartet, formed in Budapest in 1975. Two of its original Hungarian members (Károly Schranz, second violin, and András Fejer, cello) remain with the group, joined by first violin Edward Dusinberre in 1992 and viola Geraldine Walther in 2005.

Introduced by Dusinberre as “one of the craziest pieces of music we’ve played,” the work was played with passion and fidelity. Bartók’s trademark glissandi and other effects, including unexpected isolated pizzicati and spicatti, were executed with precision and feeling. The second movement’s conclusion in delicate pianissimo figures for all voices was breathtaking.

After intermission, the quartet was joined by pianist Joyce Yang, silver medalist at age 19 in the 2005 Van Cliburn International Piano Competition. Playing with the Takács Quartet, she also won the De Groote award for best performance of chamber music in that competition. Ms. Yang and the Takács Quartet were made for each other, evident in their rapt mutual attention as they played.

How often does a first violin turn around in his chair during rests to watch the pianist? How often does a pianist, while accompanying, gaze at the viola during a solo?

The result, as one might expect, was a remarkable community of interpretation. VIP Sponsors David and Gunda Hiebert, observers at the Van Cliburn competition, noted a jazzlike give-and-take there between the quartet and Ms. Yang, allowing her to impart a spur-of-the-moment mood to the music, readily adopted by the quartet.

The final work was Robert Schumann’s “Piano Quintet in E-flat Major, Op. 44.” Critics have objected to this work’s “overly prominent” piano part, but balance problems were not evident here, as the quintet seemed if possible even more closely fused than the quartet alone.