Mr. Adès, who is also a concert pianist and conductor, has led performances of both: “The Tempest” (2004), based on Shakespeare’s play, which has proved an important contribution to the contemporary repertory, and the two-act “Powder Her Face” (1995), inspired by the romantic exploits of the Duchess of Argyll, which deserves more productions in opera houses both here and abroad.

Mr. Adès, whose studies at the Guildhall School in London included marimba, writes music that is both cerebral and emotional. Unusual timbres, glittering sonorities, innovative use of percussion and overlapping rhythms mesh to create a voice distinctively his. The scores are often quirky and surreal, with rumbling low sonorities interlaced with stratospheric passages featuring piercingly high winds, for example.

These trademark high sonorities are an integral element of “The Tempest,” set to the couplets of Meredith Oakes’s libretto. The work received its premiere in 2004 at the Royal Opera House in London and was staged in 2012 at the Metropolitan Opera in a new production by Robert Lepage.

The soprano part of Ariel, brilliantly sung by Audrey Luna at the Met, is a coloratura tightrope walk so daunting it makes Mozart’s Queen of the Night aria seem like child’s play. Such quirky elements are deftly balanced with moments of haunting beauty, shimmering orchestral passages and more traditional arias, like the yearning love duet at the end of Act II. The colorfully orchestrated overture bristles and surges as it evokes the tempestuous seas.

Many operas about historical figures center on political or religious leaders, including John Adams’s “Nixon in China” and Philip Glass’s “Satyagraha,” which was inspired by the life of Gandhi. “Powder Her Face” depicts the life of the British socialite born Ethel Margaret Whigham (the Duchess of Argyll). Her 1963 divorce proceedings and myriad love affairs provided fodder for the tabloids and plentiful material for Mr. Adès’s cabaret opera, set to a libretto by Philip Hensher. Flashes of tango, Cole Porter, Berg and other influences coalesce into a fascinating whole in the four-singer chamber work, which achieved notoriety after the premiere because of a so-called “fellatio aria,” which musically simulates the act onstage.

Raunchy onstage antics are commonplace in Europe but rarer on comparatively prim and decorous American stages. Jay Scheib’s production for the New York City Opera at the Brooklyn Academy of Music last February featured about two dozen naked men strolling onstage at the same time and an innovative use of video.

The protagonist, like Anna Nicole Smith in Marc-Anthony Turnage’s recent opera “Anna Nicole,” may seem trivial by comparison with the weightier personalities portrayed in other contemporary works. But Mr. Adès creates a character both comic and tragic, framed by an intriguing portrait of social mores and class divisions. VIVIEN SCHWEITZER