Three different organizations are presenting opera in Washington this week.

The Washington Opera will end its current repertory run with the final performance of Bellini's "I Capuleti e I Montecchi" this afternoon in the Opera House, starting at 2. One hour later, in the Concert Hall, Antal Dorati will conduct the Detroit Symphony and a stellar group of singers in one of the least-performed operas of Richard Strauss. "The Egyptian Helen."

On Tuesday night, the New York City Opera will open its annual visit to the Kennedy Center with an unusual double bill, only one-half of which is operatic. They are teaming up Purcell's "Dido and Aeneas" with a ballet version of "Le bourgeois gentilhomme," for which the choreography has been devised by both George Balanchine and Jerome Robbins.

The Strauss opera, next to the last in the great list of works for which Hugo von Hoffmansthal provided Strauss with librettos, is about Helen of Troy. However, in this operatic version, the librettist and composer turned to other sources than Homer and Virgil. Their Helen is the "phantom" Helen of Euripides, who is whisked away to Egypt by Hera, the wife of Zeus. Hera is angry with Paris because he said that Aphrodite was the more beautiful of all the goddesses. So, instead of having Paris take Helen away to Troy, Hera transports Helen to Egypt where, in the seventh year after the fall of Troy, she is rounited with Menelaus, her husband.

Thanks to various highly operatic potions, Menelaus gets over his suspicions about his wife, falls in love with her a second time, and, in one of the opera's big senes, enjoys a second bridal night about which Helen sings at the top of her lungs.

"The Egyptian Helen" had its world premiere in Dresden on June 6, 1928, and its U.S. premiere at the Metropolitan Opera the following Nov. 6. The title role was sung in Dresdent by Elisabeth Rethbert, after a long and often highly emotional argument between Hofmannsthal, who said, "Rethberg is worse than mediocre as an actress and this will ruin Helen," and Strauss, who replied, "She is generally considered the best German singer with the most magnificent voice and an accomplished singing technique."

Strauss was right, and Hofmannsthal finally grudgingly wrote, "Perhaps if only Rethberg is able and willing to learn, that might be our salvation."

Fritz Busch was the conductor of the Dresden premiere; his young assistant was Antal Dorati.This afternoon, Dorati will have a cast headed by Gwyneth Jones in the title role, Barbara Hinds as the sorceress. Aethra, Birgit Finnila as the Omniscient Sea Shell, as Daud and Matti Kastu as Menelaus. The Kenneth Jewell Chorale will supply the choral passages. Following today's performance, which his been preceded by performances in Detroit and New York City, the entire opera will be recorded for London Records.

The New York City Opera, in addition to its opening double bill, is bringing another infrequent visitor for its two weeks here. Rossini's "Il Turco in Italia," Or "The Turk in Italy," will be the occasion for Beverly Sills' final operatic appearance in Washington, before she takes over the direction of the company on July 1. Sills will sing only in the gala benefit on May 5.

"The Turk in Italy" was Rossini's sequel to the immensely popular "L'Italiana in Algieri," or "The Italian Girl in Algiers," which he wrote in 1813 for the Venice season. Commissioned by La Scala in Milan for a new opera to open the 1814 season, Rossini decided that he would simply switch the direction of the tourist travel across the Mediterranean, and bring a male Turk to Italy instead of a female Italian to Algiers.

There is a nice parallel between one philosophy expressed in "Il Turco" by the elderly Don Geronio, who is married to the young Fiorilla, and the central idea of Donizetti's "Don Pasquale." Geronio himself puts it, "An old man can commit no greater folly than to take a young wife."

While it took "The Turk" over a century to achieve popularity as first-rate operatic comedy, it has all the elements, both musical and dramatic, to place it alongside Rossini's other top scores in comic vein.

With the Kennedy Center's big French festival only two weeks away, it is noteworthy that the New York City Opera's repertory is heavily weighted in the direction of France. While Richard Strauss calls his nouveau-riche bourgeois gentleman "Der Burger als Edelmann," he is, nonetheless the M. Jourdan of Moliere. And four of the operas in the New York repertory are French to the core, for all that Donizetti's "La fille du regiment" is being sung in English.

No one seeing the advertisements for the New York City Opera's "Bourgeois gentilhomme," and the Vienna Opera's "Ariadne auf Naxos" should forget that the entire origin of the opera, "Ariadne" arose out of the less-than-successful attempt by Strauss and Hofmannsthal to make a play with music out of the Moliere comedy. When the Vienna company brings "Ariadne" here next November, its first act will be set in the home of the newly rich gentleman. It is his instructions that the theater people and the opera troupe he has engaged must perform simultaneously in order to be through in time for a fireworks display that sets off one of the opera's great outbursts. How this will be done in the new ballet we shall shortly see.