Dubbed "A Salute to the Capital City," the Jan. 3 inauguration celebration for Mayor Marion Barry, City Council Chairman-elect David A. Clarke and six other members of the D.C. City Council will include a breakfast, parade and swanky black-tie ball at Washington's new Convention Center.

By law, the officials must be in-stalled at noon Jan. 2, a Sunday. On that date, D.C. Superior Court Chief Justice H. Carl Moultrie I will officially swear in Barry, Clarke and council members Betty Ann Kane (D-At Large), Hilda Mason (State-hoood-At Large), Frank Smith (D-Ward 1), Polly Shackleton (D-Ward 3), William R. Spaulding (D-Ward 5) and Nadine P. Winter (D-Ward 6). Attendance at that ceremony will be restricted primarily to members of the elected officials' families.

The public festivities will begin the next morning when 2,000 guests will gather for a $15-a-person inaugural breakfast in the International Ballroom of the Washington Hilton Hotel, beginning at 7:30 a.m.

The inaugural parade, including 65 marching units, school bands, cultural groups and floats, is scheduled to begin at 10:15 a.m. at Seventh Street and Constitution Avenue NW. It will move west on Constitution to 14th Street and then north on 14th to Pennsylvania Avenue. At that point, officials will move to reviewing stands near the District Building, and the parade will continue up 13th Street toward the Convention Center.

At 12:30 p.m., Barry, who was elected in November to his second four-year term, and the other officials will take the oath of office for the second time inside the Convention Center, which is on New York Avenue between Ninth and 11th streets NW. The crowd will be entertained by the National Symphony Orchestra

That night, about 4,000 guests are expected to begin arriving at the Convention Center at 9 for a massive ball that will be set to the music of the Duke Ellington Orchestra. Tickets to the affair will cost $35 each.

The day-long events are being sponsored by a 1,000-member 1983 Inaugural Committee. Tickets for the breakfast and ball will be sold noon to 7 p.m. daily, between Dec. 22 and Jan. 2, in the Adams Room of the Washington Hilton. Tickets may also be ordered by mail, but mail orders and payment must be received by Dec. 24.

Free passes o the inauguration and parade will be issued on a first-come, first-served basis during regular hours at the Washington Hilton ticket office. The telephone number at the ticket office is 727-2285.