What started as a night of little music yesterday grew into one of the nicest parties in town. It was the Kennedy Center's "A Night in Old Vienna," hosted by Alexander Schneider and his friends, a yearly sellout New Year's Eve ball featuring Mozart, Schubert and, of course, Strauss.

Spontaneity was the mood of the evening, which began with Lillian Kallir and Claude Frank in lively readngs of Mozart and Schubert pieces for piano four-hand. The Sonata in D Major (K. 123a), by a teen-aged Mozart, had all of the Cherubino's impetuosity, making the most of the foreshadowing of "Voi che sapete" in the first movement.

Then came a buoyant performance of Schubert's famous "Trout" quintet, led by violinist Schneider. Despite some overuse of portamento in the opening and iffy pitches by Schneider, it was a beautiful interpretation, full of imagined embraces and remembered smiles. And by the time the "Schmalzabend" of Lanner and Strauss began, the audience was ready to dance.

And dance they did. The concerts began in 1973, with virtually the same program as was played last night, but it was not until 1976 that dancing in the Grand Foyer past midnight began. This year for the first time, all the Kennedy Center patrons were invited to the ball, and with every house except the Eisenhower sold out, the guest list nearly reached 7,000.