Last night's performance of "Platinum," the musical now playing in the Kennedy Center Opera House, went on as scheduled, in spite of a strike by the members of the orchestra that began at midnight Sunday.

The show could go on since much of the score is on tape or played onstage by a half dozen rock musicians who are not members of Local 161.710, the D.C. chapter of the Musicians Union, and also because the strike was not recognized by other trade unions employed by the Center.

A mediation session between the striking musicians and the Center management has been called for this morning in the offices of the Federal Conciliation Service.

One of the chief issues in the dispute is that of tenure for the orchestra which regulary plays for operas, ballets and musicals in the Opera House. Martin Feinstein, executive director of the Center, said yesterday that "the Kennedy Center would accept the principle of tenure sought by these musicians provided it could establish a satisfactory initial screening (audition) or termination system."

Meanwhile, negotiations between striking musicians of the National Symphony Orchestra and the orchestra management, which began at 10:30 yesterday morning, were still in progress at 9 o'clock last night. This is the longest negotiating session since the beginning of the strike on Sept. 24.

If settlement is not reached in both strikes, the following concerts will be affected:

The United Nations concert, scheduled for the Kennedy Center at 6 p.m. Saturday. It is expected that soprano Clamma Dale, who had been engaged to sing with the National Symphony under Rostropovich, will sing a solo recital.

THe concert by the Pittsburgh Symphony set for 3 p.m. Sunday and that by the Philadelphia Orchestra at 8:30 p.m. Monday will not be played. The musicians of both orchestras have advised their managements that they will not play in the Kennedy Center if either the National Symphony musicians or those of the orchestra in the Opera House are on strike.