NATIONAL SYMPHONY: For many years Max Rudolf has contributed notably to operatic and symphonic activities in this country. Among the top posts he has held have been these of music director of the Cincinnati Symphony and conductor and artistic advisor to the Metropolitan Opera.

This week Rudolf will conduct the National Symphony's subscription concerts Tuesday through Friday in the Kennedy Center. He has put together a gorgeous program: Nielsen's "Maskarade" Overture; the Dallapiccola Variations; Mozart's Symphony No. 34, and the first piano concerto by Brahms with Peter Frankl as soloist.

Several weeks ago when Michael Tilson Thomas made his debut as guest conductor with the National Symphony, his outstanding account of the Ives Fourth Symphony took all the reviewing space available the following day. This left no room to speak of the remarkable performance Thomas led of the Beethoven Fifth Symphony or of the beauty of Mijran Kojian's playing in the Mozart G Major Violin Concerto.

OPERA NEWS: The Metropolitan Opera will increase its ticket prices next season to cover a part of what Met executive director Anthony Bliss referred to as "inflation and rising costs." In making the announcement, Bliss added, "As it is, the box office only pays for half of our costs." Family circle seats which have been $ 6.50 will be $ 7; orchestra seats will go up from $ 22.50 and $ 25 to $ 30. Bliss also pointed out that the Met's budget 10 years ago was just under $ 17 million. For the present season it is $ 29.7 million.

The National Opera Institute has appointed John Ludwig as its executive director to succeed George London who will continue to act as consultant for the Institute's young singers program.

Ludwig, who was general director of the Wolf Trap Foundation from 1973 to 1975, has been artistic administrator of the San Francisco Opera since that time.

The Fourth Annual Music Festival of Washington archdiocesan schools will be given in the Kenney Center at 3 p.m. Sunday. There will be music for bands and chorus. Tickets at the door.

The sixth annual Joseph Feder Memorial String Competition for D.C. junior and senior high school students of violin, viola, cello and double bass, will be held in Federal City College Music Department at 9:30 a.m. Friday.