Forty outstanding young pianists, ages 12 to 17, gather from around the world to play some of the most advanced works by Bach for the 23rd Johann Sebastian Bach International Competitions. The public is invited to hear the Bach battle for free: by the end of it, three of the best will each have won $1250. The American Bach Foundation holds the preliminaries Saturday starting at 9 a.m. and the finals Sunday begin at 2, at Lisner Auditorium, 21st and H streets NW. Call 338-1111.

And there'sa lot of horntooting to celebrate the tenth year of hte Smithsonian Jazz Program: Saturday, rare films of past jazz performances, some from the 20s and '30s, are shown at 2:30, free, Baird Auditorium. Among the clips are Louie Armstrong, Duke Ellington, Bessie Smith and Ethel Waters. Live performances start Friday with vibraphonist Red Norvo; Saturday Benny Carter goes on playing his sax as he's been doing for 50 years; and the Smithsonian's resident jazz ensemble plays big-band Sunday. All shows are at 8 in the Baird Auditorium, in the Museum of Natural History, Tenth and Constitution NW. Tickets are $10.50. Call 357-1500.

Meanwhile, Manassas' Jazz Festival, now in its 16th year, is being held this time in Reston, where there's more room. Dozens of top traditional jazz musicians in the country, including Charlie Spivak and Billy Butterfield, in shows Saturday and Sunday at 9. Other shows are Friday at 9, Saturday at 1:30, Sunday at 2:30; admission, $18 each. At the Sheraton International Conference Cneter, 11810 Sunrise Valley Drive in Reston. Call 631-1165.Back in town, ballad singer Jean Ritchie sings tales of the Applachians, and Christmas carols too, Saturday at the National Museum of American Art as part of the "More Than Land of Sky: Art From Appalachia" exhibit. The folk music is free at 2 in the Lincoln Gallery. Call 357-3095.