"I can't understand why people are frightened of new ideas," says John Cage. "I'm frightened of the old ones."

Cage, inventor of the prepared piano, of the "happening," is the Edison of the avant garde - he owns more patents on more new ideas than anyone else. And his newest ideas pretty. Sitting at a small desk in a corner of the stage, he plucks the spines of cactuses, producing an attractive ping, or plonk, that is amplified until it fills the hall. He fills seashells with water and pours the water out, getting a gentle little gulpety gulp. After all the deliberate chaos of the happenings, Cage has found a new way to shock his audience: by making noises that sound almost like melody.

Cage will be in Washington next weekend - the 25th, 26th, and 27th - for "Two Nights of New Music," a festival that will actually fill up three nights and two days, so you get three concerts for the price of two.

The important thing is that Two Nights offers you more chance to hear more new kinds of music than you've ever heard before: Established jazz greats like Cecil Taylor and Anthony Braxton. Rising new stars like Sam Rivers, The Wrold Saxophone Quartet (which plays without accompaniment - just for guys on sax, a kind of wailing hiccuppy groaning sound that can drive everything out of your kind but the music).

New avant garde classical composers Steve Reich and Philip Glass, who have both, in their separate ways, arrived at a kind of music based on repetitions of essentially simple figures - almost tunes - by musicians who slowly go in and out of sync so that they sometimes sound like an echo, sometimes a fugure, and every bit as hypnotic as the more chaotic-sounding jazz musicians.

Classical New Music audiences at their worst tend to be academic, overquiet, attenat their worst get into a kind of churching activity - people walking back and forth in the aisles, calling to friends, shouting encouragement to the musicians.

How is a jazz audience going to react to Cage's quiet plinking? What are the teachers of harmony going to feel when they hear the World Saxophone Quartet?

My guess is that Cage will wind up seducing the audience into silence - there's such an air of cheery saintliness about him that he always gets what he wants. My guess is that the World Saxophone Quartet will have the professors shaking their ringing heads in wonder. But that's only my guess. Yours is just as good - and you should be there to see what happens. Each of the concerts is scheduled for six hours, 6 to midnight. No one, least of all the organizers, believes that the concerts will take that long. They'll take much longer.

When any of these groups gets set up, it tends to stay set up, and keep playing.

So all around the DAR's Constitutuion Hall next Friday and that Sunday, you should find a kind of party in progress. People taking a break while the musicians set up, tpeople who seem to spend their lives taking a break. The crowd should include ageing rock 'n' rollers who finally learned how to play their instruments and discovered jazz, fans and followers of conceptual art who have always had a crush on the music of Reich and Glass, people who want to see what John Cage is up to now, jazz groups and groupies, music students, music groups, avant garde groupies (than whom there are no groupier).

If you manage to get inside, and decide to listen, you might discover that the music is the best fun of all. Whether it's avant garde jazz or avant garde classical, it all owes a debt to John Cage. For some of the jazz musicians that debt is unconscious or secondhand. For others, like Taylor and Braxton, who have considerable classical training, the debt is openly acknowledged.

Reich likes to say that the kind of music he and Glass compose is like the older, wall-of-sound kind of jazz - Coltrane years ago. And that new jazz is like the free improvisation of chance-determined classical music - John Cage years ago. "We've both gone zip," he says, crossing his arms and pointing a finger in opposite directions. Cage seems now to be going in one more entirely new direction.

Surely, when all those guys get together something will be happening. The organizers of Two Nights of New Music call it "the most important music festival of the '70s." And it is shaping up to be just that: the biggest music success this town's ever seen - or the biggest disaster. In either case it will be something to see. And hear.

There are two main concerts for out-of-town musicians, Friday and Sunday; Saturday the 26th there are two separate concerts of local jazz groups.

Saturday and Sunday afternoon are taken up by workshops at various places around D.C. Workshops are sometimes halfway between performances are group therapy sessions, sometimes performances, sometimes teaching sessions. Don't feel you will not be welcome at a workshop just because you don't play an instrument, can't sing Yankee Doodle and are tone-deaf.But if you play an instrument, bring it along. John Cage's workshop (noon Sunday at WPA Gallery, 1227 G. St. NW) will include a performance kind of lecture, "Silence," which is one of the most important events in the avant garde repertoire, and one of the most fun.