Rap music's appeal to the Beastie Boys ''has always been its tendency towardsinnovation,'' says B-Boy Mike D.

''What rap came out of was a group in a park, and you know, a guy who had a DJwith two turntables to provide music for this group,'' the rapper, born Michael Diamond, explains. ''So he had to figure out innovative ways to make it work, taking old records and cutting them up and coming up with a whole musical backing.''

As rap moved to clubs and recorded formats, ''the records that got the most respect and the most props were the ones that came out and broke the most ground- that came out of nowhere and changed the way everybody sounded.''

The Beastie Boys' Licensed to Ill, the first rap album ever to reach No. 1, was one such record, but Mike D's comments can also apply to the group's latest release, Check Your Head.

The Beasties - Mike D, Ad-Rock (Adam Horovitz) and MCA (Adam Yauch) - began as a New York City punk band in 1981, but put down their instruments when they picked up the fight for your right to party in 1986 and became rap superstars.

On Check Your Head, the B-Boys break new ground by backing their raps with a funky melange of live instrumentation and samples, producing what Details magazine called their ''most inspired album to date.''

The trio took a different approach from 1989's sample-saturated Paul's Boutique, which brought the group more critical respect than commercial success, to keep its sound fresh and innovative.

''We wanted to do something new, and at the same time we already had the background of playing instruments because we started out as a hardcore band,'' Mike D says.

Check Your Head grew out of late-night jam sessions at the Beasties' G-Son studio in Los Angeles, a hip-hop haven complete with an indoor basketball hoop and skateboard ramps.

''If we had like a fantasy when we started out, say like when we did that hardcore record Polly Wog Stew or when we did (an underground hit in 1983) - if we'd had someone say: 'Well, what would you guys really want?', weprobably would have said well, just like a studio where we could go play music and hang out all the time, and that's what we had.''

Although Check Your Head has been hailed as the trio's ''third masterpiece'' bythe Village Voice, the album has also been criticized for the murky quality of its vocal mixes, which Entertainment Weekly said sound as if they were recorded underwater.

''We rocked a distorted mike effect that has confused a lot of people,'' Mike Dconcedes, laughing.

''There's some people who realize how fly it is, but there's some people that just aren't with it. You can't please all the people.

''Some people think it was by accident, but really, they don't understand thatwe tried a bunch of different microphones until we could find mikes that soundedlike that.'' ''We rocked a distorted mike effect that has confused a lot of people,'' Mike Dconcedes, laughing.

''There's some people who realize how fly it is, but there's some people that just aren't with it. You can't please all the people.

''Some people think it was by accident, but really, they don't understand thatwe tried a bunch of different microphones until we could find mikes that soundedlike that.''

Of course, the new style has made for some changes in the Beasties' stage show.

The group - joined on stage by a DJ, a keyboardist and a percussionist - has taken to using what Mike D calls ''blind set lists,'' with the rappers rarely knowing where they'll be or what they'll be doing next.

''What we got into in Japan was like one of us would make a set list and not tell anybody else or show it to anybody else before we'd go on stage, so that way it would be like a jolt of surprise,'' he explains.

Of course, the new style has made for some changes in the Beasties' stage show.

The group - joined on stage by a DJ, a keyboardist and a percussionist - has taken to using what Mike D calls ''blind set lists,'' with the rappers rarely knowing where they'll be or what they'll be doing next.

''What we got into in Japan was like one of us would make a set list and not tell anybody else or show it to anybody else before we'd go on stage, so that way it would be like a jolt of surprise,'' he explains.

''You'd get out there, do the first song and then you kind of see what goes on. Kind of like rotating musical chairs, 'cause some songs I'll be playing drums, and some songs all three of us are up front rapping, and some songs I'm up front and everybody else is playing instruments.''

The Beastie Boys' ever-changing set lists keeps the trio's performances as close to the edge as its sound.

''To me that's always what rap is based on,'' Mike D says, ''just constant evolution and constant innovation.''