Warthur
Some setting of expectations is needed here: Bremen's Beat Club was not a concert venue, but was rather a television show, with King Crimson's 1972 appearance on it being the only known video record of Jamie Muir's inclusion in the band. (You've probably seen the Larks' Tongues In Aspic Part I performance on YouTube.) This Collector's Club release - also included on the Larks' Tongues In Aspic: The Complete Recordings boxed set - features the full live-in-the-studio performance from the band.
This does include some studio chatter and tuning-up of equipment before things get into full swing, but what a treat when they do - not only do we get early takes on Exiles and Larks' Tongues In Aspic Part I, but there's also an improv session which really shows what this lineup could do when they let their imaginations fly (as they frequently did). No caveats needed about sound quality here - the studio engineers did their job more than adequately, making this one of the best-sounding live-ish recordings from this particular lineup of the band to exist.