Answer by taking a quote from the following article:

King Crimson are an English progressive rock band formed in London in 1968. King Crimson have been influential both on the early 1970s progressive rock movement and numerous contemporary artists. The band has undergone numerous formations throughout its history of which 21 musicians have been members; since October 2017 it has consisted of Robert Fripp, Jakko Jakszyk, Tony Levin, Mel Collins, Pat Mastelotto, Gavin Harrison, Jeremy Stacey and Bill Rieflin. Fripp is the only consistent member of the group and is considered the band's leader and driving force.

After their first US tour, King Crimson was in a state of flux with various line-up changes, thwarted tour plans, and difficulties in finding a satisfactory musical direction. This period has subsequently been referred to as the "interregnum" - a nickname implying that the "King" (King Crimson) was not properly in place during this time. Fripp became the only remaining musician in the band, with Sinfield expanding his creative role to playing synthesizers. Fripp and Sinfield recorded the second King Crimson album, In the Wake of Poseidon, in 1970 with the Giles brothers hired back as the session rhythm section, and with jazz pianist Keith Tippett and Circus saxophonist Mel Collins as guest musicians. The group considered hiring Elton John to be the singer, but decided against the idea. Lake then agreed to sing on the album in exchange for receiving King Crimson's PA equipment, except on "Cadence and Cascade", which is sung by Fripp's friend Gordon Haskell. Though Tippett was offered band membership, he preferred to remain as a studio collaborator, performing with the band for a single gig. Upon its release in May 1970, In the Wake of Poseidon reached No. 4 in the UK and No. 31 in the US. It received some criticism from those who thought it sounded too similar to their first album. With no musicians to perform material from their new album, Fripp and Sinfield persuaded Haskell to join as singer and bassist and recruited Andy McCulloch as drummer, retaining Collins as saxophonist, flautist and occasional keyboard player. During the writing sessions for the third album, Lizard, Haskell and McCulloch had no say in the direction of the material, since Fripp and Sinfield wrote the album themselves, bringing in Tippett, Mark Charig on cornet, Nick Evans on trombone, and Robin Miller on oboe and cor anglais as additional musicians. Haskell sang and played bass. Jon Anderson of Yes was also brought in to sing the first part of the album's title track, "Prince Rupert Awakes", which Fripp and Sinfield considered to be outside Haskell's range and style. Lizard featured stronger avant-garde jazz and chamber-classical influences than previous albums, as well as Sinfield's upfront experiments with processing and distorting sound through the EMS VCS 3 synthesiser. It also featured complex lyrics from Sinfield, including a coded song about the break-up of the Beatles, with almost the entire second side taken up by a predominantly instrumental chamber suite describing a medieval battle and its outcome. Released in December 1970, Lizard reached No. 29 in the UK and No. 113 in the US. Described retrospectively as an "acquired taste"., Lizard was certainly not to the taste of the more rhythm-and-blues-oriented Haskell and McCulloch, both of whom found the music difficult to relate to. As a result, Haskell quit the band acrimoniously after refusing to sing live with distortion and electronic effects. McCulloch also departed, leaving Fripp and Sinfield to recruit new members once more. After a search for new musicians, Fripp and Sinfield secured a returning Collins and Ian Wallace on drums. Auditions for a singer included those from Bryan Ferry and John Gaydon, the band's manager,. The position went to Raymond "Boz" Burrell. Bassist John Wetton was invited to join, but declined (at the time) in order to play with Family. Rick Kemp also declined an offer to join, leaving Fripp and Wallace teaching Burrell to play bass rather than continue auditions. Though he had not played bass before, Burrell had played enough rhythm guitar to assist him in learning the instrument. With the line-up complete, King Crimson toured in 1971 for the first time since 1969. The concerts were well received, but the musical and lifestyle differences of Collins, Wallace, and Burrell began to alienate the drug-free Fripp, who began to withdraw socially from his bandmates, creating further tension. In 1971, the new King Crimson formation recorded Islands. Loosely influenced by Miles Davis's orchestral collaborations with Gil Evans and Homer's Odyssey, the album also showed signs of a split in styles between Sinfield (who favoured the softer and more textural jazz-folk approach and wanted the band to move in a Miles Davis direction) and Fripp (who was drawn more towards the harsher instrumental style exemplified by the instrumental "Sailor's Tale", with its dramatic Mellotron and banjo-inspired guitar technique). Islands also featured the band's one-and-only experiment with a string ensemble on "Prelude: Song of the Gulls" and the raunchy rhythm-and-blues-inspired "Ladies of the Road". A hint of trouble to come came when one member of the band allegedly described the more delicate and meditative parts of Islands as "airy-fairy shit". Released in December 1971, Islands charted at No. 30 in the UK and No. 76 in the US. Following a period of touring Islands, Fripp asked Sinfield to leave the band, citing musical differences and a loss of faith in his partner's ideas. The remaining band broke up acrimoniously in rehearsals shortly afterward, owing to Fripp's refusal to incorporate other members' compositions into the band's repertoire. He later cited this as "quality control", with the idea that King Crimson would perform the "right kind" of music. King Crimson reformed to fulfil touring commitments in 1972, with the intention of disbanding afterwards. Recordings from various North American dates between January and February 1972 were released as Earthbound in June 1972, noted and criticised for its sub-par sound quality and playing style that occasionally veered towards funk, with scat singing on the improvised pieces. By this time, a definite musical rift between Fripp and the rest of the band existed, since Wallace, Burrell and Collins favoured a more rhythm-and-blues style. Though personal relations improved during the 1972 tour (to the point where most of the band wished to continue), Fripp opted to part company with the existing band and to restructure King Crimson with new members, since he felt the current members wouldn't be able to play the new material he had in mind. King Crimson have incorporated improvisation into their performances and studio recordings from the beginning, some of which has been embedded into loosely composed pieces such as "Moonchild" or "THRaK". Most of the band's performances over the years have included at least one stand-alone improvisation where the band simply started playing and took the music wherever it went, sometimes including passages of restrained silence, as with Bill Bruford's contribution to the improvised "Trio". The earliest example of King Crimson unambiguously improvising is the spacious, oft-criticised extended coda of "Moonchild" from In the Court of the Crimson King. Rather than using the standard jazz or blues "jamming" format for improvisation (in which one soloist at a time takes centre stage while the rest of the band lies back and plays along with established rhythm and chord changes), King Crimson improvisation is a group affair in which each member of the band is able to make creative decisions and contributions as the music is being played. Individual soloing is largely eschewed; each musician is to listen to each other and to the group sound, to be able to react creatively within the group dynamic. A slightly similar method of continuous improvisation ("everybody solos and nobody solos") was initially used by King Crimson's jazz-fusion contemporaries Weather Report. Fripp has used the metaphor of "white magic" to describe this process, in particular when the method works particularly well. Similarly, King Crimson's improvised music is rarely jazz or blues-based, and varies so much in sound that the band has been able to release several albums consisting entirely of improvised music, such as the Thrakattak album. Occasionally, particular improvised pieces will be recalled and reworked in different forms at different shows, becoming more and more refined and eventually appearing on official studio releases (the most recent example being "Power to Believe III", which originally existed as the stage improvisation "Deception of the Thrush", a piece played on stage for a long time before appearing on record).

How did they improvise together ?
Fripp and Sinfield recorded the second King Crimson album, In the Wake of Poseidon, in 1970 with the Giles brothers hired back as the session rhythm section,