Miles et al

Music - influence of Bobby Hackett. Middle register, short spare phrases, sketches sprinkled over the beat a la Monk. Miles detaches the melody line from the chord sequence and then removes the chord sequence altogether and improvises on modes. At the same time, Coltrane is exploring polytonality by playing a melody in one key above the chord sequences in a different key.
Chronology - The 1950's was a golden decade for jazz Charlie Parker had established new music which built on the great traditions of Louis' rhythm and the Big Band swing song sequences. He discovered a new way of resolving sounds onto the chords. He could fly and swing ! The 'Cool' and 'Hard Bop' schools had established some popularity.
By 1960 jazz was apparently fragmenting - 
Dixieland Revival, Swing, Bop, Cool, Hard Bop and now Modal and Free and Fusion ... 
But in the 1960s jazz went a different way building on the esoteric minority cults of drugs and musical elitism ... no dancing, no fun ... just protest and pain ... 
Ray Charles, Louis Jordan and others were taking their mix of jazz, blues and Gospel into a new blues mainstream 'Rhythm and Blues'. They could dance and have fun! 
A big schism in jazz developed between the tradition of Louis, Duke and Bird and the iconic cult of modernism and the avant guarde ... but the audience had gone to Rock ... 
1954 Miles Davis kicks the habit and prepares to devout himself to music. Monk like tenderness with few notes, stark pure endearing music not the frenetic angles of Bop.
Blacks worshipped Miles and rejected Louis. This was a bigger schism in the music than Bop v. Traditional Jazz or East Coast v. West Coast ... 
Miles Davis had four important groups during this time.

The first 1955-58 featured John Coltrane single greatest jazz group ever.

1956 'Workin' ..., Steamin' ..., Relaxin' ..., and Cookin'' with the Miles Davis Quintet, muted ballad playing rhythm section hardest swinging in the business.

The second important Davis group. The album 'Kind Of Blue' from this group is high on most lists of favourite jazz albums. The primary style of this group is called modal, as it relies on songs written around simple scales or modes that often last for many measures each, as opposed to the quickly changing complex harmonies of bebop derived styles.

The third 1957-63 Davis group of the era was actually the Gil Evans orchestra. Miles recorded several classic albums with Gil, including 'Sketches Of Spain'.

The fourth important Miles group of this period 1964-68 included Wayne Shorter on saxophone, Herbie Hancock on piano, Ron Carter on bass, and Tony Williams on drums. The early recordings of this group, including 'Live At The Plugged Nickel', as well as the earlier My Funny Valentine

A stream of records for Prestige and a stream of sidemen - Sonny Rollins, Horace Silver, Ed Garland, Philly Joe Jones, Paul Chambers, Jackson, John Coltrane.

1957 'Birth of the Cool' - Gil Evans, Gerry Mulligan
1956/7 'Miles Ahead', 'Porgy and Bess', 'Sketches of Spain' ... with Columbia and searching for the lost mainstream of American music, Miles calls for Gil Evans again and he becomes an icon, the best suits, the best women, the shades, a hero emerges, the best loved albums for years. 
Gil Evans wrote arrangements with plenty of space for Miles to develop his beautiful solos. Exquisite sounds but a rude man. Miles was angry and frightened? Nobody loved Miles, he was a 'cult' figure but Louis was still producing magic fun music.
1959 'Kind of Blue' - Miles goes into scalar music and melody, chords and harmony no longer restrict. Cannonball Adderley and Bill Evans, best selling album of all time. 'Free' jazz was ahead but this recording was the first to ever feature truly modal Jazz. Modes brought back improvisation to the melody line. 
1960 violent times produced violent music, but the apocalyptic protest music didn't have an audience - Charles Mingus, Cecil Taylor, Archie Shepp, Max Roach ... 
1961 'Free Jazz' - Ornette Coleman with Don Cherry, Billy Higgins and Charlie Hayden abandons chord sequences, rhythm time and harmony and goes completely 'free' ... inspire or divide !?
1961 'Chasin' the Trane' at The Village Vanguard - after Dizzy's Big Band and Miles' Quintet, Trane has a spiritual awakening and emerges from drugs clean and restless, champing at the bit, restless energy, dedicated to sheets of sound and 80 choruses of the blues ...
1961 'My Favourite Things' John Coltrane - with McCoy Tyner, Jimmy Garrison, Elvin Jones, second only to Miles in popularity.
1964 'A Love Supreme' John Coltrane lays out his soul with sustained intensity ... the ultimate protest music ... 'earnest, the lyrical shout of the preacher converting his congregation' ... 
1967 'Nefertiti' Miles Davis' group started to play 'outside' the chords as he had done initially with Gil Evans and his improvisations on modal scales ... he formed a new quintet with Herbie Hancock, Wayne Shorter, Ron Carter and Tony Williams ... no chords but one group from intimate musical knowledge ... Miles flirts with another cult - avant guarde
1970 'Bitches Brew', Miles reacted to the popularity of Rock and incorporated rock beats and electrified instruments and started playing at the rock venues for the kids ... flirting with another cult to try and find popular music - rock fusion. In 1967 Gary Burton, Jeremy Steig, Larry Coryell, the group Soft Machine, and others toy with the idea of a kind of jazz-rock fusion. In 1969 it buries free jazz.

The problem -
Jazz was too big an umbrella to hold such fragmentation and rivalry
hard to play, hard to listen to, 'serious' music when the kids wanted fun, singing and dancing
barrier of a cult which was not welcoming but resentful and intensely emotional and exclusive a music for musicians only 
when you're in a hole stop digging
jazz became hate not the love of Louis and Duke ...

Miles Davis, Modal, Free and Fusion jazz and black rights somehow become intertwined and were pushing Bop further and further away and out of view. 
Elvis and The Beatles had stolen the music. The black kids wanted the Soul jazz of Ray Charles and Stevie Wonder ...
Some jazz was still heard, Louis sang 'Hello Dolly' ... 
and Stan Getz imported the Bossa Nova from Brazil in 'Desafinado' ... 
Wynton Marsalis - 'we all stand on the shoulders of giants and like Democracy you get a taste and you're hooked for life' ...

John Coltrane is another giant of this period. In addition to his playing with Miles, he recorded the album 'Giant Steps' under his own name, which showed him to be one of the most technically gifted and harmonically advanced players around. After leaving Miles, he formed a quartet with pianist McCoy Tyner, drummer Elvin Jones, and a variety of bass players, finally settling on Jimmy Garrison. Coltrane's playing with this group showed him to be one of the most intensely emotional players around. This group evolved constantly, from the relatively traditional post bop of My Favourite Things to the high energy modal of A Love Supreme to the wailing avant garde of Meditations and Ascension.
Charles Mingus was another influential leader during this period. His small groups tended to be less structured than others, giving more freedom to the individual players, although Mingus also directed larger ensembles in which most of the parts were written out. Mingus' compositions for smaller groups were often only rough sketches, and performances were sometimes literally composed or arranged on the bandstand, with Mingus calling out directions to the musicians. Alto saxophonist, bass clarinettist, and flautist Eric Dolphy was a mainstay of Mingus' groups. His playing was often described angular, meaning that the interval in his lines were often large leaps, as opposed to scalar lines, consist mostly of steps. The album Charles Mingus Presents Charles Mingus featuring Dolphy is a classic.