Sheets of sound was a term coined in 1958 by Down Beat magazine jazz critic Ira Gitler to describe the new, unique improvisational style of John Coltrane. Gitler first used the term on the liner notes for Soultrane (1958).

Coltrane employed extremely dense improvisational yet patterned lines consisting of high speed arpeggios and scale patterns played in rapid succession: hundreds of notes running from the lowest to highest registers. The lines are often faster than sixteenth notes, consisting of quintuplets, septuplets, etc., and can sound like glissandos. The saxophonist invented this style while playing with Thelonious Monk and later developed it further when he returned to Miles Davis' group. Both leaders are known to have facilitated a free atmosphere where Coltrane was able to experiment on the bandstand.

The saxophonist used the "sheets of sound" lines to liquidise and loosen the strict chords, modes, and harmonies of Hard Bop, whilst still adhering to them (at this stage in his musical development). Playing with the Miles Davis groups, in particular, gave Coltrane the free musical space in which to apply harmonic ideas to stacked chords and substitutions. Further, this open approach allowed Coltrane to arpeggiate three chords simultaneously, a style Monk initially taught Coltrane. The "three-on-one chord approach" gave the music a fluid, sweeping sound that was harmonically vertical. Concepts of vertical (chordal) versus horizontal (melody) are key ideas in the work of George Russell, whom Coltrane had recorded with in September 1958. This approach reflected Coltrane's fascination with third relations. Sometimes he used diminished chords, other times he used augmented chords. At times, Coltrane might use scales or licks in the passing keys instead of arpeggios. Coltrane employed these harmonic ideas during his "sheets of sound" stage in 1958. At other times, he would simply play rapid patterns of diminished-scales.

John William Coltrane (September 23, 1926 – July 17, 1967) was an American jazz saxophonist and composer. Working in the bebop and hard bop idioms early in his career, Coltrane helped pioneer the use of modes in jazz and later was at the forefront of free jazz. He organized at least fifty recording sessions as a leader during his recording career, and appeared as a sideman on many other albums, notably with trumpeter Miles Davis and pianist Thelonious Monk.

As his career progressed, Coltrane and his music took on an increasingly spiritual dimension. His second wife was pianist Alice Coltrane, and their son Ravi Coltrane is also a saxophonist. Coltrane influenced innumerable musicians, and remains one of the most significant tenor saxophonists in jazz history. He received many posthumous awards and recognitions, including canonization by the African Orthodox Church as Saint John William Coltrane. In 2007, Coltrane was awarded the Pulitzer Prize Special Citation for his "masterful improvisation, supreme musicianship and iconic centrality to the history of jazz."