John Coltrane Draws a Picture Illustrating the Mathematics of Music - The Coltrane Circle

"I’d like to point out to people the divine in a musical language that transcends words. I want to speak to their souls."
〜 John Coltrane
The “Coltrane Circle,” which resembles what any musician will recognize as the “Circle of Fifths,” but incorporates Coltrane’s own innovations.
Coltrane gave the drawing to saxophonist and professor Yusef Lateef in 1967, who included it in his seminal text, Repository of Scales and Melodic Patterns.
Lateef sees Coltrane’s music as a “spiritual journey”.
Thelonious Monk once said
‘"All musicians are subconsciously mathematicians."
Musicians like John Coltrane though have been very much aware of the mathematics of music and consciously applied it to his works.
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John William Coltrane (September 23, 1926 – July 17, 1967) was an American jazz saxophonist, bandleader and composer. He is among the most influential and acclaimed figures in the history of jazz and 20th-century music.
John Coltrane was born in his parents' apartment at 200 Hamlet Avenue in Hamlet, North Carolina, on September 23, 1926.
His father was John R. Coltrane and his mother was Alice Blair.
He grew up in High Point, North Carolina and attended William Penn High School. While in high school, Coltrane played clarinet and alto horn in a community band before switching to the alto saxophone, after being influenced by the likes of Lester Young and Johnny Hodges.
Beginning in December 1938, his father, aunt, and grandparents died within a few months of one another, leaving him to be raised by his mother and a close cousin.
In June 1943, shortly after graduating from high school, Coltrane and his family moved to Philadelphia. In September that year, his mother bought him his first saxophone, an alto.
From 1944 to 1945, Coltrane took saxophone lessons at the Ornstein School of Music with Mike Guerra. From early to mid-1945, he had his first professional work: a "cocktail lounge trio" with piano and guitar.
An important moment in the progression of Coltrane's musical development occurred on June 5, 1945, when he saw Charlie Parker perform for the first time. In a DownBeat magazine article in 1960 he recalled: “the first time I heard Bird play, it hit me right between the eyes.”
Working in the bebop and hard bop idioms early in his career, Coltrane helped pioneer the use of modes and was one of the players at the forefront of free jazz.
He led at least fifty recording sessions and appeared on many albums by other musicians, including trumpeter Miles Davis and pianist Thelonious Monk. Over the course of his career, Coltrane's music took on an increasingly spiritual dimension, as exemplified on his most acclaimed albums A Love Supreme (1965) and Ascension (1966).
Decades after his death, Coltrane remains influential, and he has received numerous posthumous awards, including a special Pulitzer Prize, and was canonized by the African Orthodox Church.
His second wife was pianist and harpist Alice Coltrane. The couple had three children: John Jr. (1964–1982), a bassist; Ravi (born 1965), a saxophonist; and Oran (born 1967), a saxophonist, guitarist, drummer and singer.
John Coltrane died July 17, 1967 (aged 40) in Huntington, New York.