Alvin Batiste, the late clarinetist and influential educator, considered jazz “a continuum.” By that he meant the music made by artists of the past casts an instrumental language into a flow of time that gathers the best work of younger players, extending the vernacular, pushing the current on. Batiste’s roaming lyricism on the reed found its place in that continuum well before his funeral, a sound that at certain moments echoed the melodic layers that John Coltrane unfurled in songs like “Naima” or the scales and cascades of “Giant Steps.”

T.S. Eliot sketched the idea of Batiste’s continuum in an essay, “Tradition and the Individual Talent,” long before Batiste got his start.  The essay assumes a responsibility on the part of the artist to understand the body of literature that his own work seeks to extend. And so with painting, and so with jazz – one has to be grounded in the great tradition to grasp it, draw from it and finally expand it in any meaningful way. Gabriel Garcia Marquez could never have written One Hundred Years of Solitude had he not absorbed the works of Miguel de Cervantes and William Faulkner.

New Orleans music has had so many popular offshoots since the early days of the continuum as to prompt me to wonder whether Batiste would start the line with Buddy Bolden, the primeval cornet player who electrified dancers and musicians in the first few years of the last century, before the day he pulled out of a parade and sat down on the sidewalk, holding his head after days of cataclysmic mood swings, and was soon packed off to a mental institution where he lived another quarter-century, never again playing in public the music for which he was a supreme catalyst.

It is a long haul from Bolden’s blues-based horn play to the wild keyboard improvisations of James Booker, the self-styled Piano Prince, an artist who forged a singular rhythm-and-blues sound that radiated the persona of the black-patched lone ranger whose sound still swirls in its island of time. The reminders of Booker linger on in Dr. John and Jon Cleary, among others. Each of the instrumental voices in Batiste’s continuum stay with us, the ones who have gone now achieving a territory re-imagined in the works of later players, young and old.

A proper jazz gentlemen such as Dr. Michael White has had long encounters with the compositional complexities of Jelly Roll Morton, who famously played the piano as if an orchestra lay beneath his fingers. White’s scholarly writing on the jazz tradition draws a bead on the early brass bands as well as the church parades he interpreted in songs like “Sunday Morning.” Morton the pianist had little interest in brass band parades as other than a mild inspiration; his ensemble work with the Red Hot Peppers from the 1920s ranks with the most challenging compositions for a group of musicians to play. Morton came of age at the same time as Bolden, in the generation of King Oliver and Louis Armstrong. Morton left in 1907, just as Bolden was going down. The continuum began about that time with the diverse interpretations of city life, ringing sonorous impressions of the rural blues and gathering certain church hymns into the changing repertoire of brass bands as the years advanced toward World War I. Across New Orleans, people danced in halls, honky tonks and swankier venues to the syncopated music and improvisational melodies that by ’17 had acquired the name jazz.

As the continuum rolled out, jazz evolved as a succession of styles, broadening the dance roots with the swing music of the big band era, going a long step beyond with bebop in the midcentury years, while the older blues impulse came jumping back in the up-tempo R&B cavalcade led by Fats Domino, Roy Brown, the Nevilles, Irma Thomas, Tommy Ridgley, Huey Smith, Dr. John and sundry others. Although I never asked him, I suspect Batiste held a sufficiently generous view of the continuum to embrace R&B as an extension or perhaps a grand cul-de-sac that leads back to the jazz tradition, its momentum and progress. In a sense, Wynton Marsalis enshrined Batiste’s notion of the continuum with the Jazz at Lincoln Center programs that treated jazz as a canon of work, with concerts that gave equal weight to Armstrong and the music of the founding generation and to such later luminaries as Theolonius Monk and Coltrane.

The emphasis on jazz education provided by Alvin Batiste, Ellis Marsalis, Kidd Jordan and Harold Battiste has a large influence on grounding the continuum in the lives of students at the New Orleans Center for Creative Arts, Southern University, University of New Orleans and other places where the tradition is handed down. The quality of education in the last generation has produced a memorable line of artists, from Wynton and Branford Marsalis to Terence Blanchard and Donald Harrison Jr., down to a new generation in Trombone Shorty, Shamar Allen and Jonathan Batiste, to name but three. Learning the tradition in order to expand upon it is the shape of any educational discipline. Still, Batiste’s notion of the continuum becomes more elusive as the music changes, reaching deeper complexities.

I suppose an argument can be made that rap, hip-hop and bounce have some connection to the older flow that began with jazz. Perhaps it’s an academic point to suggest that culture, or society, has the power to draw a line that excludes an extreme edge. Lil Wayne, the surreal rapper who spent seven months in prison on gun charges, is back on the road, having sold 1.3 million albums the year before he was put away, more in that year than the entire output of jazz recordings.

The continuum rose from impoverished streets where Louis Armstrong was drawn into the Onward Brass Band as a teenager after a stint in reform school. No one called it a continuum then, but the embryonic tradition of black brass band music was a point of origin just the same; an enveloping community with a sense of musical discipline and underlying values that the music carried – giving the old marches and church songs new polish. In recent weeks, several young rappers have been murdered in the mentality of gang violence that seems to grip the culture of bounce music. As young brass players turn out for the burial parades, the continuum reaches out, absorbing jagged currents of the city as the slaughter of young people continues like some ancient curse upon the house.