There are at least two major reactions I have whenever I hear the earliest jazz musicians talk about the roots of jazz. The first is the chills, like, "These guys were present at the creation! And they have charmingly unusual, aged accents!"
The wonderment eventually wears a little, which leads to the second reaction: How we think about jazz now is not how what they thought about it then. The language the pioneers had for their creations was so inexact, so undefined that you begin to wonder just how much has been lost in translation over the years.
The great folk music historian Alan Lomax once asked Creole violinist and guitarist Paul Dominguez Jr. about how the first "hot" (or "ragtime," or syncopated, or "jazz") artists played. Dominguez couldn't put words to it. He hummed the William Tell overture in both written and "jazzed-up" ways, and described it thusly: "Well, I wouldn't know what to use for it. But it's a make-up of their own. ... In other words, it's original." He later offered that the essence of jazz playing was simply playing a piece with more notes than in the original written version.
Lomax interviewed several statesmen of New Orleans jazz in 1949 for a biography of Jelly Roll Morton, including banjo player Johnny St. Cyr, clarinetist Alphonse Picou and Leonard Bechet (brother of Sidney Bechet, soprano saxophone legend). I was recently shown that all that audio lives online under the auspices of the Association for Cultural Equity, the organization Lomax founded. There are music demonstrations, discussions of the early giants and other attempts to put the unnameable to words. Here's Picou on the man often called the first jazz musician, Buddy Bolden: "He used to blow that cornet that you could hear him for blocks." Also: "That's what put him to his grave, is women!" [Cultural Equity: New Orleans Jazz Interviews 1949]