"So we’re messing around with my worst nightmare—and that’s re-harmonizing trad tunes.” Ashlin Parker smiles, his demeanor as bright as the red and yellow paint-spatter design on his t-shirt. He’s seated at a keyboard in his dining room in Uptown, facing the handful of trumpeters who have convened for a Trumpet Mafia rehearsal ahead of their Satchmo SummerFest closing set on August 5. “Let’s do an open voicing,” he suggest...