“I try really hard as a writer to write light and airy songs,” says jazz singer and songwriter Carmela Rappazzo. “And I suck at it.”

Rappazzo is trying to identify the thread that connects the songs on her new album. There are nine originals, interspersed with three from the American songbook (the wistful Hoagie Carmichael/Johnny Mercer tune “Skylark,” Cole Porter’s heart-as-captive “So In Love” and Billy Strayhorn’s op...