Have Mario wag his tail a fraction of a second after collecting a 1-Up to hear an "extended" 1-Up sound effect. The exact moment to wag his tail is five frames (1/12 of a second) after the 1UP icon appears. The two sound effects will conflict, causing the game to play extra notes at the beginning of the 1-Up theme.

Credit goes to BMF54123 and Xkeeper for working out the technical details, which were posted along with Xkeeper's Youtube video of the glitch.