Leave it to Tibet to come up with Singing Bowls. When struck with a special small mallet, these bronze bowls create sing, with deep tones evolving from higher ones, and overtones waxing and waining. When the leather covered part of the mallet is rubbed around the outer edge of the bowl they begin to sing - like a crystal goblet will sing when you rub a dampened finger around its lip.
Why can't your next turned bowl - sing?
OK - so maybe singing is something to shoot for - but - rather than just sit there - why not invite interaction - which will create sounds?
One approach is sort of obvious - a take on African Thumb Pianos - you know - a little hollow box, with a hole in the top and four, or five or six flat spring steel "keys" to flick down with your thumbs.
Or how about a bowl with in interior texture - which - when a ball inside the bowl is set to rolling - will generate a chattering sound - the pitch going up as the ball is revolved faster and faster - and overhanging lip keeping it from flying up out of the bowl. Have a coarse texture near the bottom, finer texture going up the sides, transitioning into a smooth sanded surface. The sound would change as the ball slows down or speeds up.
What if you cut notches on the outside of the rim, and close together grooves on the inside of the rim? Now if you add a turned "rubbing stick" - which you rub around the outside or inside of the rim - you'd get sounds.
What if you did something similar - with a hollow form - with a texture on the outside?
How might the type of wood change the resulting sound? Would rosewood or cocobolo produce a noticably different sound -than say -walnut or spruce? If the texture were crisp would the sound be different than if the texture were sanded smoother?
What kind of sound would a wooden bell make when struck?
The idea of getting people to actually interact with, rather than just LOOK AT, one of your pieces has some interesting things going for it. If you've done any craft shows you know that getting a person to actually hold a piece can start their attachment to the piece - and increase the chances he or she will buy it. And by interacting with a piece, the person is let in on a little secret - that only someone who has played with the piece will know about. People like secrets.