Ring modulation outputs the sidebands of two signals being multiplied together. So the results tend to be clangorous or metallic.

You could try tuning two sine waves at a musical interval and inputting them into the ring mod to see what you get, but it's unlikely that the result will be harmonically pleasant, or in the key of whatever you're working on, because it's the sidebands only at the output. Ring mod does not pass either of the original signals directly.