I have found that the "worst" audible beating has frequencies between 6hz and 20hz. Higher than 20hz you do not perceive it, and lower than about 6hz it becomes an agreeable "tremolo" instead of as annoying beating. Thus, it would seem that when the frequencies of two notes differ between 6 and 20hz you get the worst dissonance possible. When you are in the middle of the scale, this is more or less about a semitone.