I'm not 100% convinced by these plots; and also I think their selected examples might be stacking the deck a bit, since Eeyore is stereotypically (since the Disney movie, at least) someone who signals a depressed state by speaking almost in a chant, in which minor-third intervals are prominent. But still, this is really interesting stuff.
Yes, it is. I'm not sure I grasp everything in Liberman's piece, but I have noticed that professional speakers -- especially news casters and voice-over talent -- tend to have a sing-song style of speech, and that certain pitches and intonations are consistent with punctuation. A uptick here falls in line with a comma, a falling tone there matches with a period, a pause indicates a colon, and so on. Each speaker seems to have his own speech shape, and I sometimes listen to casual speakers to see if I can pick out similar patterns. I tended to think I was the only one that really noticed and pondered this. But it's nice to know I'm not.