Well, the 6th on the E string (Tuned 41.2hz) I think is the 7th harmonic, so a very slightly sharp D (more learned TBers, correct me if its flat), its about 5-10 cents off if i remember correctly, it is 73.0537hz. So for the note at the 6th is the same pitch as the note two semitones down from the open string.
For the 8th fret, its a B on the E string. Its minutely flat (0.3704hz). So same pitch as the fifth below. The B is 61.4306hz
http://upload.wikimedia.org/wikipedi..._Harmonics.jpg
For others you could use the table to find the fraction of the string used for the harmonic. And then the 3rd calculator on
http://www.dolmetsch.com/intervalcalculator.htm for the frequency and note values. 1/7 on the chart = 7 in the harmonic drop down boxes, 2/5 = 10 etc
But I couldn't start to explain why this occurs apart from the usual nodes stuff. Hope thats a little helpful, but I'm sure others will fill my gaps/mistakes.