I am trying to understand how to construct the pythagorean scale. I have gathered, that the basic idea is to use only the 3/2 ratio starting from some base frequency. As this takes you out of the octave quickly, using the 1/2 ratio (=one octave) you move back into the original octave. The videoexplains this quite well. However for the last step he suddly starts from the base frequency with a 4/3 ratio and calls this "the oddball one". Using the same approach as all notes before and starting from the previous note would take you (in this example) to 372.525 Hz. This is not the same but within the octave so i do not understand why the approach is suddenly different for the "last" note (This is another question: where to stop).
The combination of Information from the comments made it much clearer. I actually used this method to calculate the resulting frequencies starting with 440Hz and you can see quite nicely how two frequencies (618.05Hz and 626.48Hz) are really close to each other and "mess up" the otherwise almost equal distribution.
This approach is suddenly different for the last note, because the last note, the subdominant of the scale, does not exist in the harmonic series of the tonic. 4/3 is not a harmonic of 1. You could also construct the scale only using 3/2 ratios (and bringing down into one octave) by starting on the subdominant (say, F in a C major scale) and going up from there. This is because the subdominant is the "flattest" note in a major scale.
And do check out the wiki that Tom suggested.