It is not so easy to play a tune continually whilst playing two notes an octave apart on the Englich as it is on the Anglo because of the distance that the fingers have to move on both sides of the English between notes. Having said that please note that this is one of exercises in the original Wheatstone tutor book for the English.
Because I am nearly always playing two notes an octave apart It means that I tend to use other notes from a wider range to make up a chord of three or four notes, thus the tendency to have notes that are more distant in pitch from each other and less likely to generate beat frequencies between harmonics.
Returning to the computer analysis displays it is possible to have a harmonic on some notes that is actually louder than the fundamental note. You do not notice this as there are other harmonics, at the octaves, that override it.
Having spent some years doing the Tidal Predictions for the Hydrographic Office it all looks rather familiar!