Talking about going up or down an octave here is just nomenclature. Musically speaking, changes in a chord progression don't go up or down - this is because rom

Talking about going up or down an octave here is just nomenclature. Musically speaking, changes in a chord progression don't go up or down - this is because roman numerals refer to pitch classes (like C, E, G), not to specific pitches (like C4, E5, G3). The matter of which notes to play for a given chord is called "voicing", and it's orthogonal to anything mentioned in your article.