Correct variation of chords over multiple octaves?

I understand that what defines an I chord in the root position is:

  1. the bass note (i.e. the lowest note) must be of scale degree 1 and,
  2. scale degree 3 and 5 must appear as higher notes (in no particular order),
    and any particular degree can be repeated over multiple octaves, see e.g. Section 1.3 of Hooktheory 1. I tried to reproduce some of the examples in the book by using chords in their “closest” form, e.g. 0-4-7 semitones for a major chord. This of course gives rise to very discontinuous and unnatural chord progressions. I’m wondering if there is a theoritically proper way to spread the notes of a chord over multiple octaves? For example, if I’m reading a music sheet with chord names only, is the author assuming I know the common variation to play? or is it left to the instrument player to interpret the chords and find what is best sounding?

P.S. After playing with Hookpad a bit, I noticed you always duplicate the bass an octave lower and play the highest three notes possibly in an inverted configuration. For example in C major, I, vi and vii^o have their three highest notes in root position, with their root note duplicated an octave below. Similarly, the three highest notes of ii and iii are in their second inversion, while iv and v are in their first inversion. Is there any kind of rule I can extrapolate from this that would apply to any key/mode and more complex chords, such as inversions or 7th chords?

Thank you

This is called voicing, and no, a chord symbol alone does not hint at the voicing of the chord. It is up to the performer to interpret the chord appropriately.

Hookpad determines the voicing of any chord using the rules listed here.

Thank you for the quick reply. Since voicing matters so much, this appears to me as a huge gap in music theory, no? For example, an author might want her track to be voiced a specific way, but she does not have the theoric tools to do so. Also, if the set of voicing rules you are using in hooktab can be considered as the ‘default’ state for chords, why is the theory isn’t presented as such, instead of focusing on the somewhat useless ‘nearest’ form (or do this form have any use in practice?) I understand that for educational purposes the nearest form is to be presented first. As an absolute beginner, I would have really benefited from being taught that chords must be voiced using your set of rules in order to sound good. Then, I could have deviated creatively from your rules if I wished. Wouldn’t this be more pedagogical than letting beginners trying to build good sounding variations on their own or back-engineer harmony voicing they hear?

Thank you