As far as I understand, the concept you look for is Scale.
An scale can be used for either modality or tonality. It all depends on the tonal center (or root if you want it generic since it would be more appropiate "modal center" in the distinction), in the shape of a drone note, emphasis on mode alterations or traditional cadences.
For instance, the principal example is the diatonic scale and its 7 grades which has been used for ages for both tonal and modal pieces, it is the minimum reduction shared concept or structure from my point of view.
We could also say, at least when dealing with harmony (and if you only have in mind ancient or greek modes), that both tonal and modal music can be categorized as ternary in 99.999% of cases, as they are both stacked in thirds, and usually as diatonic as well, but I am not sure that would be correct, as analogously, a quartal armony or non-diatonic scale can have grades and modes and even form a superset where some chords could be actually thirds-based and conform a tonal piece for a while.