We can remove this difference by representing any interval as though the lower of the two frequencies is the tonic. However, things get even more complicated because while the intervals relative to different tonics sound the same in isolation, they are most often encountered in musical contexts that set up some harmonic expectations. An individual interval is experienced within the context of the perceived key. The perceived key can shift over time in a piece of music, but there is a kind of stability or perhaps inertia to our sense of the current key of a piece of music. We will continue to hear new notes, intervals and chords in reference to the established key until the combinations of notes ceases to be significantly compatible with the established key and another key presents a more stable reference for the current harmonies.
If the apparent key at a certain point in a piece of music can be determined, then the most musically relevant visual presentation can be arranged, by referring the visual representation of the notes to the tonic of that key. This reduces the number of visual patterns possible for intervals, since a major 7th interval in relation to a tonic represented by its higher note is the same as a semitone interval in relation to its lower note (both involve notes one semi-tone apart. This sort of scenario presents the visual information in a more musically relevant (and generally simpler) form.
The set of possible visual states is reduced, and the relationship to the musical experience is increased, since discrepancies irrelevant to the way these tones are heard is ignored.