Shape and size won't really help since we'd need to know the string tension and spacing. Otherwise it could be literally any scale with any shape and size. It's hard to express just how enormous the difference between musical modes can be when you leave modern tuning and standards behind. My favorite example of a completely different system of music is Gagaku, Japanese court music with ancestors extending back to Han dynasty China and even beyond. Listen to that next to some Bach; that seems like the possible range of interpretations we might end up with!
Relative changes in pitch are only the simplest level of abstraction in examining a melody. Beyond that, all note events exist relative to chord structure, harmonic ideas, and even other music that performers and listeners are already familiar with. We would be missing everything except that base layer, which I'd argue conveys next to nothing (even pitch, while technically one dimensional, is interpreted cyclically with each octave. So, note 1 is higher than note 2. But is it really the same note, just 1 octave higher? Or is it something in an entirely different key?).
EDIT: Just for illustration, in Bach, the most similar note to a C (with the simplest harmonic relation) is an octave higher/lower C, but the second most similar is a G or F, halfway across the octave! But the most dissimilar is a Gb, a difference of only a half step and directly between those two! From this we can see distance tells us nothing about harmonicity. This is the same issue we see with the difference between major and minor - qualitatively enormous but quantitatively tiny.
Relative changes in pitch are only the simplest level of abstraction in examining a melody. Beyond that, all note events exist relative to chord structure, harmonic ideas, and even other music that performers and listeners are already familiar with. We would be missing everything except that base layer, which I'd argue conveys next to nothing (even pitch, while technically one dimensional, is interpreted cyclically with each octave. So, note 1 is higher than note 2. But is it really the same note, just 1 octave higher? Or is it something in an entirely different key?).
EDIT: Just for illustration, in Bach, the most similar note to a C (with the simplest harmonic relation) is an octave higher/lower C, but the second most similar is a G or F, halfway across the octave! But the most dissimilar is a Gb, a difference of only a half step and directly between those two! From this we can see distance tells us nothing about harmonicity. This is the same issue we see with the difference between major and minor - qualitatively enormous but quantitatively tiny.