[contingo]

A piano roll visualization gives a somewhat more immediate depiction of intervallic information. But it isn't absolutely proportionately spaced, it's mapped to keyboard topology. Two neighboring white keys could be a major or minor second apart, etc. (And if real piano topology is shown, asymmetric positioning of black keys mean that identical intervals with one white key and one black key are different in span.)

In relation to the staff, pitches in standard notation are just as "proportionally spaced". Instead of squeezing in black keys, you have to squeeze in accidentals, but then accidentals are an extremely useful way of "showing how chords work", especially in the context of progressions in tonal harmony, which a piano roll gives you no meta-information about. It's less intuitive only in that you need some study to parse it fluently, at which point you gain the advantage of being untied to the layout of a particular physical instrument.

In any quest to "understand how music actually works", as soon as you take some baby steps beyond the basic alphabet of intervals, a piano roll visualization is going to hold you back.

[codeulike]

In all the software I've used, it is proportionally spaced. You're just used to thinking the old way. Trust me, the whole thing is a lot simpler if you just accept 12 equally spaced semitones, with 7 of them in play for any particular key.

[contingo]

I don't trust you. You're just used to thinking in terms of the piano keyboard. As I said before, the distance between two adjacent white keys on a piano roll could be a major second, or it could be a minor second. In other words the same distance encodes different intervals. You don't know which it is until you also examine the position of the black keys. A keyboard where the twelve semitones were actually equally spaced would not have groupings of two vs. three black keys. Looking at the adjacency of the keys trivial to do, but so is reading an accidental, which gives you additional information about the functional role of the pitch it alters.