I find the 'piano roll' visualisation, as used by most major sequencers/DAWs is a much more intuitive way of showing how chords and intervals work, precisely because it is proportionally spaced.
I'm not saying traditional notation isn't useful, I'm saying it's unhelpful if you're trying to understand how music actually works.
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.
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.
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.
OK, I looked at some piano roll layouts in DAWs, and found examples with equal spacing between semitones, you're right.
I looked at some music mapped onto this layout. The layout allowed for speedy recognition of lone intervals and simple chords, but no more so than standard notation, and it was far worse than standard notation at showing any higher level musical content (the harmonic function of those intervals and chords in the context of the whole piece or local progression, polyphony and independent voices in general, counterpoint, organization of rhythms and cross rhythms, phrasing, larger compositional structures...). Also, because it's just a homogenous field of repeating piano octaves there is much less to positionally anchor the eye on as it reads through, like a staff with ledger and bar lines and key signature would provide to a fluent sight reader. All this musical meaning is stripped away and to reinstate it would be a case of painstakingly decoding the piano roll rather than just fluently reading the music.
I can see how this layout is really useful in a DAW for MIDI input and editing. As for learning the absolute basics of harmony, yeah it's accessible, if you can't be bothered to learn the basics of standard notation. After which point it's a dead end.
Thanks. The piano roll helped me to look at things from first principles - to see how, say, progressing chords towards a change of key you can pivot into the 'allowed' semitones of the new key. Learning about music, the jargon is quite dense, epsecially with the naming of chords and intervals. Thinking of a fifth as seven semitones (and a 2/3 frequency ratio) and so on made it more digestible for me. But perhaps it is a dead end, I might have to take your word for that. Maybe its something like how in chemistry, learning the Bohr modelof electron shells helps you grasp the structure of the periodic table, but then to really get further you have to forget all that and start again with the valence electron model.
Those same relationships are apparent when reading a traditional score. Once you reach a certain level of proficiency reading music it's easy to spot the intervals which make up a chord as written. I don't think the same amount of proficiency isn't needed to interpret a piano roll, it's just proficiency in seeing the same relationships notated differently.
All that to say I think they're both conveying similar pitch information and take a similar amount of effort to ready correctly. Piano roll doesn't convey rhythmic information and that's where I think piano roll falls short as a method of straight notation.
Imagine you are composing a piece of music that will move through a series of key changes (as most pieces of music do). On a piano roll you can see exactly which semitones are shared in common by the different major and minor keys. You can map your way through the transitions visually. A major triad uses 4 and 7 semitone gap, a minor triad uses 3 and 7. It's all so much simpler and clearer if you are starting from scratch.
Traditional notations are obsessed with pretending there are only 7 notes when there are in fact 12. Accidentals and key changes are obfuscated.
How are accidentals obfuscated on a traditional score? They are explicitly marked. It's on a piano roll that they would be easy to miss -- they appear the same as any other note.
Similarly, key changes are explicit in sheet music but hard to see on a piano roll without careful inspection.
What's obfuscated is the _actual_ semitone interval between the accidental and the other notes around it. And the actual semitone interval is the most important bit of information - it's what our ears hear.
I think what you're missing is that a big part of the design of traditional music notation is that it is intended to be read easily and efficiently, even sight-read. The musician reading the score knows the intervals that apply in the given key, down to muscle memory. The fact that a note lies outside the key is important, and that is why an accidental is marked explicitly.
Likewise, when a musician sees a run of adjacent notes without accidentals, they immediately know what to play. They don't need to inspect each one in turn to determine how many semitones it lies from the previous note. Likewise, when a composer wants to write such a run, they can just draw some black dots in a row. They don't need to squint at a grid and select the correct rows each time.
To sum up, traditional notation is uses a form of compression that makes reading and writing diatonic music easier.
Taking this even farther, some systems of music notation compress things even further and don't explicitly list all of the notes to be played. For example: figured bass, basso continuo, or even just chords that accompany lyrics. In fact, even regular sheet music doesn't usually precisely represent of duration of all of the notes. Some notes are sustained and bleed into others, some are meant to be played strictly in time. Human interpretation is an important part of the process.
On the other hand, the piano roll is a MIDI editor. It is a great way to tell a computer exactly what to play, but it is not easy to read quickly and it is impractical to print or write by hand. Both forms of notation have advantages and disadvantages but it seems to me you haven't spent enough time with the standard notation to fully appreciate its advantages. In other words, the piano roll notation might be your blub language for music. [1]
Fine. But I'm saying if you want to actually understand how music works (rather than play an instrument) the standard notation IMHO
actually gets in the way.
Because the most important thing is the actual semitone intervals, and the standard notation hides them and gives them weird names like augmented fourth (it's just six semitones, just call it that). And it names the 12 semitones based on the c major mode even though that's only one of about 50 modes/scales/keys you might want to use.
I'm not saying traditional notation isn't useful, I'm saying it's unhelpful if you're trying to understand how music actually works.