Why aren't notes and intervals plain numbers?
Beginner question:
If we were to leave the historical context aside and redesign the system of musical notation: would we base this around the 12 steps we've divided octaves in?
What strikes me as very confusing and weird is that the notes and intervals (and even the layout of some instruments like the piano) is based around the major scale.
Am I correct in assuming this is just born from the historical context, where perhaps this 7 notes array is all there was, or is there any other reason?
Could we simply call the notes by numbers and their intervals maybe in flat ordinals (or the other way around)? What would we lose by doing that?
It would be awesome if answers can cite technical advantages of the current system vs flat numbers (I already assume a great deal of what we have nowadays is historical, but it's still a struggle for every beginner, I wonder if there are other reasons)
Edit: I'm interested in finding motivation to study theory, but I'm having trouble getting over the feeling that it's way more complex than it should be, so any argument helps
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You are correct- the reason standard notation is not orthogonal (i.e. a step can be a half tone or a whole tone (or more or less, with accidentals) depending on where it is on the staff, clef, and key signature) is historical. In some sort of orthogonal notation it would certainly be easier to learn the intervals.
But that's not all there is to reading music. As Todd mentioned in the comments above, reading music has more to do with art than technical advantages. And the art of Western music is still, even today, mostly based around scales that have the same pattern of whole and half steps they did when notation was being developed. This pattern is built into the standard staff notation, so you can depict music from Bach to the Beatles in a way that's easy to read.
Sure, there is the drawback you mentioned: there's a fair amount to learn. And an orthogonal system would be simpler for twelve-tone music. But for the bulk of the music most people do, standard notation is pretty hard to beat for readability. And that's what notation is intended for: not for easy frequency analysis, but for musicians.
Western music makes harmonic sense in relation to diatonic scales. A simple-minded accompaniment to nuersery school kind tunes is singing a third or sixth above or below. That's conceptually simple but it doesn't map to a simple concept in chromatic intervals: you get a haphazard sequence alternating between minor and major thirds (3 or 4 semitones). Trying to play this kind of thing on an inherently chromatically organized instrument (like a chromatic button accordion) takes quite a bit of practice.
And if you want to analyze that kind of stuff (as well as the harmonic frame a melody moves in), there just is no way around relating it to the diatonic scale it is based on. There are a few instruments with uniform keyboard layouts: apart from the mentioned chromatic button accordion, there is the Jankó keyboard for pianos. Their principal advantage is that they make transposition easy and thinking in semitones. This advantage was not enough to let the Jankó keyboard survive/thrive compared to the disadvantage of not being related to any diatonic scale (which our notation is based on as well as our harmonies). The chromatic button accordion is basically the only thriving member of uniform keyboard layouts and that's mainly because it's so much more compact than a piano keyboard, making a better fit for the instrument class.
So in short: it has been tried. There were lots of treatises particularly around the musical theoretical advantages of the Jankó keyboard and predictions that everybody would be using it. This hasn't happened.
For better or worse, Western music (several developments outside of the classic frameworks aside) is rooted in diatonic scales and trying to ignore this is a hindrance rather than a help to understanding.
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