There's actually established notation in music theory for this[0]. Because it IS a super convenient way to look at notes. Doing otherwise would be akin to using Roman numerals for calculus.
From personal experience, I worked with this notation a little bit. I spent a lot more time getting the hang of traditional notation. Not only is integer notation intuitive immediately, but number combinations like {0,4,7,12} become memorable very quickly and yes when I look at it (even if I saw it outside of musical context!), I would know it's a major chord.
That is, personally, I learned about the traditional notations (because you can't learn music theory and avoid those, or miss out on most of the material :) ). But that took me deliberate effort. On the other hand I wrote some python classes for converting between notes and chords and traditional notation and integer notation, seeing the patterns in those numbers required no effort at all, it's right there. The traditional notation has of course the same patterns, but they are obscured by layers of translation.
I think integer notation could be used a lot more, especially when teaching music theory. But traditional notation is also useful, partly because many people know it, partly because integer notation is less suitable for certain instruments.
{2, 5, 7, 11} -> {0, 4, 7, 12}
There's actually established notation in music theory for this[0]. Because it IS a super convenient way to look at notes. Doing otherwise would be akin to using Roman numerals for calculus.
From personal experience, I worked with this notation a little bit. I spent a lot more time getting the hang of traditional notation. Not only is integer notation intuitive immediately, but number combinations like {0,4,7,12} become memorable very quickly and yes when I look at it (even if I saw it outside of musical context!), I would know it's a major chord.
That is, personally, I learned about the traditional notations (because you can't learn music theory and avoid those, or miss out on most of the material :) ). But that took me deliberate effort. On the other hand I wrote some python classes for converting between notes and chords and traditional notation and integer notation, seeing the patterns in those numbers required no effort at all, it's right there. The traditional notation has of course the same patterns, but they are obscured by layers of translation.
I think integer notation could be used a lot more, especially when teaching music theory. But traditional notation is also useful, partly because many people know it, partly because integer notation is less suitable for certain instruments.
[0] https://en.wikipedia.org/wiki/Pitch_class