[reikonomusha]

I don't agree with this "multiplication table" idea. Octaves have the same physical distance between notes on the page in traditional notation, so they can be identified at a glance. People typically do not read octaves by deciphering the bottom note, deciphering the top note, and saying "ah, this is an octave".

[abhorrence]

And even if they did, the stems of the notes (excluding half and whole notes) traditionally are as long as the distance between octaves. One of the things that I think makes traditional notation more robust for experts is the redundancy of information.

It also helps that for many instruments there’s a mapping between the layout of the instrument and the notation! This is less true for brass and the violin family, though I think even with them there are probably some arguments to be made about the harmonic series, or the spacing of strings in fifths.