"Almost Tonnetz" fail:
https://en.wikipedia.org/wiki/Stradella_bass_system
Accordion buttons have a row of roots with major thirds off on a diagonal, but in a shifted way that you don't have minor thirds on the opposite diagonal. E.g. there is no CEG triangle.
If the layout did that, you could hit minor and major triads chords by pressing triangles on the first two rows.
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