My need to play notes directly on the square grid predates Stacy. The main idea is that the piano keyboard is fundamentally non-symmetric: every scale has a different fingering depending on the key. On the other hand, it is possible to map the keys of a regular grid (e.g. hexagonal or square) to the usual notes in a symmetric way. This is called an isomorphic keyboard.

I have chosen a particular layout related to the harmonic table but in a square grid. In this layout, the two vectors of the basis are the minor third (3 half-tones) and the major third (4 half-tones).

This table represents all the notes relative to the central cell in count of half-tones. The notes in green are the octaves. You'll note that, unlike with the piano keyboard, there are duplicate notes on the grid. You can verify that a step up always amounts to +4 half-tones and likewise, a step to the left is always +3 half-tones. Thus, the fifths (7 half-tones) are on one diagonal and the half-tones are on the other.

For the moment, that layout is hard-coded inside my synths and my "note wrapper" component (G5). Eventually, I would like to express this in the circuit using linear transformations.