I find the piano quite illogical. Playing a chromatic scale requires to jump from white to black keys. The guitar with its "basic" strings is actually much closer to the underlying physics (and thus mathematics), imho.
This might be true from a physics standpoint, but it's not from a musical standpoint. The vast majority of all western music was composed on a piano first. It really does help to know it when learning any western music. Even the chromatic scale on a guitar doesn't accurate represent the physics. It's still based on sqrt 2^12 mathematics, not natural waves. If you want true temperament it looks more like this:
In my view the "logic" of any historical instrument emerges as you gain experience. You eventually reach a stage where you can think and hear the music in your head, and it comes out of the instrument. At this point, the pianist finds "shapes" of their hands, that correspond to what they want to play. So in a sense the arrangement of the keys is a kind of memory aid.
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